Physics lessons

369 lessons

• AC Generator and Transformer – An AC generator turns a coil in a magnetic field. The flux through it keeps changing, so it makes an emf e = NBAω sin ωt with peak NBAω. A transformer uses mutual induction between two coils on one iron core: Vs/Vp = Ns/Np. A step-up transformer raises voltage and lowers current; a step-down does the opposite. Power stays nearly the same (Vp Ip ≈ Vs Is).
• Acceleration Due to Gravity and Its Variation with Height and Depth – The acceleration of a freely falling body near the Earth is g = GM/R² ≈ 9.8 m/s². It does not depend on the falling body's mass. Going up to a height h, g falls: g_h = g R²/(R + h)², which is about g(1 − 2h/R) for small h. Going down to a depth d, g also falls: g_d = g(1 − d/R). At the centre of the Earth, g = 0. So g is largest at the surface.
• Acoustics: How Rooms, Ears and Audio Tools Handle Sound – Acoustics is the science of sound: how it is made, how it travels and reflects in rooms, how we hear it, and how we record it. In a room we hear the direct sound plus many reflections; the time the sound takes to die away is the reverberation time, T = 0.161 V / A (Sabine). Soft materials absorb sound and shorten T. Loudness is measured in decibels, pitch depends on frequency and timbre on the mix of overtones. Microphones turn sound into electrical signals, which computers sample into numbers; MIDI sends note instructions, not sound.
• Air-Conditioning Equipment – A central air-conditioning plant makes cold water in a chiller; an air handling unit (AHU) filters, cools and pushes air through ducts to rooms. Individual units such as split ACs serve one room. A thermostat and valve control the cooling, and energy is saved by a sensible set point, insulation, inverters and variable airflow. Simple design: airflow V = Q / (rho cp deltaT), duct area A = V / v, COP = cooling / power.
• Alternating Current – An alternating current (AC) changes size and direction again and again: I = I₀ sin ωt. Its rms value is I₀/√2, the steady DC that gives the same heating. A resistor keeps V and I in step; an inductor makes I lag by 90° (Xʟ = ωL); a capacitor makes I lead by 90° (Xᴄ = 1/ωC). In a series LCR circuit Z = √(R² + (Xʟ − Xᴄ)²), resonance happens when Xʟ = Xᴄ, and average power is P = Vrms Irms cos φ.
• Amplifier Circuits – An amplifier makes a small signal bigger by using energy from a power supply. Voltage gain = Vout / Vin; in decibels, gain = 20 log10(Vout / Vin). Low-frequency (audio) amplifiers boost sound-range signals. High-frequency (radio) amplifiers boost signals of thousands to millions of hertz, often tuned to one station. Every amplifier has a bandwidth and a limit set by its supply.
• Analogue Signal Processing: LC Resonance Filters and the Ideal Op-Amp – An analogue signal changes smoothly. We process it in two big ways: an LC circuit picks out one frequency (a filter), and an operational amplifier (op-amp) makes a small difference in voltage much bigger. The LC circuit resonates at f₀ = 1/(2π√LC). The quality factor Q = f₀/Δf tells how sharp the peak is. An ideal op-amp has infinite open-loop gain, infinite input resistance, zero output resistance and infinite bandwidth.
• Applied Electronic Measurement – To keep radios and cables working, we measure them. An oscilloscope shows a signal against time (f = 1/T). A transmitter is checked for frequency, power and modulation depth. A receiver is checked for sensitivity. Microwave and light losses are counted in decibels (dB). An antenna is tested by field strength, which falls with distance.
• Archimedes' Principle: Why Things Float or Sink – Any object in a liquid (or gas) is pushed up by a force called upthrust or buoyant force. Archimedes' principle says this upthrust equals the weight of the liquid the object pushes aside: F = ρ g V. An object floats if its density is less than the liquid's, sinks if it is more. A floating object sinks just deep enough that upthrust equals its weight.
• Architecture and Living Environment – A comfortable home works with the climate. Deep eaves shade the high summer sun but let in the low winter sun. Windows on opposite walls give cross ventilation; a high vent lets warm air rise out by the stack effect. A draught is unwanted leaking air, ventilation is planned fresh air: Q = n × V ÷ 3600. Light colours reflect sunlight and keep roofs cooler; colour also changes mood and helps people find their way.
• Astrobiology: Is There Life Beyond Earth? – Astrobiology is the science that asks whether life exists beyond Earth. Life as we know it needs liquid water, energy and carbon chemistry. The habitable (Goldilocks) zone is the range of distances from a star where a planet could keep liquid water. Scientists search Mars, icy moons such as Europa and Enceladus, and thousands of exoplanets, look for biosignatures in their air, and listen for signals (SETI). The Drake equation estimates how many talking civilisations might exist; the Fermi paradox asks why we have not heard from any.
• Astronomy in India – Indian astronomers watched the Sun, Moon and planets for thousands of years to keep time and fix festival and farming dates. They divided the Moon's path into 27 nakshatras of 13°20′ each, defined a tithi as every 12° the Moon gains on the Sun, and built a lunisolar calendar that adds an extra month about every 3 years. Aryabhata, Brahmagupta, Bhaskara II and the Kerala school computed eclipses and planet positions with mathematics. In the 1700s Jai Singh II built giant masonry instruments at Jantar Mantar. Today, telescopes, spacecraft and computers make predictions far more precise.
• Atmospheric Pressure – Air has weight. The whole column of air above a surface pushes down on it; this push per square metre is atmospheric pressure. At sea level it is about 101 kPa (101 300 Pa), the same as a 760 mm column of mercury or about 10 m of water. Higher up there is less air above you, so pressure falls. In still air, the upward push of pressure on a layer balances the layer's weight (hydrostatic balance). Air flows from high pressure to low pressure, which is wind.
• Atmospheric Refraction and Scattering of Light – Air is denser near the ground, so light from space bends gradually as it comes down (atmospheric refraction). This makes stars twinkle and look higher, and lets us see the Sun about 2 minutes before it rises and after it sets. Tiny particles in air throw light sideways (scattering). Very small air molecules scatter blue far more than red, so the sky is blue; at sunrise and sunset sunlight crosses so much air that the blue is scattered away and the Sun looks red.
• Atoms: From Alpha Scattering to the Bohr Model – Rutherford shot alpha particles at thin gold foil and found that an atom is mostly empty, with a tiny, heavy, positive nucleus in the middle. Bohr then said the electron in hydrogen can move only on fixed orbits where its angular momentum is nh/2π. In orbit n the radius is 0.529 n² Å, the speed is (2.19 × 10⁶)/n m/s and the energy is −13.6/n² eV. When the electron jumps down, the energy difference comes out as light of one exact colour, which gives the line spectrum of hydrogen.
• Audio-Visual Equipment – Audio equipment turns sound into an electric signal (microphone), makes it bigger (amplifier) and turns it back into sound (loudspeaker). Imaging equipment turns light into an electric signal (camera sensor made of pixels) and back into light (screen). Digital equipment stores the signal as numbers: samples per second for sound, pixels and frames per second for pictures.
• Automotive Electrical Systems – A vehicle runs on a 12 V system (24 V in many trucks, 48 V or high-voltage packs in hybrids and EVs). Current flows from the battery +, through protection, switches and loads, and returns through the metal body (chassis ground). Ohm's law V = I × R and power P = V × I size wires and fuses. The three main faults are open circuits (no current), shorts to ground (very high current, fuse blows) and high resistance (dim or slow). Fuses, circuit breakers and fusible links protect wiring. A lead-acid battery has six 2.1 V cells; the alternator recharges it at about 14 V. A multimeter tests voltage, continuity, resistance and voltage drop.
• Auxiliary Machinery on Ships – The main engine drives the ship, but many helper machines keep it running: pumps move water, oil and fuel; hydraulic systems turn small pushes into big forces for cranes, winches and steering; fresh-water generators boil sea water at low pressure and condense it into drinking water; and pollution-control equipment such as the oily-water separator cleans waste before it leaves the ship. Each one uses a simple physics idea: pressure, Pascal's law, boiling and condensing, or floating by density.
• Balanced Forces: Equilibrium of Concurrent Forces – Concurrent forces all act on the same point. A point is in equilibrium when the forces cancel: the vector sum is zero, so ΣFx = 0 and ΣFy = 0. Then the object stays at rest or keeps moving at a steady speed in a straight line. Three forces in equilibrium make a closed triangle when drawn tip to tail.
• Basic Electronics: Components and Circuits – Electronics uses small components to control electric current. A battery or power supply gives energy; a switch opens or closes the path. A resistor limits current (V = IR), a capacitor stores charge and can smooth or delay a signal, a diode lets current flow only one way, an LED is a diode that gives light, and a transistor uses a small base current to switch or amplify a much bigger current. Each part has a standard circuit symbol. Circuits are planned on paper or in a simulator, tried on a breadboard, and made permanent by soldering on a circuit board, using the right materials and safety steps. Analogue circuits handle smoothly changing signals; digital circuits handle on/off signals.
• Basic Physical Quantities – A physical quantity is anything we can measure with a number and a unit: speed, volume, weight, density, pressure, temperature, heat and electric charge. Each has a formula or a meter, and each links to everyday things such as floating, a ramp, a thermometer or a bulb in a circuit.
• Basics of Construction Planning – A construction plan answers four questions: what will we build, in what order and how long, what helps us build it, and what will it cost. It has a time chart of tasks, a plan for temporary works like scaffolds and formwork, a specification of materials and quality, and an estimate: quantity × price.
• Beats – When two sounds of slightly different frequencies f₁ and f₂ are heard together, they add by superposition. The loudness rises and falls regularly. Each rise is one beat. The number of beats per second is the beat frequency, f_beat = |f₁ − f₂|. Beats are used to tune musical instruments and to find an unknown frequency.
• Binary Stars: Weighing Stars with Orbits – A binary star is a pair of stars bound by gravity, circling their common centre of mass. The heavier star is closer to that point and moves in a smaller circle: r1 / r2 = m2 / m1. Kepler's third law gives the total mass: m1 + m2 = a³ / P² (a in AU, P in years, masses in Suns). This is how astronomers weigh stars.
• Biological Measurement: the ECG – An electrocardiogram (ECG) records the tiny voltages made by heart muscle as it depolarises and repolarises. Electrodes on the skin, with conducting gel, pick up about 1 mV. A high-input-resistance amplifier makes the signal bigger (about 1000 times) and it is shown against time. A normal beat has a P wave (atria depolarise), a QRS complex (ventricles depolarise, atria repolarise) and a T wave (ventricles repolarise). The time between two R peaks is one beat; heart rate (beats per minute) = 60 ÷ R–R time in seconds.
• Biophysics: The Physics of Living Bodies – Biophysics uses physics to understand the body. The heart is a pump that makes pressure; blood flows through vessels, and narrowing a vessel cuts the flow a lot because flow depends on radius to the power 4. Bones and muscles work as levers. We use units, graphs and safety limits to study and protect the body.
• Black Body Radiation – All objects, at any temperature, give out (emit) and take in (absorb) infrared radiation. The hotter an object is, the more radiation it emits each second and the shorter the wavelength of the strongest radiation. Dark matt surfaces are good absorbers and good emitters; light shiny surfaces are poor absorbers and poor emitters. A perfect black body absorbs all radiation that falls on it and is also the best possible emitter. An object's temperature stays steady when it absorbs radiation at the same rate as it emits it; this balance, along with gases in the atmosphere, sets the Earth's temperature.
• Boilers, Refrigeration and Air-Conditioning Equipment – A boiler burns fuel to heat water into steam at high pressure; a gauge and a safety valve keep it safe. A refrigerator or air conditioner does not make cold; it moves heat. A refrigerant circles through a compressor, condenser, expansion valve and evaporator, taking heat in at the cold side and giving it out at the hot side.
• Brownian Motion and Diffusion: Motion and Interaction of Particles – All matter is made of particles that never stop moving. Fast, tiny water particles hit a bigger grain from all sides and make it jiggle in a zigzag path: this is Brownian motion. The same restless motion makes different substances mix by themselves, which is diffusion. Heat makes particles faster, so both speed up. Between particles there are forces: they pull when a little apart and push when very close.
• Build a Dimmable Desk Lamp – A dimmer is a variable resistor in series with a lamp. Sliding a contact along a graphite rod changes how much rod the current must pass. A longer path means more resistance, less current and a dimmer lamp. A thicker rod has less resistance. A separate switch is needed to turn the lamp fully off.
• Build a Simple DC Motor – A DC motor turns electrical energy into spinning motion. A coil carrying current sits in a magnetic field and feels a force on its two sides, one up and one down, so it turns. A split ring (commutator) flips the current every half turn so the coil keeps turning the same way. More voltage, more turns or a stronger magnet make it spin faster.
• Build a Simple Heat-Engine Model – A heat engine turns heat into movement. In a simple air engine, a flame heats the air in a flask. The hot air expands and pushes a piston up, lifting a load. This is work. Cooling brings the piston back. Only a part of the heat becomes work; the rest escapes. Efficiency = work out ÷ heat in.
• Build a Sound-Proof Room Model – A sound-proof room keeps noise out (or in). Sound is a vibration, so we stop it with heavy, dense walls that reflect it, soft porous materials that soak it up, and layers with air between them. A tiny gap lets sound leak, so every crack must be sealed. In this project you test different materials with a fair test, record the noise level in decibels, then build a small room model and judge it against clear goals such as noise level, cost and thickness.
• Building Construction Work: Methods, Contracts, Planning and Supervision – A building job is organised by a construction method (separate trades, general contractor or design-build), tied by a contract (fixed price or cost-plus), run by a plan of tasks, weeks and order, and checked by a supervisor who compares real progress with the plan.
• Building Cost Estimation – An estimate predicts the cost before building. The core rule is cost = quantity x rate. A rough estimate (area x rate per m²) is quick and about 20% accurate. A detailed estimate lists every item with its measured quantity and is about 5% accurate. In tendering, builders bid for the job and the owner picks the lowest acceptable bid.
• Building Farm Canals, Roads and Other Civil Works – Farm civil works are built in a clear order. First collect good materials (soil, sand, gravel, cement, steel). Then do earthwork (dig and fill), spread a firm foundation, lining or structure in concrete, put steel bars inside when the part must be strong in pulling (reinforced concrete, RCC), build the road in layers, and finally plant grass and trees on slopes. Each step makes the next one safe.
• Building Materials – Main building materials are timber, steel, concrete, reinforced concrete (RCC) and brick. Compare them by squeeze (compressive) strength, stretch (tensile) strength, weight, fire safety and cost. Concrete and brick are strong in squeeze but weak in stretch, steel is strong in both but softens in fire, timber is light but burns. Choose by the job.
• Building Services – Building services are the systems that make a building safe and comfortable: water supply, drainage and sanitation, heating, ventilation and air-conditioning (HVAC), electrical and communication wiring, fire protection and lifts. Each uses simple physics: water pressure p = ρgh, slopes for drainage, heat pumping for AC, and energy = power × time for saving electricity. Each also uses the right materials, such as PVC, copper and PPR pipes and insulated copper cables.
• Building Structure Related to Services: Planning, Structure and Structural Mechanics – A building must carry its loads to the soil and still leave space for services such as pipes, ducts and cables. Planning puts shafts and plant rooms in the right places. The structure (columns, beams and slabs) carries the loads. Structural mechanics tells how much a beam bends: the sag grows with load and falls fast as the beam gets deeper (about 1 ÷ depth³).
• Building Trades: Who Builds a House and How, Step by Step – A building is made by many trades in a set order. A surveyor marks the plot; public-works crews lay roads and pipes; masons build the walls; carpenters make the roof frame; roofers cover it; joiners fit windows and doors; fit-out and metalwork trades finish the inside. Studies and drawings (architecture, costs, digital models) come before all of them.
• Car Structure – An engine is described by torque and power. It needs helper systems: fuel, air and exhaust, cooling and oil. The body has crumple zones and a strong passenger cell. Springs and dampers (suspension) smooth the ride, steering turns the front wheels, and tyres and fuel economy shape how the car performs on the road.
• Cars and Safety – Car safety has two jobs. Preventive (active) devices such as ABS, stability control, radar braking and lane help try to stop a crash from happening. Collision (passive) devices such as crumple zones, seat belts and airbags protect people when a crash cannot be avoided.
• Celestial Coordinates: Finding Any Star in the Sky – Astronomers imagine the sky as a huge celestial sphere around the observer. In the horizon system a star is fixed by its altitude (angle above the horizon) and azimuth (angle from north towards east); both change as Earth turns. In the equatorial system a star is fixed by declination (angle from the celestial equator, like latitude) and right ascension (hours east of the March equinox point, like longitude); these stay almost constant, so star maps use them. The altitude of the celestial pole equals the observer's latitude. Brightness is given by magnitude: smaller numbers mean brighter stars.
• Centre of Mass: Two Particles, Rigid Body and Uniform Rod – The centre of mass is the one point that moves as if all the mass of a system were packed there. For two particles on a line, x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies on the line joining them, closer to the heavier one. For many particles, x_cm = Σmx/Σm (same for y and z). For a uniform rod of length L, the centre of mass is at L/2, its middle. Internal forces cannot move the centre of mass; only an outside force can: M·a_cm = F_ext.
• Centripetal Force, Car on a Level Road and on a Banked Road – A body moving in a circle is always changing direction, so it needs a net force towards the centre: the centripetal force F = mv²/r. It is not a new kind of force; tension, gravity, friction or a part of the normal force supplies it. On a level road only friction supplies it, so vmax = √(μs r g). On a road banked at θ, a part of the normal force helps: with no friction the ideal speed is v₀ = √(r g tanθ), and with friction vmax = √[r g (μs + tanθ)/(1 − μs tanθ)].
• Changes of State: Melting, Boiling, Evaporation and More – A substance can change between solid, liquid and gas when we heat it or cool it. Melting, boiling, evaporation and sublimation need heat. Freezing, condensation and deposition give heat out. While the state is changing, the temperature stays the same, because the heat is used to break (or is released by making) the pull between particles. This hidden heat is called latent heat. Evaporation happens at any temperature, only from the surface, and it cools things down. Changes of state are physical changes: no new substance forms and the mass stays the same.
• Chaos Theory: Order That Cannot Be Predicted – In chaos, the rules are exact (deterministic) but the future cannot be predicted for long, because a tiny change at the start grows very fast. This is the butterfly effect. Phase space draws the state of a system as one point; its path often settles on an attractor, and chaotic attractors are fractals.
• Charged Particles in Electric Fields – A charge q in a field E feels a force F = qE, so it has acceleration a = qE/m. Released from rest through a potential difference U it gains kinetic energy qU, giving v = √(2qU/m). Shot in across the field, it follows a parabola, like a thrown ball, with deflection y = qUL²/(2mdv₀²). A cathode-ray oscilloscope uses this to move an electron beam on a screen.
• Circular Motion: Period, Speed and Acceleration – In circular motion an object goes round a circle. One full round takes the period T and the number of rounds per second is the frequency f = 1/T. The speed is v = 2πr/T and the angular speed is ω = 2π/T, so v = ωr. Even if the speed is steady, the direction keeps changing, so the velocity changes and there is an acceleration a = v²/r that points to the centre.
• Civil Engineering Materials – Roads, bridges and buildings are made from concrete, steel, soil and polymers. Each material has a property profile: how well it takes a push (compression), a pull (tension), water and time. Good engineers choose the material whose strengths match the job and combine materials, such as steel inside concrete.
• Civil Engineering: How Buildings Stand Up and Keep the Weather Out – Civil engineers design and build structures such as houses, bridges, roads and dams. A building has a frame (columns, beams, slabs, bracing) that carries loads down to the foundation and soil, and an envelope (walls, curtain walls, roof) that protects people inside. Engineers choose materials (wood, steel, concrete), check forces and plan for the site and the environment.
• Composite Structures – A composite structure uses steel and concrete together in one part so each covers the other's weakness. In steel-reinforced concrete (SRC) a steel H-frame sits inside reinforced concrete. In a concrete-filled steel tube (CFT) concrete fills a steel pipe. They carry more load, resist fire and earthquakes better, and are good for tall buildings.
• Compton Effect: When a Photon Bounces Off an Electron – In the Compton effect an X-ray or gamma photon hits a free (or loosely bound) electron and scatters. The photon loses some energy, so its wavelength gets longer by Δλ = (h/mc)(1 − cos θ), where θ is the scattering angle and h/mc = 2.43 pm. The electron recoils with the lost energy. This shows that light behaves like a particle with momentum p = h/λ.
• Concrete, Reinforced Concrete and Steel Structures – Concrete is strong when squeezed but weak when stretched. Steel bars placed where the stretch happens turn it into reinforced concrete (RCC). Steel frames made of triangles are light and cross long gaps. Farms use all three: canal linings, water tanks, silos, bridges and sheds.
• Conduct as a Small-Vessel Operator – A small-boat operator, called the master or skipper, is responsible for the boat and everyone on it. Water transport is different from road transport: boats have no brakes, drift with water and wind, and help is far away. So the master checks the boat and weather, carries only the safe load, keeps a lookout, and obeys the rules on speed, safety gear, licences and pollution.
• Conductors, Insulators and Semiconductors – Every material is made of atoms with electrons. In a conductor (metals) some electrons are free, so current flows easily. In an insulator (rubber, glass) all electrons are held tight, so almost no current flows. A semiconductor (silicon) has few free electrons when cold and more when warm or when impurities are added, so it conducts a little and can be controlled.
• Conservation of Energy – Energy cannot be created or destroyed. It only changes from one form to another, or moves from one object to another. The total energy of a closed system stays the same. When there is no friction, mechanical energy (potential + kinetic) stays constant: mgh + ½mv² = constant. With friction, some mechanical energy turns into heat (thermal energy), but the total is still the same. Efficiency = useful energy out ÷ total energy in × 100%.
• Construction Machinery and Electrical Facilities – Construction machines each do one job: excavators dig, cranes lift, rollers compact, trucks carry. A crane stays upright only if the load moment is no more than the counterweight moment. Site electricity runs from a generator or supply to a distribution board and tools, protected by earthing and circuit breakers that trip on overload.
• Construction Machinery and Related Tools – Construction machines save time and heavy work: excavators dig, bulldozers push, dump trucks haul, rollers compact, cranes lift, and mixers, pumps and vibrators handle concrete. Hand and measuring tools such as the spirit level and plumb bob keep work straight. Every machine needs a trained operator and a pre-start safety check.
• Construction Management: Organisation, Time, Quality and Safety – Managing a construction job means running people (organisation), keeping to the plan (process control), making sure the work is good enough (quality control) and keeping everyone safe (safety management). The manager checks all three against targets and fixes problems early.
• Construction Techniques – Civil works follow a few core techniques: earthwork (cut and fill), foundation work (spread footings and piles), concrete work (formwork, bars, pouring, curing), paving (layers of a road), tunnel work (excavate, support, line) and ICT-based construction that uses digital guidance to dig and build accurately.
• Construction Technology: How Buildings Are Planned and Built – Construction technology is the knowledge of how to plan, build, finish and look after structures. A building has a foundation, a frame (columns and beams), walls and a roof. Every load (dead load of the building itself, live load of people and furniture, wind and snow) must travel down a clear load path to the soil. Concrete is strong in compression, steel in tension, so reinforced concrete uses both. Builders work from scale drawings (plan, elevation, section), use maths to find areas and volumes, follow building codes for safety, and fit systems for water, power and air.
• Cosmology: The Expanding Universe and the Big Bang – Cosmology is the study of the whole universe: its structure, history and future. Galaxies gather in groups, clusters and filaments around huge voids. Distant galaxies are moving away from us, faster the farther they are (Hubble's law, v = H₀d), because space itself is expanding. Running the expansion backwards leads to a hot, dense beginning about 13.8 billion years ago, the Big Bang. The main evidence is redshift, the cosmic microwave background and the amounts of hydrogen and helium. Most of the universe is dark matter and dark energy.
• Coulomb's Law: The Force Between Two Charges – Charged objects push or pull each other without touching. Like charges repel and unlike charges attract. For two small (point) charges, the force is F = k·q₁·q₂ / r², where k ≈ 9 × 10⁹ N·m²/C². Double a charge and the force doubles; double the distance and the force falls to one quarter. Charge is never made or destroyed, only moved.
• Current in a Metal: Drift Velocity and Mobility – In a metal, free electrons move very fast in random directions, so on average they go nowhere. An electric field adds a small, steady shift opposite to the field: the drift velocity vd = eEτ/m. The current is I = n e A vd, and the current density is j = n e vd. Mobility μ = vd/E tells how easily a charge drifts. Drift speed is only about a millimetre per second, yet a bulb lights at once because the field is set up in the whole wire almost instantly.
• Curvilinear Motion and Composition of Motion – A body moves on a curve when the net force is not along its velocity. Its velocity always points along the tangent to the path. A motion can be built from two independent motions (composition) or split into two parts (resolution). A boat crossing a river has speed v = √(u² + w²); the crossing time depends only on the boat's speed across the river.
• Dark Matter: The Invisible Mass Holding Galaxies Together – Stars far from a galaxy's centre orbit about as fast as stars near it. If only the visible matter pulled on them, far stars should move slowly. This flat rotation curve means there is extra, invisible mass: dark matter. It does not shine or block light, but its gravity is real. Today's best picture of the cosmos is about 5% ordinary matter, 27% dark matter and 68% dark energy, which makes the expansion speed up.
• Data Communication Systems – A communication system sends information from a transmitter through a channel to a receiver. The channel can be copper wire, optical fibre or radio waves. To send a message by radio we put it on a fast carrier wave: in AM the carrier's amplitude follows the message, in FM its frequency does. Time-division multiplexing lets many signals share one channel by giving each a short time slot in turn.
• Degrees of Freedom, Equipartition of Energy and Specific Heats – A degree of freedom is one independent way in which a molecule can move and store energy. A single atom can only move along x, y and z (f = 3). A dumbbell molecule like O₂ can also spin about two axes (f = 5), and when hot it can vibrate (2 more). The law of equipartition of energy says that in thermal balance each degree of freedom holds, on average, ½kT of energy (a vibration holds kT because it has both kinetic and potential energy). So one mole has U = (f/2)RT, giving Cv = (f/2)R, Cp = Cv + R and γ = 1 + 2/f. For solids, each atom vibrates in 3 directions, giving C = 3R.
• Density – Density tells how much mass is packed into each unit of volume: ρ = m ÷ V. Its SI unit is kg/m³; in the lab we often use g/cm³ (1 g/cm³ = 1000 kg/m³). Water has density 1 g/cm³. An object less dense than a liquid floats in it; a denser one sinks.
• Design of Foundations and Retaining Structures – A foundation passes the building load to the ground without the soil failing or sinking too much. A spread footing makes the area big so the bearing pressure q = Q ÷ A is small. A pile reaches deeper, strong soil and carries load by skin friction and end bearing. A retaining wall holds soil back against earth pressure P = ½ Ka γ H², and must not slide, tip over or overload the soil.
• Design of Reinforced Concrete Structures – Concrete is strong when squeezed but weak when pulled. In a beam, the top is squeezed and the bottom is pulled, so steel bars go near the bottom. The squeezing force C in the concrete and the pulling force T in the steel are equal, and together they make the moment capacity M = T × arm. Columns are mainly squeezed. Prestressed concrete squeezes the beam in advance so that cracks do not open.
• Design of Steel Structures: H-Beams and Plate Girders – Designing a steel beam means choosing a size so that the stress stays below the allowed limit. We find the bending moment M and the shear V, then choose a section with enough section modulus Z (σ = M / Z) and enough web area for shear. An H-beam puts most steel in the flanges, far from the middle, so it bends less. A plate girder is a tall welded beam with a thin web held straight by stiffeners.
• Design of Various Structures: Timber, Reinforced Concrete and Steel – Timber is light, renewable and strong along the grain but weak across it and sensitive to moisture and rot. Concrete is strong in compression and weak in tension, so steel bars (rebar) are placed where the beam is stretched: reinforced concrete (RC). Steel is strong in both push and pull, ductile and light for its strength; slender steel members can buckle and steel loses strength in fire. In all three the load follows one path: slab, beam, column, foundation, ground.
• Diffraction of Light – Diffraction is the spreading of waves when they pass a narrow gap or an edge. A gap of width a gives dark spots where a sin θ = nλ. A grating with spacing d gives sharp bright lines where d sin θ = nλ. The smaller the gap or the longer the wavelength, the more the light spreads.
• Digital Signal Processing: Combinational Logic, Sequential Logic and Astables – Digital signals have only two levels: 1 (high) and 0 (low). Combinational logic (gates such as AND, OR, NOT, NAND, NOR, XOR) gives an output that depends only on the inputs now. Sequential logic (flip-flops, counters) also depends on what happened before, so it has memory; it changes on clock pulses. An astable circuit has no stable state and switches by itself, making the clock square wave. Its frequency f = 1/T.
• Dimensions and Dimensional Analysis – The dimensions of a quantity show how it is built from base quantities: mass [M], length [L], time [T] (and current [A], temperature [K], amount [mol], luminous intensity [cd]). Force = [M L T⁻²]. In a correct equation every term has the same dimensions (principle of homogeneity). We use this to check equations, to convert units from one system to another, and to find how one quantity depends on others. It cannot give number constants like 2π, and it cannot handle sums or trig and log functions.
• Direct Heating Equipment: Boiler, Pipes and Radiators – In direct (hot-water) heating, a boiler heats water, a pump sends it through a supply pipe to radiators, and the cooler water returns to the boiler in a closed loop. The heat delivered is Q = flow × 4.186 × ΔT. An expansion tank takes up the extra water volume, valves control each room, and pipes are sized so water speed stays low and quiet.
• Distance to Stars: Parallax and Brightness – Nearby stars are measured by parallax: the star seems to shift as Earth moves round the Sun, and distance in parsecs d = 1 / p (p in arcseconds). Farther stars are measured by brightness: the distance modulus m − M = 5 log10(d / 10) links how bright a star looks (m) with how bright it really is (M). 1 parsec = 3.26 light-years.
• Diving Techniques – A diver needs air, a safe way down, a slow way up and a plan for the work. Air comes from the surface by a hose or from a cylinder on the back. Pressure rises by about 1 bar every 10 m, so air shrinks going down and swells coming up. Rise slowly, never hold your breath, and work with a partner and clear signals.
• Domestic Electric Circuits – A house gets 220 V, 50 Hz AC through a live and a neutral wire; appliances are joined in parallel on separate 5 A and 15 A circuits, and a fuse or MCB in the live wire plus an earth wire keep the house safe.
• Drainage and Ventilation (Vent) Installations – Used water leaves a building by gravity through sloping drain pipes, a vertical stack and the sewer. Every fixture has a trap, a U-bend that holds a water seal to block sewer gas. A vent pipe lets air into the system so flushing cannot suck the seals dry. In a house, pressurised supply pipes bring clean water in and unpressurised drain pipes take used water out.
• Dynamics: Forces, Friction, Inclines and Circular Motion – Dynamics explains why things move the way they do. Newton's laws work in inertial (non-accelerating) frames; in accelerating frames we feel fictitious forces. Draw a free-body diagram, add the forces (gravity, normal, applied, tension, friction) and use ΣF = ma. Static friction holds things still up to μₛN; kinetic friction μₖN acts while sliding. On an incline, weight splits into mg sinθ and mg cosθ. Connected objects share one acceleration. In uniform circular motion a = v²/r points to the centre and F = mv²/r.
• Earth’s Magnetic Field (Geomagnetism) – Earth has a magnetic field like a tilted bar magnet. It is made by moving liquid iron in the outer core (the dynamo). A compass lines up with it. The angle between magnetic and true north is declination; the angle the field makes with the ground is dip (0° at the equator, 90° at the magnetic poles). The field forms a shield, the magnetosphere, that bends the solar wind. Some particles slip in near the poles and make the aurora.
• Effects of Electromagnetic Radiation on Matter – Electromagnetic radiation comes in packets called photons. Each photon carries energy E = hf, so higher frequency means more energy per photon. Low-energy radio and microwaves make molecules move (heating), visible light lifts electrons to higher levels (colour, vision, photosynthesis), UV can break chemical bonds, and X-rays and gamma rays can knock electrons out of atoms (ionising). How much harm radiation does depends on photon energy, intensity and time of exposure.
• Elastic and Inelastic Collisions in 1D and 2D – In every collision, total momentum is conserved (no outside force during the short hit). In an elastic collision kinetic energy is also conserved. In an inelastic collision some kinetic energy becomes heat, sound or dent energy; if the bodies stick together it is perfectly inelastic. In 1D, elastic collision gives v₁ = (m₁ − m₂)u₁/(m₁ + m₂) and v₂ = 2m₁u₁/(m₁ + m₂) when body 2 starts at rest. In 2D, momentum is conserved separately along x and y.
• Elastic Force and the Spring Balance – When you stretch, squeeze or bend a spring, it pushes or pulls back. This pull-back is the elastic force. Inside the elastic limit, the stretch grows in step with the pulling force (double the load, double the stretch), and the spring returns to its old length when you let go. A spring balance uses this to measure force in newtons.
• Electric Cells and Batteries: How a Cell Makes Electricity – An electric cell turns chemical energy into electrical energy. It needs two different metals (electrodes) dipped in a liquid or paste that conducts (the electrolyte). A chemical reaction leaves extra electrons on one metal (the negative terminal); when a wire joins the two terminals, electrons flow through it as an electric current. A battery is two or more cells joined together; in series their voltages add up.
• Electric Charges and Fields – Charge comes in two kinds, is conserved and comes in whole-number packets of e = 1.6 × 10⁻¹⁹ C. Two point charges push or pull with F = kq₁q₂/r² (k = 9 × 10⁹ N m² C⁻²). Forces and fields from many charges add as vectors (superposition). The field E = F/q₀ of a point charge is kq/r²; field lines show it. A dipole (±q a distance 2a apart) has moment p = q·2a; in a uniform field it feels zero net force but a torque τ = pE sinθ. Electric flux Φ = E·A, and Gauss's law says the flux out of any closed surface is q_enclosed/ε₀, which quickly gives E for a long wire (λ/2πε₀r), a plane sheet (σ/2ε₀) and a thin spherical shell (kq/r² outside, 0 inside).
• Electric Current in Metals, Liquids, Gases and Vacuum – Current is moving charge, but the moving charges are different in each medium. In a metal they are free electrons. In an electrolyte they are positive and negative ions. A gas conducts only after it is ionised (a spark or glow discharge). A vacuum conducts only if electrons are boiled off a hot cathode (thermionic emission). Heating raises the resistance of a metal, lowers that of an electrolyte or semiconductor, and a superconductor drops to zero resistance when cold enough. Faraday's laws say the mass freed in electrolysis is m = Z I t.
• Electric Current, Potential Difference and Electric Circuits – Electric current is the rate of flow of charge, I = Q/t, measured in amperes with an ammeter joined in series. Potential difference is the work done to move a unit charge between two points, V = W/Q, measured in volts with a voltmeter joined in parallel. Charge flows only in a closed circuit.
• Electric Field and Field Strength – A charge changes the space around it so that any other charge placed there feels a force. This region is the electric field. Its strength at a point is the force on a small positive test charge divided by that charge: E = F/q, measured in N/C (same as V/m). For a point charge, E = kQ/r², with k = 9 × 10⁹ N m²/C². E is a vector: it points away from + charges and towards − charges. Field lines show its direction and, by how close they are, its strength. Fields from several charges add as vectors (superposition).
• Electric Power and Electrical Energy – Electric power is the rate of using electrical energy: P = VI = I²R = V²/R, in watts. Energy used = power × time. At home energy is measured in kilowatt-hours: 1 kWh = 1 unit = 3.6 × 10⁶ J. Bill = units × rate.
• Electrical Installations in a Building – An electrical installation brings power from the distribution board to lamps, sockets and machines through protected circuits. Light sources differ in power and brightness; machines turn energy from one form to another; low-current lines (bell, network, alarm) run at low voltage from a transformer.
• Electrical Laws: Keeping Electricity Safe – Electricity can start fires and cause shocks, so countries make laws. Three groups of rules matter: rules for companies that supply power, rules for people who do wiring work, and rules for appliances that are sold. Together they keep the voltage steady, the wiring safe and the appliances tested.
• Electrical Machines: Generators, Motors and Transformers – Electrical machines change energy from one form to another. A generator turns motion into electricity and a motor turns electricity into motion, both using magnets and coils. A synchronous machine spins exactly with the magnetic field (Ns = 120f/P). An induction motor spins slightly slower (slip). A DC machine uses a commutator. A transformer changes voltage using Vs/Vp = Ns/Np. Emergency supplies (battery and engine generator) keep power on when the mains fails.
• Electrical Materials: Conducting, Magnetic and Insulating – Electrical machines use three families of materials. Conductors (copper, aluminium, nichrome) have free electrons and low resistivity. Insulators (porcelain, rubber, mica, oil) hold their electrons and fail only at the breakdown voltage. Magnetic materials are soft (easy to magnetise and demagnetise, for cores) or hard (keep their magnetism, for permanent magnets).
• Electrical Meters, Measurement and Automatic Control – Electrical meters show a quantity on a scale. An ammeter joins in series and has very low resistance; a voltmeter joins in parallel and has very high resistance. Measurement means comparing with a standard and knowing the error. Automatic control lets a machine hold a value by itself: an open-loop system never checks the result, a closed-loop system uses a sensor and feedback to correct the error. Examples are thermostats, motor speed control and water-level control.
• Electrical Technology in Production – Factories run on electricity. DC flows in one direction (batteries, electronics). AC changes direction many times a second (50 Hz in India, 60 Hz in some countries) and is used for the mains. Power P = V x I, energy = power x time. A safe installation uses wires of the right size, a breaker to cut power on overload and an earth wire to protect people.
• Electricity and Magnetism – Electric charge and magnets are two sides of one idea. Rubbed objects hold static charge; magnets have poles and a field; a current makes a magnetic field; and a changing magnetic field makes a current (electromagnetic induction). Motors, generators and transformers all use these four steps.
• Electromagnetic Induction – When the magnetic flux through a coil changes, an emf is produced in it: ε = −N dΦ/dt (Faraday). The minus sign is Lenz's law: the induced current always opposes the change that made it. Moving a rod in a field gives motional emf ε = Blv. A changing current makes an emf in its own coil (self-induction, L) and in a nearby coil (mutual induction, M).
• Electromagnetic Induction: Making Electricity with Magnets – When the magnetic field through a coil changes, a voltage (potential difference) is made across the coil. This is electromagnetic induction. If the coil is part of a closed circuit, a current flows. A faster change, more turns or a stronger magnet give a bigger voltage. Generators, microphones and transformers all use this idea, and transformers let the power grid send electricity far with little waste.
• Electromagnetic Waves – A changing electric field acts like a current, called the displacement current, and it makes a magnetic field. A changing magnetic field makes an electric field. Together they travel as an electromagnetic (EM) wave at c = 3 × 10⁸ m/s, even through empty space. E and B are at right angles to each other and to the direction of travel, so EM waves are transverse. Sorted by wavelength, they form the spectrum: radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.
• Electromechanical Devices and Production Lines – An electromechanical device mixes moving parts (mechanics) with electricity and electronics. It has a sensor (eyes), a controller (brain) and an actuator such as a motor (muscle). Factories join such devices into a production line, where boxes move from station to station and machines do the work faster, safely and in the same way each time.
• Electronic Navigation Equipment: Radar, Satellite Navigation, Sonar – Radar sends a radio pulse and measures the time for the echo: distance = c × t / 2. Satellite navigation (GPS, GNSS) measures the distance to at least four satellites from signal travel time and finds position. Sonar sends a sound pulse and times the echo from the seabed or a target: depth = v × t / 2 with v ≈ 1500 m/s in sea water. Other aids include the gyrocompass, speed log, AIS and electronic charts.
• Electrostatic Potential and Capacitance – Electrostatic potential V at a point is the work done per unit positive charge to bring it from infinity: V = kq/r for a point charge, and potentials of many charges add as plain numbers. Potential difference V_B − V_A = W_AB/q. Equipotential surfaces join equal-V points; E is perpendicular to them and E = −dV/dr. Potential energy of two charges is U = kq₁q₂/r, and of a dipole in a field U = −pE cosθ. Conductors have free charges (E inside = 0); dielectrics have bound charges that polarise and cut the field to E₀/K. A capacitor stores charge Q = CV. A parallel plate capacitor has C = ε₀A/d, and KC with a dielectric. In series 1/C = 1/C₁ + 1/C₂ + …; in parallel C = C₁ + C₂ + …. Energy stored U = ½CV² = Q²/2C = ½QV.
• Electrostatics: Induction, Polarisation and Sharing of Charge – Electrostatics is the study of charges at rest. Objects get charged by friction (rubbing), by contact (conduction) or by induction (bringing a charge near, without touching). In a conductor, free electrons move: a nearby charge pushes them to one side (induction), and earthing then leaves the conductor with the opposite charge. In an insulator (dielectric), electrons cannot travel, but each molecule stretches into a tiny dipole and lines up with the field (polarisation); that is why a charged comb attracts neutral paper. When charged conductors are joined by a wire, charge flows until their potentials are equal. For spheres far apart, V = kq/r, so the charge divides in the ratio of the radii: q₁/q₂ = r₁/r₂, and the smaller sphere has the larger surface charge density. Total charge is always conserved.
• Elements of Electric Circuits – Every circuit is built from a source (battery) and three basic parts: a resistor, which limits current (R = V/I); a capacitor, which stores charge (C = Q/V); and an inductor, a coil that opposes changes in current and stores energy in a magnetic field.
• EMF, Internal Resistance, Power and Combination of Cells – A cell does work on charges; the work per coulomb is its emf ε. Inside the cell there is a small internal resistance r. With current I, the terminal voltage is V = ε − Ir and I = ε/(R + r). Electrical power P = VI = I²R = V²/R, and energy W = Pt. Power delivered to R is largest when R = r. Cells in series: εeq = ε1 + ε2, req = r1 + r2. Cells in parallel: εeq = (ε1r2 + ε2r1)/(r1 + r2), 1/req = 1/r1 + 1/r2.
• Energy Efficiency – Every machine changes energy from one form to another. Part of the energy becomes what we want (useful energy). The rest spreads out, mostly as heat (wasted energy). Efficiency = useful energy out ÷ total energy in × 100 %. No real machine reaches 100 %. Using efficient devices and wasting less energy saves money and cuts pollution.
• Energy in Systems and Electric Power – A system is the set of objects you choose to study. Its total energy stays the same unless energy crosses the system boundary as work, heat or radiation: ΔE_system = W + Q. Inside, energy moves between stores such as kinetic, gravitational, elastic, thermal, chemical and electric. Power is the rate of energy transfer, P = ΔE/Δt, in watts. In a circuit the electric power is P = IV; for a resistor this also equals I²R and V²/R. Real devices waste part of the input as heat, so efficiency η = useful output ÷ input is always less than 100%. Designing a device means choosing the input store, the output store and cutting the waste.
• Energy Storage: Keeping Energy for Later – Energy from the sun or wind is not always there when we need it. A store keeps energy for later. Mechanical stores keep it in height, springs or spinning wheels (E = mgh for a raised weight). Chemical stores keep it in fuels and batteries (energy in watt-hours = volts × amp-hours). Thermal stores keep it as heat in hot water or hot material (Q = m × c × ΔT). Around the store sit the power parts: converters, modulators and adapters change the form of the electricity; gearboxes, belts and couplings pass motion on; bearings and slides guide moving parts; seals keep fluids in and dirt out. No store gives back everything that goes in, so efficiency is below 100%.
• Energy Stores and Transfers – Energy is what makes things change. It is kept in stores (chemical, kinetic, gravitational, elastic, thermal, magnetic, electrostatic, nuclear) and moves between them by four pathways: a force doing work, an electric current, heating and radiation (light, sound). Energy is measured in joules (J). It is never made or destroyed; it only moves. Some always spreads out as heat, so no machine is 100% efficient.
• Energy Transformations: How Energy Changes Form in Devices and Power Stations – Energy exists in many forms (chemical, kinetic, gravitational, elastic, electrical, thermal, light, sound, nuclear). Devices change one form into others. Energy is never made or destroyed, so input energy = useful output + wasted energy. Efficiency = useful output ÷ input × 100 %. Power = energy ÷ time. Power stations differ a lot in efficiency, cost and pollution, and we choose between renewable and non-renewable sources.
• Energy-Saving Plan: Audit Your Home and Save kWh – An energy-saving plan has five steps: list the appliances, measure their energy with E = P × t (in kWh), find the biggest user, change habits (use for fewer hours), and change devices (use more efficient ones such as LEDs). Then check the new total and the cost saved.
• Engineering Trades: Who Builds and Fixes Our Machines – Many jobs build, install and repair machines. They fall into five families: aircraft, mechanical and industrial manufacturing, digital and energy, vehicle and equipment maintenance, and automated installations. Each family has its own tools, safety rules and careers.
• Engines, Powertrain and Vehicle Systems – A four-stroke engine turns the chemical energy of fuel into motion through intake, compression, power and exhaust strokes. Cylinders can be inline, V or flat. Fuel, lubrication, cooling and ignition systems keep it running, and timing makes sparks and valves act at the right moment. Size is given by displacement = π/4 × bore² × stroke × cylinders. Power flows engine → clutch → gearbox → drive shaft → differential → wheels. Gears trade speed for torque: gear ratio = driven teeth ÷ driver teeth. Technicians use specifications, trouble charts and safe tools to inspect, measure wear and repair.
• Escape Speed, Orbital Velocity and Energy of an Orbiting Satellite – Throw something fast enough sideways and it keeps falling around the Earth without landing: that speed is the orbital velocity, v₀ = √(GM/r), about 7.9 km/s just above the surface. Throw it faster, at the escape speed vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km/s, and it leaves Earth for ever. vₑ = √2 × v₀. A satellite in a circular orbit has KE = GMm/2r, PE = −GMm/r and total energy E = −GMm/2r. The total is negative, so the satellite is bound. Higher orbits are slower and take longer: T = 2π√(r³/GM).
• Exoplanets: How Do We Find Planets Around Other Stars? – An exoplanet is a planet that goes round a star other than the Sun. Planets are tiny and dim next to a star, so we mostly find them by clues. In the transit method, a planet crosses in front of its star and the star's light dips by about (planet size / star size) squared. In the radial velocity (wobble) method, the planet's pull makes the star move in a tiny circle, and its light shifts blue and red. The time between dips or wobbles gives the planet's year. Other methods are direct imaging and microlensing. More than 5,000 exoplanets are known.
• Experiments with Electricity – Five simple experiments cover school electricity. An electroscope shows whether something is charged: its two foil leaves spread apart. Like charges push apart and unlike charges pull together. A bulb tester shows if a material is a conductor or an insulator. In a circuit, the ammeter goes in series and the voltmeter goes across the part you measure. Divide the voltmeter reading by the ammeter reading to get resistance: R = V ÷ I.
• Factors Affecting Resistance and Resistivity – A wire's resistance grows with its length and falls as it gets thicker: R = ρL/A. The constant ρ (rho) is the resistivity of the material, in Ω m. It depends only on the material and its temperature. Metals have low resistivity, alloys higher, insulators very high.
• Fields and Forces – Some forces need touch, like a push with your hand. Others act across empty space: gravity, the electric force and the magnetic force. We explain these with a field: a region around an object where another object feels a force. Mass makes a gravitational field, charge makes an electric field, and magnets or currents make a magnetic field. We draw fields with field lines: the arrow shows the direction of force, and lines close together mean a strong field. Gravity and electric force get weaker with distance by the inverse-square law: double the distance, one quarter of the force. Fields also store energy. All forces in nature come from four fundamental forces: gravity, electromagnetism, the strong force and the weak force.
• First Law of Thermodynamics – Internal energy U is the total energy of the molecules inside a system. It changes in only two ways: by heat Q (energy that flows because of a temperature difference) and by work W (energy moved by a force, like a moving piston). First law: ΔQ = ΔU + ΔW. Heat given to a gas partly raises its internal energy and partly lets it do work. Work by a gas at constant pressure is PΔV. For an ideal gas Cp − Cv = R.
• Fluid Flow: Flow Rate, Continuity, Bernoulli and Venturi – The flow rate Q = A × v is the same at every point of a pipe full of flowing liquid, so the fluid speeds up where the pipe narrows (A₁v₁ = A₂v₂). Bernoulli's equation, p + ½ρv² + ρgh = constant, then says pressure drops where speed rises. A Venturi meter uses that pressure drop to measure speed.
• Fluid Machinery: Pumps, Turbines, Fans and Hydraulic Machines – A fluid machine uses a liquid or a gas to move energy. Pumps and compressors add energy to a fluid. Turbines take energy from a fluid. Fans move air. Hydraulic (oil) and pneumatic (air) machines turn a small push into a big push, because pressure p = F/A is the same everywhere in the closed fluid.
• Fluid Speed and Pressure – Where a liquid or gas moves faster, its pressure is lower. Where it moves slower, the pressure is higher. This is Bernoulli's principle. In a pipe that narrows, the fluid speeds up and the pressure drops. Over an aeroplane wing the air above moves faster, so pressure above is lower and the higher pressure below pushes the wing up (lift).
• Fluids: Internal Structure and Density – A fluid is any substance that can flow: liquids and gases. Its particles can slide past one another, so a fluid takes the shape of its container. Density ρ = m/V tells how much mass is packed into each cubic metre (water: 1000 kg/m³). Relative density = ρ / ρwater. Physicists often model a liquid as an ideal fluid: incompressible (constant density) with no internal friction.
• Food Manufacturing Equipment: Boilers and Freezers – A food factory uses machines to heat, cook, cool and freeze food in large amounts. A boiler burns fuel to turn water into steam, and the steam cooks or sterilises food. A refrigeration machine moves heat out of a freezer using a gas that goes round a loop: compressor, condenser, expansion valve, evaporator. Fish is stored at -18 °C or colder.
• Force and Laws of Motion – A force is a push or a pull. Balanced forces (net force zero) do not change motion; an unbalanced force changes speed or direction. Friction opposes sliding. First law: a body keeps its state of rest or uniform motion unless an unbalanced force acts (inertia; heavier bodies have more inertia). Momentum p = mv. Second law: F = ma (rate of change of momentum), 1 N = 1 kg m/s². Third law: forces come in equal and opposite pairs acting on two different bodies. For a system with no outside force, internal forces cancel and total momentum is conserved.
• Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.
• Forces Acting on Machines – A machine moves because forces act on it. Net force = push − friction, and acceleration a = net force ÷ mass. Work = force × distance (joule). Power = work ÷ time (watt). Efficiency = useful output ÷ input × 100%. Friction wastes some energy as heat, so oil and bearings are used.
• Forces Acting on Structures – A structure carries loads (dead, live, wind, earthquake) down to the ground. To stand still it must be in equilibrium: forces up = forces down, and turning effects balance (ΣFx = 0, ΣFy = 0, ΣM = 0). Supports give reactions: a roller gives 1, a pin gives 2, a fixed support gives 3. If the unknown reactions equal 3 (in a plane) the beam is statically determinate; fewer means unstable, more means indeterminate.
• Forces and Stresses on Materials – Every product carries forces. Five kinds matter most: tension (pulling, gets longer), compression (pushing, gets shorter), bending (one side squashed, other side stretched), torsion (twisting) and shear (layers sliding across each other). Stress is force per area: σ = F ÷ A, in N/m² (pascal) or N/mm² (MPa). When a part is too weak or bendy we reinforce it: change its shape (fold, rib, corrugate, use an I-section or triangles) or combine layers (laminate, add webbing or interfacing).
• Forces in Statically Determinate Structures – A structure is statically determinate when the three equilibrium equations (sum of horizontal forces = 0, sum of vertical forces = 0, sum of moments = 0) are enough to find every support reaction and every internal force. For a simply supported beam, R_A = P(1 - a) and R_B = P a when the load sits at a fraction a of the span. Bending moment is biggest under the load (M = P a (1 - a) L). In a triangle truss every bar only pulls or pushes. Stress is force divided by area: sigma = F / A.
• Forces in Statically Indeterminate Structures – A structure is statically indeterminate when it has more unknown reactions or members than the three equilibrium equations can solve. The extra unknowns are called redundants; degree of indeterminacy = unknowns - equations. To solve it we add compatibility (how the parts must bend together) and use the material stiffness EI. The gain: a beam with an extra support or fixed ends has much smaller bending moment and sag (a two-span beam sags about 38 times less than a simple beam of the same total span). The price: a settling support now creates stress.
• Forces: Pushes and Pulls – A force is a push or a pull between two objects. It is measured in newtons (N). Contact forces need touching (push, friction, normal force, tension, buoyancy); non-contact forces act at a distance (gravity, magnetism, electric). A force is drawn as an arrow: start = point of application, direction, length = size. Forces can change an object's speed, direction or shape. If forces balance, a still object stays still (equilibrium). Forces always come in pairs: if A pushes B, B pushes A back equally (Newton's third law).
• Free Fall – A body is in free fall when gravity is the only force acting on it. Near the Earth every freely falling body speeds up by about 9.8 m/s every second, whatever its mass. This is the acceleration due to gravity, g ≈ 9.8 m/s². For a body dropped from rest: v = g t and h = ½ g t². Air resistance makes light, wide things like feathers fall slower. Weight is the pull of gravity: W = m × g.
• Friction: Static, Kinetic and Rolling Friction, Laws and Lubrication – Friction is the force that opposes relative motion (or its start) between surfaces in contact. Static friction adjusts itself up to a maximum, the limiting friction fs,max = μs N. Once sliding starts, kinetic friction fk = μk N acts, and μk < μs. Friction depends on the normal force and the nature of the surfaces, not on the area of contact. Rolling friction is much smaller than sliding friction; lubricants and ball bearings reduce friction.
• Friction: The Force That Opposes Sliding – Friction is a contact force between two surfaces. It always acts against the motion, or against the way an object is trying to move. Surfaces have tiny bumps that catch on each other. Static friction stops a still object from moving; it grows to match your push, up to a limit. Once the object slides, sliding (kinetic) friction acts, and it is a little smaller. Rolling friction is much smaller still. Friction is bigger when the surfaces are rougher and when they are pressed together harder (more weight). It hardly depends on the area of contact. Friction helps us walk, write and brake, but it wastes energy as heat and wears things out. We increase it with treads and grip, and reduce it with oil, smooth surfaces, wheels and ball bearings.
• Functional Materials – Functional materials are chosen for what they do, not for how strong they are. Magnetic materials make magnets and transformers, piezo materials turn electricity into sound and back, glass guides light, solar cells turn sunlight into electricity, and sensor materials change a property when the surroundings change.
• Future Built by Physics – New technology grows out of physics ideas about atoms, light and energy. Atom energy levels give lasers and LEDs, tiny switches give chips, qubits could give quantum computers, cold superconductors carry current with no loss, fusion could give clean energy, and ripples in space let us study the universe.
• General Relativity: Gravity as Curved Space-Time – General relativity says that mass and energy bend space-time, and things move along the bent paths. That is what we call gravity. It predicts that light bends near a mass (gravitational lensing), that clocks run slower in strong gravity, and that a very dense mass can form a black hole.
• Geophysics: The Physics of the Earth and Its Climate – Geophysics uses physics to study the Earth. Sunlight in must equal heat out, or the planet warms or cools. A greenhouse layer sends some heat back, lifting the average temperature from about -18 °C to about 15 °C. Seismic waves show the layers inside the Earth, and graphs of data show trends.
• Gravitational Field of Mass Systems – A mass changes the space around it. The gravitational field strength at a point is the pull on 1 kg placed there: g = F/m. For a point mass (or a sphere, outside it) g = GM/r², pointing to the mass. For several masses, add the field arrows as vectors. A body released in a field accelerates with a = g, whatever its own mass.
• Gravitational Potential Energy and Gravitational Potential – Gravitational potential energy (U) of a mass m at distance r from the centre of the Earth is U = −GMm/r, taking U = 0 at infinity. It is negative because gravity attracts: you must do work to pull the mass away to infinity. Near the ground, the change in U for a small lift h is mgh. The work to lift a mass from the surface to height h is GMm(1/R − 1/(R + h)). Gravitational potential V is the PE per kilogram: V = −GM/r, in J/kg. Potential is a scalar, so potentials of many masses just add.
• Gravity – Gravity is the pull between all masses. Earth pulls every object towards its centre. A freely falling object speeds up by about 9.8 m/s every second (g), and this does not depend on its mass. Weight is the pull on your mass, W = m × g, so it changes from world to world while mass does not. A ball thrown sideways fast enough keeps missing the Earth and goes into orbit (about 7.9 km/s); at about 11.2 km/s it escapes.
• Gravity and Weight: W = m × g – Earth pulls every object towards its centre. This pull is the weight of the object, a force that always points straight down. It is found with W = m × g, where g is about 9.8 N for every kg on Earth. Every object acts as if its whole weight pulls at one point, the centre of gravity.
• Handling Small Boats: Checks, Mooring, Knots and Direction – Handling a small boat means being ready before you leave and calm at the jetty. Check weather, fuel, engine, life jackets and ropes. Moor with bow and stern lines and fenders, and cast off one line at a time. Learn a few knots (cleat hitch, bowline, round turn and two half hitches, reef knot). Find direction with a compass: a bearing is the angle from North, clockwise, from 000 to 359 degrees.
• Heat Engines – A heat engine is a machine that turns heat into mechanical work. Fuel burns and releases heat Q = q × m, where q is the heat value (heat of combustion) of the fuel and m is its mass. Hot gas expands and pushes a piston or spins a turbine. A four-stroke engine repeats intake, compression, power and exhaust. Only part of the heat becomes useful work; the rest leaves as waste heat. Efficiency η = W ÷ Q × 100%. Engines also release CO₂ and other gases that harm the air and warm the planet.
• Heat Management in Buildings – Heat always flows from the warmer side to the cooler side of a wall. The flow through a wall is q = ΔT ÷ R, where R = L ÷ k adds up layer by layer. A thicker wall, or a layer of foam with very small k (it traps air), cuts heat loss. Sealing gaps stops convection, double glazing traps air, and light roofs reflect radiation. The same ideas keep a house cool in summer.
• Heat Transfer: Conduction, Convection and Radiation – Heat moves in three ways. In conduction, heat passes from particle to particle while the particles stay in place; the rate through a slab is H = kA(T₁ − T₂)/L, where k is thermal conductivity. In convection, the fluid itself moves: hot fluid is lighter and rises, cool fluid sinks. In radiation, heat travels as electromagnetic waves and needs no medium. A blackbody absorbs all radiation and is the best emitter. Its peak wavelength falls as temperature rises (Wien: λmT = b), and its total emitted power grows as T⁴ (Stefan: P = σAT⁴). Newton's law of cooling says a body cools at a rate proportional to its temperature excess over the surroundings.
• Heating Effect of Electric Current – When current flows through a resistor, electrical energy turns into heat. Joule's law: H = I²Rt, so heat grows with the square of current, with resistance and with time. Heaters, irons, toasters, bulbs and fuses all use this effect.
• History of Astronomy: How Our Picture of the Sky Changed – For thousands of years people thought Earth sat still at the centre and the sky turned round it. Careful watching of planets, then the telescope, showed a better picture: Earth and the other planets circle the Sun on ellipses, held by gravity. New ideas won because they explained more and could be tested.
• Household Appliances: Types, Power and Safe Use – Home appliances turn electrical energy into heat, motion, cold or light. The label shows voltage and power in watts (W). Energy used = power × time, counted in kilowatt-hours (units). Smart plugs and timers switch appliances by schedule or by phone. Safe use means dry hands, a matching socket, no overloaded boards, and regular cleaning and checking of wires.
• How Electricity Is Generated – Most electricity is made by spinning a magnet inside coils of wire (or coils near magnets). This is electromagnetic induction, and the machine is an alternator. A turbine does the spinning; steam, water or wind turns the turbine. Solar cells are different: light makes current directly. Transformers raise the voltage so the grid can carry power far with little loss.
• How Light Travels – Light comes from sources like the Sun or a lamp and travels in straight lines. We see an object when light from it enters our eyes. Transparent things let light through, translucent things let some through, and opaque things block it. Blocked light makes shadows; a wide source gives a dark umbra and a lighter penumbra. A pinhole camera makes an upside-down image. Light is very fast: about 300 000 km every second.
• How to Use a Multimeter – A multimeter is one meter that can measure voltage (V), current (A) and resistance (Ω). Choose the dial mode first. Voltage is measured in parallel (across the part), current in series (in the wire), and resistance with the power off and the part out of the circuit. Start with the biggest range and go down.
• Humidity: How Much Water Vapour Is in the Air – Air always carries some invisible water vapour. Absolute humidity is the mass of vapour in 1 m³ of air. Warm air can hold more vapour than cold air. Relative humidity is the vapour present divided by the most the air could hold, as a percent. When air cools to its dew point, it is full and the extra vapour turns into drops.
• Hydraulics: Water at Rest, Water on the Move, Water in Waves – Hydraulics is the study of water for building things like dams, canals and pipes. Still water pushes on a wall with pressure p = ρgh that grows with depth. Flowing water has a flow rate Q = A × v. In open channels, Manning's equation gives the speed from the shape, slope and roughness. Waves and currents add extra push on piers and sea walls.
• Image Communication – A picture is a grid of pixels, and each pixel is a number. To send a picture we send the numbers. Compression makes the list shorter, encryption hides it with a key, and a TV draws the picture again line by line.
• Images in Mirrors and Lenses – An image is the copy of an object that a mirror or lens makes by bouncing or bending light. A plane mirror gives a virtual, upright image as far behind the mirror as the object is in front. A concave mirror or convex lens can give a real, upside-down image (object far) or a bigger, upright virtual image (object close). A convex mirror or concave lens always gives a smaller, upright, virtual image. Real images can be caught on a screen; virtual images cannot.
• Inertia, First Law, Momentum, Second Law and Impulse – A body keeps its state of rest or uniform motion unless a net external force acts on it (first law). Inertia is this laziness to change, and mass measures it. Momentum p = mv. The rate of change of momentum equals the net force: F = dp/dt, which gives F = ma when mass is constant (second law). Impulse J = F × Δt = Δp; a longer stopping time means a smaller force.
• Installing Air-Conditioning: Piping, Testing and Maintenance – To install a split air conditioner, fix the indoor unit high on a wall and the outdoor unit on a firm stand with free air around it, join them with insulated copper refrigerant pipes and a drain that slopes down, then test for leaks with dry nitrogen, evacuate the air and moisture with a vacuum pump, open the valves and commission by checking the air temperature drop. Regular cleaning keeps it efficient.
• Installing Building Services – Installing services is managed through four goals: time, cost, quality and safety. A Gantt chart shows tasks as bars, and the critical path is the longest chain that decides the finish date. A cost estimate = sum of (quantity x unit rate), plus overheads, profit and a small contingency.
• Instruments and Navigation Methods at Sea – Basic instruments: compass (direction), log (speed), echo sounder (depth), clock and chronometer (time). Position is fixed by coastal navigation (bearings of landmarks), radio navigation (GNSS satellites, radar) or celestial navigation (sextant sights of Sun and stars). Two or more position lines that cross give a fix.
• Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.
• Interior Construction – Inside a room, every surface is built in layers: a base first, then a finish. Floors, walls and ceilings follow this rule. Doors and windows are openings held by a lintel. Stairs need the right step height and tread. Joinery means built-in wooden or board fittings like cupboards. Good construction management sets the right order of work.
• Interior Maintenance and Renovation – Rooms age: paint fades, cracks and damp appear, floors wear. Maintenance means regular care and early repair, which costs less than waiting. Renovation means improving an old room, in a fixed order: survey, plan and budget, strip out, pipes and wires, finishes, clean and handover. Choose between repair, renovation and rebuild by how much must change and what it costs.
• Internal Energy – Everything is made of tiny particles. They move (kinetic energy) and are held by forces between them (potential energy). The total of all these energies is the internal energy U. Heating a substance raises its internal energy: either the particles move faster (temperature rises, Q = mcΔT) or bonds are broken (state changes at constant temperature, Q = mL). Doing work on it, like rubbing or squashing, also raises U.
• Kepler's Laws of Planetary Motion – Kepler gave three rules for how planets move. 1) Each planet moves on an ellipse with the Sun at one focus. 2) The line from the Sun to the planet sweeps equal areas in equal times, so the planet moves faster when it is near the Sun. 3) The square of the time for one round (T²) is proportional to the cube of the semi-major axis (a³). The second law is really conservation of angular momentum. The third law follows from Newton's law of gravitation.
• Kinetic Theory of Gases: Pressure, Temperature and rms Speed – Kinetic theory explains gas behaviour by picturing a gas as tiny, fast, randomly moving molecules that bounce elastically and do not pull on each other. Each hit on a wall reverses the molecule's velocity and hands the wall momentum 2mvₓ. Adding the hits of all molecules gives the pressure P = ⅓ n m v̄² = ⅓ ρ v̄². Comparing with PV = N k T shows that the average kinetic energy of a molecule is (3/2) k T: temperature is a measure of the average kinetic energy of the molecules. The root mean square speed is v_rms = √(3RT/M) = √(3kT/m), so lighter gases move faster at the same temperature.
• Kirchhoff's Rules and the Wheatstone Bridge – Junction rule: at any junction, the sum of currents entering equals the sum leaving (ΣI = 0), because charge is conserved. Loop rule: around any closed loop, the algebraic sum of potential changes is zero (ΣΔV = 0), because energy is conserved. Sign rules: a resistor crossed along the current gives −IR; a cell crossed from − to + gives +ε. A Wheatstone bridge of four resistors P, Q, R, S is balanced (no galvanometer current) when P/Q = R/S; this lets us find an unknown resistance, as in the metre bridge.
• Lasers: How Stimulated Emission Makes a Beam of Light – LASER stands for Light Amplification by Stimulated Emission of Radiation. A pump lifts atoms to a higher energy level. When a photon of the right energy passes an excited atom, the atom gives out a second, identical photon. With more atoms excited than unexcited (population inversion) and mirrors at each end, the light builds up into a narrow, single-colour, coherent beam. X-rays are also high-energy light, made when fast electrons hit a metal target.
• Laws on Building Services – Work on building services is controlled by four groups of rules: safety and health laws (protect workers), building laws (strength and fire safety), services laws (licensed work on power, gas and water) and environmental laws (limit pollution and harmful gases). One job often falls under several of them. Names differ in each country, but the ideas are the same.
• Laws on Interior Fittings – Interior work is controlled by laws to protect people from fire, falls and bad air. Typical rules: fire grade of wall and ceiling finishes, a short distance to a safe exit, safe stair and handrail sizes, and limits on harmful gas from boards and glues with enough ventilation. Numbers differ by country; the local building code and fire rules decide. An inspector checks the work before use.
• LC Oscillations – An LC circuit is a capacitor (C) joined to a coil (L). A charged capacitor pushes current through the coil; the coil keeps the current going and charges the capacitor the other way. Energy swings between the electric field of the capacitor and the magnetic field of the coil. With no resistance the swing never stops. Its period is T = 2π√(LC) (Thomson formula) and its frequency is f = 1 / (2π√(LC)). Resistance makes the oscillations damped; a generator with a transistor tops up energy to keep them going.
• Levers: How a Small Push Lifts a Big Load – A lever is a stiff bar that turns about a fixed point called the fulcrum. It balances when load × load arm = effort × effort arm (the law of moments). A longer effort arm means less effort is needed. By where the fulcrum, load and effort sit, levers are Class 1, 2 or 3.
• Light and Colour: Mixing, Seeing and Energy of Light – White light is a mix of colours (red to violet). Lights add: red + green + blue make white (additive mixing, used by screens). Paints take away: cyan + magenta + yellow make near-black (subtractive mixing). An object has a colour because it reflects some colours and absorbs the rest. Eyes use three kinds of cone cells. Light colour tells its energy: E = hf, blue photons carry more energy than red.
• Light and Heat: Properties and Everyday Uses – Light travels in straight lines, makes shadows, bounces off mirrors (angle in = angle out) and carries energy. Dark surfaces take in more of it and get hotter. Heat is energy that always flows from a hotter thing to a colder thing. It moves by conduction, convection and radiation.
• Light Sources: Sun, Lamps, Optical Fibres and Lasers – A light source makes its own light. Natural sources are the Sun, stars, lightning and fireflies. Artificial sources are lamps: a filament bulb wastes most energy as heat, a fluorescent tube is better, an LED is best. The colour rendering index (CRI, 0 to 100) tells how truly a lamp shows colours. An optical fibre guides light by total internal reflection. A laser gives a thin, straight, single-colour beam.
• Light: Reflected, Absorbed or Transmitted – Light travels in straight lines at about 3 × 10⁸ m/s and needs no material to travel through. When it meets an object it can be reflected (bounce back), absorbed (taken in, warming the object) or transmitted (pass through). On a smooth surface the angle of incidence equals the angle of reflection. When light enters glass or water it slows and bends (refraction). A prism splits white light into a spectrum, and an object's colour is the colour it reflects.
• Living Environment and Facilities: Heat, Air and Light in a Building – Comfort in a room comes from three things. The natural environment (sun, wind, temperature outside) is the source. The indoor environment (temperature, light, fresh air, sound) is what we feel. Fluid and thermal mechanics explain how air and heat move: warm air rises, wind pushes air through openings, and heat flows through walls at the rate Q = U × A × ΔT.
• Lorentz Force, Torque on a Loop and the Moving Coil Galvanometer – A charge q moving with velocity v feels F = q(E + v × B), the Lorentz force. The magnetic part qvB sinθ is at right angles to v, so it bends the path into a circle (r = mv/qB) without changing speed. A wire feels F = IL × B. Parallel wires attract if the currents are in the same direction: F/L = μ₀I₁I₂/2πd. A loop in a field feels a torque τ = m × B with magnetic moment m = NIA, so a loop acts as a magnetic dipole. A moving coil galvanometer uses this torque: its deflection φ = (NAB/k)I. A small shunt turns it into an ammeter; a large series resistance turns it into a voltmeter.
• LR Circuits: How an Inductor Slows a Current – An inductor is a coil that opposes any change in the current through it by making a back emf ε_L = −L dI/dt (L in henry). In a circuit with a battery ε, a resistor R and an inductor L in series, the current cannot jump. When the switch closes it grows as I = (ε/R)(1 − e^(−t/τ)), where the time constant τ = L/R. At t = τ the current is about 63% of its final value ε/R, and after about 5τ it is practically steady; then the inductor acts like a plain wire. If the battery is removed and the loop is closed through R, the current decays as I = I₀ e^(−t/τ), falling to 37% after one τ. The energy that keeps it going was stored in the inductor's magnetic field, U = ½LI². Kirchhoff's loop rule with the inductor gives ε − IR − L dI/dt = 0.
• Machine Design: Fasteners, Shafts and Gears – A machine is built from small standard parts called machine elements. Fasteners (bolts, nuts, screws, rivets, pins) join parts. Shaft elements (shafts, keys, couplings, bearings) carry turning motion. Gears, belts and chains pass motion on; gear ratio = teeth on driven gear / teeth on driver gear.
• Machines, Boilers and Cooling Equipment in a Food Factory – A food factory uses machines to move, cut, mix, cook, cool and pack food faster, more evenly and more cleanly than hands can. A boiler heats water into steam to cook and clean. Cooling equipment (refrigeration) removes heat so food passes quickly through the danger zone. Safe use means guards, clean machines, trained workers and regular checks.
• Magnetic Effect of Electric Current – A wire carrying electric current makes a magnetic field around itself. The field forms circles around a straight wire, becomes nearly straight at the centre of a loop, and is uniform inside a solenoid, which then acts like a bar magnet.
• Magnetic Field due to a Current: Biot-Savart Law and Ampere's Law – A current makes a magnetic field around it (Oersted, 1820). The Biot-Savart law gives the field of a tiny piece of wire: dB = (μ₀/4π)·I dl sinθ / r². Adding all pieces of a circular loop gives B = μ₀NI / 2R at the centre and μ₀NIR² / 2(R² + x²)^{3/2} on the axis. Ampere's circuital law ∮B·dl = μ₀I gives B = μ₀I / 2πr for a long straight wire. A long solenoid has a strong, uniform field B = μ₀nI inside and almost none outside.
• Magnetism and Matter – A bar magnet behaves like a solenoid: tiny current loops of electrons inside it line up. Its field on the axis (2m/r³ form) is twice the field on the equator at the same distance, and points the other way. In a uniform field a magnet feels a torque τ = m × B that turns it to line up with B. Field lines are closed loops that never cross. Materials react differently: diamagnetic ones are pushed out of a field (χ small and negative), paramagnetic ones are pulled in weakly (χ small and positive), ferromagnetic ones are pulled in strongly (χ very large). Magnetisation M is the magnetic moment per unit volume; B = μ₀(H + M), χ = M/H, μᵣ = 1 + χ. Heating reduces magnetism: paramagnets follow Curie law χ = C/T, and a ferromagnet turns paramagnetic above its Curie temperature.
• Magnetism: Magnets and the Compass – A magnet pulls iron, nickel and cobalt. Its pull is strongest at its two ends, the north (N) and south (S) poles. Like poles repel and unlike poles attract. Around a magnet is a magnetic field, drawn as lines from N to S; a compass needle lines up with it. Inside a magnet, tiny atomic magnets all point the same way. The Earth is a giant magnet, so a compass points north. An electric current in a coil makes an electromagnet.
• Manufacturing Engineering Technology: How Things Get Made – Manufacturing engineering technology is about turning raw materials into useful products safely, accurately and at a fair cost. A factory is a system: inputs (materials, energy, people, information) go through processes (cutting, forming, joining, finishing) to give outputs, with feedback to improve. Engineers plan the process steps and times, choose materials by their properties, run machine tools and CNC machines, automate with control systems (sensors, PLCs, pneumatics, hydraulics, robots), and check quality against standards so every product meets the customer's specification. It is also a business, with product development, marketing and costs to manage.
• Marine Leisure – Marine leisure means fun and sport on the sea: sailing, canoeing, kayaking, surfing and more. Safe fun needs three things: know the sea rules, read wind, waves and tide, and use the right kit. A sail turns wind into push; a paddle pushes water back so the boat moves forward.
• Mass and Weight – Mass is the amount of matter in an object. It stays the same everywhere and is measured in kilograms (kg) with a pan balance. Weight is the pull of gravity on that mass. It is a force, measured in newtons (N) with a spring scale, and it changes from world to world: W = m × g.
• Mass Spectrometer and Cyclotron – A magnetic force is always sideways to the motion, so a charge in a magnetic field moves in a circle of radius r = mv/qB. A mass spectrometer first speeds ions up with a voltage V, then bends them in a field B; heavier ions make bigger circles (r = (1/B)√(2mV/q)), so masses can be told apart. A cyclotron keeps a particle spinning between two D-shaped boxes and pushes it each time it crosses the gap. The time for each half-turn is the same, so the particle gains energy and moves to bigger circles (f = qB/2πm).
• Matter Waves and the de Broglie Relation – Light behaves like a wave and a particle. In 1924 Louis de Broglie said matter does the same: every moving particle has a wave with wavelength λ = h/p = h/mv. For a body of kinetic energy K, λ = h/√(2mK); for an electron accelerated through V volts, λ = 1.227/√V nm. Everyday objects have far too tiny a λ to notice, but electrons have λ about the size of atoms.
• Mean Free Path of Gas Molecules – Gas molecules are fast, yet a smell spreads slowly because each molecule keeps bumping into others and changing direction. The average distance a molecule travels between two collisions is its mean free path λ. A molecule of diameter d hits any other molecule whose centre comes within d of its path, so it sweeps a collision tube of cross-section πd². Counting molecules in that tube gives λ = 1/(√2 n π d²) = k_BT/(√2 π d² P). The mean free path is shorter when the gas is crowded (large n or P) or the molecules are big, and longer at low pressure and high temperature. For air at room conditions λ is about 0.1 micrometre.
• Measurement and Units: How We Measure Anything – To measure something is to compare it with a fixed amount called a unit. Every measurement has a number and a unit. Scientists everywhere use the SI system, with seven base units such as the metre, kilogram and second. Prefixes like kilo (×1000), centi (÷100) and milli (÷1000) make units bigger or smaller. A good measurement starts at zero, is read with the eye straight above the mark, and is only as accurate as the smallest division (least count). Rounded values hide a small range, given by upper and lower bounds.
• Mechanical Efficiency: How Much Work Is Really Useful? – No real machine turns all the work you put in into useful work. Some is wasted on friction and on moving the machine parts. Efficiency η = useful work ÷ total work × 100%. It is always less than 100%. Oiling and using lighter parts raise it.
• Mechanical Engineering: How Machines Are Designed and Made – Mechanical engineering is the branch of engineering that designs, makes and looks after machines: anything with moving parts that uses forces and energy, from a bicycle to a jet engine. Mechanical engineers use physics (forces, motion, energy, heat), materials science and maths. Key ideas: mechanisms change motion and force (gears, levers, cranks), energy is converted (heat to motion in engines, electricity to motion in motors), parts must be strong enough (stress, bending, safety), and parts are made by machining, fitting and assembly to exact sizes with tolerances. Mechatronics adds electronics, sensors and computer control.
• Mechanical Properties of Solids: Stress, Strain and Elasticity – When you pull, push or twist a solid, it changes shape a little. If it comes back when you let go, it is elastic. Stress is the restoring force per area (F/A). Strain is the fractional change in size (like ΔL/L). Up to the elastic limit, stress is proportional to strain (Hooke's law), and the ratio is a modulus: Young's modulus Y for stretching, bulk modulus B for squeezing all round, shear modulus G for sliding faces. A stretched wire also gets thinner (Poisson's ratio), and it stores energy ½ × stress × strain × volume.
• Mechanics of Members: Materials, Sections and Deflection – A structural member (bar, beam, column) is judged by three things. The material: stress σ = F/A, strain ε = ΔL/L and stiffness E = σ/ε. The section: area A, second moment of area I = bh³/12 and section modulus Z = I/y. The deformation: a bar stretches ΔL = FL/(AE); a simply supported beam with a central load sags δ = PL³/(48EI). Depth h matters most: doubling it makes I eight times bigger and the sag eight times smaller.
• Mechanisms: How Machines Change Motion and Force – A mechanism takes an input motion and force and gives a different output motion and force. There are four kinds of motion: rotary, linear, reciprocating and oscillating. Levers turn on a fulcrum; mechanical advantage (MA) = load ÷ effort. Gears and pulleys pass on turning motion; gear ratio = driven teeth ÷ driver teeth, and output speed = input speed ÷ gear ratio. Meshing gears turn opposite ways; a belt keeps the same direction. Cams, cranks and sliders, and rack and pinion change rotary motion into linear or reciprocating motion. Mechanisms trade speed for force: you never get more work out than you put in.
• Medical Physics: Ultrasound, X-ray, CT and Radiation Safety – Ultrasound sends sound pulses into the body and times the echoes: depth = speed × time ÷ 2. X-rays pass through the body and bone stops more of them, making a shadow picture. CT joins many X-ray views from all angles into slices. X-rays are ionising, so we cut the dose with short time, long distance and a shield. Ultrasound uses sound and is not ionising.
• Methods of Astronomy: How We Study Faraway Stars – Astronomers cannot touch stars, so they study the waves that reach Earth: light, radio, infrared, ultraviolet, X-rays and gamma rays. An optical telescope uses a big mirror or lens to collect light. A radio telescope uses a dish and works through clouds and in daytime. The air blocks X-rays, ultraviolet and most infrared, so those are watched from space telescopes. A wider mirror collects more light, so it shows fainter objects.
• Microwave Circuits, Antennas and Feeder Lines – An antenna changes an electric signal into a radio wave and back. Its size is tied to the wavelength: a half-wave dipole is λ/2 long. Antennas differ in their radiation pattern: whip and dipole spread power around, Yagi and dish aim it in one direction (more gain). A feeder line (coax, twin-lead, waveguide) carries power between radio and antenna. Microwave circuits (waveguide, stripline, resonators, couplers, circulators) handle signals of 1 to 30 GHz and above.
• Modern Physics: Quantum Theory and Relativity – Modern physics began around 1900, when classical physics failed for the very small and the very fast. Quantum theory says energy comes in packets: a photon has E = hf. The photoelectric effect shows light acts as particles, while interference shows particles such as electrons act as waves (λ = h/p). Special relativity says the speed of light is the same for all observers, so moving clocks run slow (t = γt₀), moving lengths shrink, and mass is energy (E = mc²). These ideas power lasers, solar cells, electron microscopes, GPS and nuclear energy.
• Moment of Inertia, Radius of Gyration and Rotational Motion – Every idea of straight-line motion has a turning twin: θ for x, ω for v, α for a, I for m, τ for F, L = Iω for p. Moment of inertia I = Σmr² tells how hard it is to change a body's spin; it grows fast when mass sits far from the axis. Radius of gyration k is the distance at which all mass could sit to give the same I: I = Mk². Standard values: ring MR², disc ½MR², solid sphere ⅖MR², rod about centre ML²/12. With constant α: ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ, and τ = Iα.
• Motion in a Straight Line (Class 11) – To describe motion we first choose a frame of reference: an origin, a direction and a clock. Position x changes with time t. Velocity v = dx/dt is the slope of the x–t graph; acceleration a = dv/dt is the slope of the v–t graph, and the area under the v–t graph is the displacement. For constant a: v = u + at, x = ut + ½at², v² = u² + 2as.
• Motion in a Vertical Circle – A ball on a string moving in a vertical circle speeds up at the bottom and slows down at the top, because gravity does work on it. At every point the net force towards the centre must be mv²/r. At the bottom T = mg + mv²/r (largest); at the top T = mv²/r − mg (smallest). The string stays tight at the top only if v_top ≥ √(gr). Using energy conservation, this needs u ≥ √(5gr) at the bottom.
• Motion: Distance, Speed, Velocity, Acceleration and Graphs – An object is in motion when its position changes with time. Distance is the full path length (a scalar); displacement is the straight gap from start to finish with a direction (a vector). Speed = distance ÷ time; velocity = displacement ÷ time. Acceleration = change in velocity ÷ time. The slope of an s–t graph gives velocity, the slope of a v–t graph gives acceleration, and the area under a v–t graph gives the distance. For uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
• Navigation Methods: How Boats Pass Each Other Safely – To avoid collisions, boats follow shared rules. In open water: meeting head-on, both turn right; in a crossing, the boat that has the other on its right gives way; an overtaking boat keeps clear. In harbours, go slowly and keep right in the channel. In designated sea areas follow the traffic lanes. On rivers and lakes keep to your right bank and follow local rules.
• New Materials: Nanomaterials, Superconductors and Functional Materials – Nanomaterials have pieces about 1 to 100 nm across. Splitting a solid into tiny pieces keeps the volume but makes the surface much larger, so properties change. A superconductor loses all electrical resistance below a critical temperature and pushes magnetic field out, so a magnet floats above it. Functional materials change in a useful way when heat, light, pressure or electricity acts on them.
• Newton's Universal Law of Gravitation – Every mass in the universe pulls every other mass. The pull between two point masses m₁ and m₂ a distance r apart is F = G m₁ m₂ / r². It acts along the line joining them. The two bodies pull each other with equal and opposite forces. G = 6.67 × 10⁻¹¹ N m² kg⁻² is the same everywhere, so it is called the universal gravitational constant. When many masses pull one body, the forces add as vectors (superposition).
• Non-Ionising Imaging – Ultrasound, endoscopes and MRI let doctors see inside the body without X-rays or gamma rays, so there is no ionisation damage. Ultrasound sends short pulses (1–15 MHz) from a piezoelectric probe; echoes return from boundaries. Depth = c t ÷ 2 and the fraction reflected depends on acoustic impedance Z = ρc: R = (Z₂ − Z₁)² ÷ (Z₂ + Z₁)². Gel removes air, which would reflect almost everything. An endoscope uses optical fibres: light stays in the core by total internal reflection. An incoherent bundle carries light in; a coherent bundle carries the image out. In MRI a strong magnetic field lines up hydrogen nuclei, which precess at the Larmor frequency; a radio pulse tips them, and the radio signal they give out as they relax is used to build a detailed image of soft tissue.
• Nuclear Fission and Fusion – Fission is the splitting of a large, unstable nucleus such as uranium-235 or plutonium-239. A slow neutron is absorbed, the nucleus splits into two smaller nuclei and releases 2 or 3 neutrons, gamma rays and a lot of energy. The new neutrons can split more nuclei: a chain reaction. In a nuclear reactor, a moderator slows neutrons and control rods absorb some, so the chain reaction stays steady. Fusion is the joining of two light nuclei, such as hydrogen, to make a heavier nucleus, such as helium. Some mass turns into energy. Fusion powers the Sun and stars, but it needs very high temperature and pressure.
• Nuclear Fusion – In nuclear fusion, light nuclei join to make a heavier nucleus and release energy. In the Sun's core, at about 15 million °C, four hydrogen nuclei join in steps (the proton–proton chain) to make one helium nucleus. The helium weighs about 0.7% less than the four hydrogens; that missing mass becomes energy by E = mc². Gravity squeezing in and fusion heat pushing out keep a star steady for billions of years.
• Nuclear Physics: the Nucleus and Radioactivity – The nucleus holds protons (Z) and neutrons (N); mass number A = Z + N. Isotopes have the same Z but different N. Unstable nuclei decay at random: alpha decay removes 2 protons and 2 neutrons (A − 4, Z − 2), beta-minus decay turns a neutron into a proton and an electron (Z + 1), and gamma is energy only. Half-life is the time for half the nuclei in a sample to decay.
• Nuclei: Size, Nuclear Force, Binding Energy, Fission and Fusion – A nucleus is made of Z protons and N neutrons (A = Z + N nucleons). Its radius is R = R₀A^(1/3) with R₀ ≈ 1.2 fm, so every nucleus has almost the same huge density. A very strong, short-range nuclear force holds the nucleons together. The nucleus weighs a little less than its loose parts; this mass defect Δm is the binding energy, E = Δm c² (1 u = 931.5 MeV). Binding energy per nucleon is highest near iron (A ≈ 56), so heavy nuclei give energy when they split (fission) and light nuclei give energy when they join (fusion).
• Ocean Engineering Practice: Floating, Water Pressure, Mooring and Rust – Four ideas help build things for the sea. A block floats if its density is below sea water (about 1025 kg/m³). Pressure grows with depth: P = P0 + ρgh, about +100 kPa every 10 m. A moored boat needs rope at least 3 times the depth. A zinc block rusts first, so the steel is saved.
• Ohm's Law – At constant temperature, the current through a conductor is directly proportional to the potential difference across it: V = I × R. R is the resistance, measured in ohms (Ω); 1 Ω = 1 V/1 A. The V–I graph of an ohmic conductor is a straight line through the origin.
• Ohm's Law, Resistivity and Effect of Temperature – Using drift velocity, V = IR with R = ml/(ne²τA) = ρl/A. Resistivity ρ = m/(ne²τ) depends only on the material and temperature; conductivity σ = 1/ρ. Ohm's law in vector form is j = σE. Metals, wires and resistors give a straight V–I line (ohmic); bulbs, diodes and devices like GaAs give curved or one-way graphs (non-ohmic). For metals ρ rises with temperature: ρT = ρ0[1 + α(T − T0)]; alloys like nichrome change very little; semiconductors get lower ρ when hot.
• Operating Small Boats: Basic and Advanced Handling – A boat has no brakes. It turns around its middle when the rudder is turned, and it keeps gliding after the throttle is cut. Wind and current push it sideways. Basic handling is steering, speed control, stopping and keeping a lookout. Advanced handling covers person overboard, anchoring, rough weather, narrow channels and poor visibility. Always go slowly near people and other boats.
• Operational Amplifier Configurations: Inverting, Non-Inverting and Summing – An op-amp with negative feedback gives a fixed, useful gain set only by resistors. Inverting amplifier: G = −Rf/Rin (output flipped). Non-inverting amplifier: G = 1 + Rf/Rin (same way up). Summing amplifier: Vout = −Rf(V1/R1 + V2/R2 + …), used in audio mixers and digital-to-analogue converters. Real op-amps have finite gain, finite bandwidth (gain × bandwidth ≈ constant) and their output saturates near the supply voltages.
• Optical Instruments: Microscopes and Telescopes – How big a thing looks depends on the angle it makes at the eye. A simple microscope (one convex lens) gives m = 1 + D/f (image at D) or D/f (image at infinity). A compound microscope uses a short-focus objective and an eyepiece: m = mₒ × mₑ ≈ (L/fₒ)(D/fₑ). An astronomical telescope uses a long-focus objective and short-focus eyepiece: m = fₒ/fₑ in normal adjustment, with tube length fₒ + fₑ. Reflecting telescopes use a concave mirror as objective.
• Optics Experiments: See How Light Behaves – Five simple experiments show how light behaves. It travels in straight lines, bounces off a mirror with angle in = angle out, bends when it enters glass, is gathered by a convex lens at the focus, and splits into colours in a prism.
• Oscillations of a Spring and a Simple Pendulum – A block on a spring feels a pull back F = −kx, where k is the force constant (stiffness). It does SHM with T = 2π√(m/k). A simple pendulum, for small swings, feels a pull back mg sinθ ≈ mgθ and does SHM with T = 2π√(L/g). The pendulum’s period does not depend on the bob’s mass or (for small swings) on the amplitude.
• Overview of Air Conditioning – Air conditioning controls temperature, humidity, cleanliness and air movement. Systems can be all-air, air-water or refrigerant-based. The cooling load is the heat that must be removed (sun, people, lights, hot walls and fresh air); the heating load is the heat that must be added in cold weather. Moist air is described by dry-bulb temperature, relative humidity and dew point.
• Overview of Building Construction – Construction turns a drawing into a real building in a fixed order: plan, site set-up, foundation, frame, finishing. Safety management finds hazards before work starts and controls them. After handover, regular maintenance keeps the building safe and useful for decades.
• Overview of Building Structures – A building structure carries loads (its own weight, people, wind, earthquakes) safely down to the ground. The load travels roof, beam, column, footing, ground. Two common systems are wall structures and frame structures. Bracing resists sideways wind, and a wide footing spreads the load so the ground does not sink.
• Overview of Ships – A ship is a floating steel building. It floats because the water it pushes aside weighs as much as the ship (Archimedes' principle). Ships have a hull (bow, stern, keel, deck), come in many types (cargo, tanker, fishing, passenger) and follow international safety rules such as the load line.
• Overweight and Weightlessness – A scale shows the push N it gives you, not your true weight. In a lift with upward acceleration a, N = m(g + a): you feel heavier (overweight). With downward acceleration, N = m(g - a): you feel lighter. In free fall a = g, so N = 0 and you are weightless. Gravity has not gone away; you and the floor are falling together.
• Particle Physics: Quarks, Leptons and the Standard Model – Particle physics studies the smallest building blocks of matter. Protons and neutrons are made of quarks. Electrons belong to a family called leptons. Every particle has an antiparticle. Particles feel four forces, and three of them are carried by messenger particles called bosons. All of this together is called the Standard Model.
• Perfect Gas Equation PV = nRT and Work in Compressing a Gas – A gas is made of countless tiny molecules flying about. Their hits on the walls make pressure. For a low-density gas, three simple laws hold: at fixed temperature, P × V stays constant (Boyle); at fixed pressure, V grows in step with kelvin temperature (Charles); at the same P and T, equal volumes hold equal numbers of molecules (Avogadro). Put together they give the perfect gas equation PV = nRT = N k T. One mole holds Avogadro's number, 6.022 × 10²³, of particles. Pushing a piston in does work on the gas; the work equals the area under the P–V graph, and at fixed temperature W = nRT ln(V₁/V₂).
• Photoelectric Effect and Einstein's Equation – When light of high enough frequency falls on a metal, electrons jump out at once. Light comes in packets called photons, each with energy E = hν. One photon gives all its energy to one electron: hν = φ + KEmax, where φ is the work function. Below the threshold frequency ν₀ = φ/h no electron comes out, however bright the light.
• Physics and Human Understanding: Cosmology, Galileo, Relativity and Quanta – For thousands of years people thought Earth sat still in the middle of the sky. Careful watching, the telescope and experiments changed that. Galileo showed that we should test ideas with measurement. Later, Einstein showed that time and space depend on speed, and Planck showed that energy comes in small packets called quanta. Scientists from many countries built this story together.
• Physics and Society: Steam, Electricity, Chips and Nuclear Power – New physics ideas changed how people live. The steam engine turned heat into movement. The generator turned movement into electricity. Microchips shrank switches so a phone can hold billions of them. Nuclear fission turns a little mass into a lot of heat.
• Physics as a Natural Science: Phenomena and Links – Physics is the science that studies nature: how things move, heat, light, sound, electricity and magnets behave. Anything that happens in nature is a phenomenon. Physicists watch phenomena, find the rule behind them and write the rule with maths. Physics is connected to chemistry, biology, geography and technology, because their stories also use the same rules.
• Physics in Civic Life: Energy, Lasers, Fibre and Spaceflight – Physics runs through public life. Energy used is power times time (1 kWh = 1 unit on the bill). Light bounces along glass fibre to carry internet and phone calls. A laser beam is thin, straight and one colour. A rocket pushes gas down and is pushed up; a satellite is a body always falling but moving sideways fast enough to miss Earth.
• Physics of the Ear – The ear turns tiny pressure waves into nerve signals. The eardrum vibrates, three small bones (ossicles) act as a lever, and because the eardrum is much bigger than the oval window the pressure rises about 20 times. In the cochlea the basilar membrane vibrates at a place that depends on frequency: high frequencies near the base, low near the apex. Hair cells there send signals to the brain. A healthy young ear hears about 20 Hz to 20 kHz and is most sensitive at 2–5 kHz. The threshold of hearing at 1 kHz is I₀ = 1.0 × 10⁻¹² W m⁻². Intensity level is L = 10 log₁₀(I/I₀) dB. Hearing gets worse with age (mostly high frequencies) and with loud noise (a dip near 4 kHz).
• Physics of the Eye: How We See and How Lenses Fix Vision – The eye is a converging lens system: the cornea does most of the bending and the lens fine-tunes the focus (accommodation). Light lands on the retina, where rods give sensitive night vision with poor detail and three types of cones give colour and fine detail. A normal eye has a near point of about 25 cm and a far point at infinity. Myopia (eye too long) is corrected with a diverging lens of f = −far point; hypermetropia (eye too short) with a converging lens; astigmatism with a cylindrical lens. Lens power P = 1/f in dioptres (D), and powers of thin lenses in contact add.
• Physics Practicum: Measurement, Error Bounds and Review – In a practicum we measure some quantities directly (length, time) and get others indirectly from a formula (g = 4π²L/T²). Every reading has an error bound, set by the instrument and by repeating. Errors combine: relative errors add for products and quotients, and powers multiply the error (T² counts twice). We test a hypothesis by plotting a straight-line graph (T² against L) and checking if the result agrees with the expected value within the error. The same habits help to review the whole physics course.
• Piston Pump: Air Pressure at Work – A piston pump lifts water with the help of air pressure. Pulling the piston up lowers the pressure below it, so the air pressure on the well water pushes water up through the inlet valve. Pushing the piston down closes that valve and moves the water above the piston. The next upstroke lifts it out of the spout. Air pressure alone can push water up only about 10 m.
• Planning Building Services – Building services (water, drainage, air conditioning, power, fire safety, lifts) must be planned together with the building. Planners choose each system, draw its route, and reserve space in shafts, ceiling voids and machine rooms. Simple checks like headroom = floor height - beam - duct - gap and drain slope = drop / length show whether everything fits.
• Pneumatics and Hydraulics – Hydraulic systems use a liquid (usually oil) and pneumatic systems use compressed air to carry force through pipes. A pump or compressor makes pressure p = F/A, valves choose the path, and a cylinder turns the pressure back into a push: F = p x A. Liquid hardly squeezes, so hydraulics is strong and steady; air can be squeezed, so pneumatics is fast, clean and springy.
• Polarisation of Light – Light is a transverse wave: its electric field shakes at right angles to the direction it travels. In ordinary light the shaking happens in all directions. A polaroid lets through only one direction, so the light becomes plane polarised and half as bright. A second polaroid at angle θ lets through I = I₀cos²θ (Malus's law). Polarisation proves light is transverse and is used in sunglasses, LCD screens, cameras and 3D films.
• Potential Energy, Spring Energy and Conservative Forces – Potential energy U is energy stored because of position or shape. Near the Earth U = mgh; in a stretched or squeezed spring U = ½kx². A force is conservative if its work depends only on the start and end points, not on the path (gravity, spring force). Then F = −dU/dx and mechanical energy K + U stays constant. Friction and air drag are non-conservative: they turn mechanical energy into heat.
• Power Distribution and Electrical Work in Ships and Factories – Distribution carries electricity from the source (generator or grid) to many loads. A main switchboard receives the three-phase supply and sends it through feeders, each with a breaker or fuse. Transformers give the right voltage (for example 440 V down to 230 V). Ships and factories use the same ideas: separate circuits for power and lighting, protection against overload and short circuit, and an earth wire. Electrical work means installing, testing and repairing this system safely.
• Power Electronics: Devices, Power Conversion and Converter Circuits – Power electronics changes electrical power from one form to another using switches that are either fully ON or fully OFF, so little energy is wasted. Rectifiers change AC to DC, choppers change DC to a different DC level (output = duty cycle × input), inverters change DC to AC. Common devices: diode, thyristor (SCR), power MOSFET and IGBT.
• Power Grid and High-Voltage Transmission – A power line wastes energy as heat: loss = I²R. For a fixed power P = V × I, raising the voltage lowers the current, so the loss falls with the square of the voltage. Transformers step the voltage up at the power station and down near homes. The grid is a network of lines (a graph) with many routes, so supply continues if one line fails.
• Power Supply, Oscillator, Pulse and Modulation Circuits – A power supply turns AC into steady DC: a rectifier flips the negative half, a capacitor filter smooths the bumps and a regulator makes it flat. An oscillator makes a wave by itself using feedback. A pulse circuit switches ON and OFF with a set duty cycle. Modulation puts a message on a high-frequency carrier, and demodulation takes it back.
• Practical Communication: Sending, Receiving and Operating – In Morse code a dot lasts 1 unit and a dash 3 units; letters are patterns of both. To send, you key the transmitter on and off; to receive, you listen or watch and write down the pattern. Good operating follows a fixed order (call sign, "this is", message, "over"), uses clear spelling with the phonetic alphabet, keeps distress calls on the proper channel and records every contact in a log.
• Practice of Agricultural Civil Construction: Build a Farm Road – Practice means doing a whole small job. Here the job is a 100 m farm road, 3 m wide, with a side drain. We set out the line with pegs and string, do the earthwork part by part, spread and press a 0.15 m gravel layer, check level and compaction, keep the site safe, and work out the gravel volume (45 m³), the days needed (worker-days ÷ workers) and the cost (volume × price).
• Practice of Civil Design: Sizing a Farm Channel – Design means turning a need into a drawing with numbers. We follow six steps: know the need, study the site, choose a shape, calculate the size, add a safety margin, then draw it and work out the cost. As a practice job we size an open channel with Q = A × v.
• Pressure in Fluids and Pascal's Law – A fluid (liquid or gas) pushes on every surface it touches. Pressure is this normal force per area, P = F/A. Because of gravity, the fluid above a point has weight, so pressure grows with depth: P = P₀ + ρgh. Points at the same depth in a still liquid have the same pressure, whatever the vessel's shape. Pascal's law says an extra pressure applied to an enclosed fluid reaches every point equally. The hydraulic lift and brakes use this: a small force on a small piston becomes a big force on a big piston, F = f × A/a.
• Pressure: Force on Each Square Metre – Pressure is the force acting on each unit of area: P = F ÷ A. Its SI unit is the pascal (1 Pa = 1 N/m²). The same force on a smaller area gives a bigger pressure, which is why pins, knives and nails are sharp, and why tractors and camels have wide feet or tyres. Liquids press in all directions, and their pressure grows with depth (P = ρgh). Gases press because their particles keep hitting the walls; squeezing a gas or heating it raises its pressure. The air around us presses with about 101 kPa. Blood pressure is the pressure of blood on the walls of the arteries.
• Principles of the Car – A petrol engine burns fuel in a four-stroke cycle (intake, compression, power, exhaust). The power goes through the clutch, gearbox, drive shaft and differential to the wheels. Gears trade speed for push. A car speeds up until the driving force equals drag. Brakes use friction to turn motion into heat.
• Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
• Project Learning in Agricultural Civil Construction – Project learning means learning by doing one real, small job from start to end. In farm construction, a team finds a problem (a muddy path), plans it, builds it safely, checks the result, then shares a report and improves. The cycle is: problem, plan, build, check, share.
• Projectile Motion and Uniform Circular Motion (Class 11) – In a plane, r = r₀ + v₀t + ½at² and v = v₀ + at, applied separately along x and y. A projectile has constant horizontal velocity u cos θ and a vertical velocity that changes by g each second, so its path is a parabola: y = x tan θ − gx²/(2u²cos²θ). T = 2u sin θ/g, H = u² sin²θ/2g, R = u² sin 2θ/g (maximum at 45°). In uniform circular motion speed is constant but the velocity turns, giving a centripetal acceleration a = v²/r = ω²r towards the centre.
• Properties of Matter – Matter is anything that has mass and takes up space. Some properties, like mass and volume, depend on how much you have. Others, called characteristic properties, are the same for any amount of a pure substance and help identify it: density (mass ÷ volume), melting point, boiling point and solubility. In a physical change (melting, boiling, dissolving) no new substance forms and the total mass stays the same. In a chemical change a new substance forms. Particles are close in solids and liquids and far apart in gases, which is why gases have very low density; moving particles also explain diffusion and Brownian motion.
• Properties of Water and Soil – Water has a fixed density (1 litre weighs 1 kg) and its pressure grows with depth (about 10 kPa per metre). Soil is solid grains with pores filled by water and air. The size of the grains (sand, silt, clay) decides how much water soil holds, how fast water drains and how high water climbs by capillary action.
• Pulleys: How Ropes Make Lifting Easier – A pulley is a grooved wheel that guides a rope. A fixed pulley only changes the direction of the pull. A movable pulley and a pulley block share the load between several rope strands, so effort = load ÷ number of strands, but you pull more rope. The wheel and axle and the inclined plane also trade a longer distance for a smaller force.
• Quality of Energy: Why Energy Spreads Out and Loses Value – Energy is never destroyed, but its quality can fall. Concentrated energy, like the chemical energy in fuel or heat at a high temperature, can do much work. When energy spreads out as warm air, it is still there but can do very little. In every conversion some energy goes to low-quality heat, so efficiency is below 100%.
• Quantum Physics Basics: Double Slit, Superposition and Measurement – Tiny things like photons and electrons are "quantum objects". Each one is detected as a single dot (like a particle), but where the dots land follows a wave of probability, which makes stripes. Before we measure, a quantum object can be in a superposition of possibilities. If we find out which path it took, the stripes disappear. Quantum computers and quantum cryptography use these rules.
• Quantum Tunnelling: Passing Through a Barrier – In quantum physics a particle is described by a wave. When this wave meets a barrier, it does not stop sharply. It shrinks inside the barrier but is not zero, so a small part comes out on the other side. This leak is called tunnelling. The chance falls very fast as the barrier gets thicker or higher: T ≈ e^(−2κL). Tunnelling powers the Sun, flash memory and the scanning tunnelling microscope.
• Radio Communication Equipment – A radio transmitter has an oscillator (makes the carrier), a modulator (adds the message) and a power amplifier, then an antenna. A receiver has an antenna, a tuner, a detector and a speaker; a superheterodyne receiver first mixes the signal down to a fixed intermediate frequency. Microwave links use dishes in straight lines. Ships carry distress radios (VHF, DSC, EPIRB, SART) for emergencies.
• Radio-Wave Propagation – Radio waves travel in three main ways. Ground waves (below about 2 MHz) follow the ground. Sky waves (about 2 to 30 MHz) bend back from the ionosphere and can reach very far. Space waves (VHF and above) go in straight lines and are limited by the horizon, d ≈ 4.12(√h1 + √h2) km. On the way waves can be reflected, refracted, diffracted, absorbed or scattered, and the signal can fade because of the changing ionosphere and multipath.
• Radio, TV and Mobile Phones: How Signals Travel – Radio, TV and mobile phones send information with radio waves. Sound and pictures are turned into a small electric signal. The signal rides on a strong carrier wave from a tower. A receiver tunes to one frequency and turns the signal back into sound and pictures. Mobile networks split land into cells, each with its own tower.
• Radioactivity: Alpha, Beta, Gamma and Half-Life – Some atomic nuclei are unstable. They give out radiation at random to become more stable. This is radioactive decay. Alpha (2 protons + 2 neutrons), beta (a fast electron) and gamma (a wave of energy) are the three main kinds. Half-life is the time for half of the unstable nuclei to decay.
• Radionuclide Imaging and Therapy – In radionuclide imaging a radioactive tracer is put into the body; it collects in an organ and gives out gamma rays that a gamma camera detects. Technetium-99m is the most used tracer: pure gamma emitter, 140 keV, physical half-life 6 hours, easy to attach to many chemicals. The amount in the body falls by decay (physical half-life Tp) and by the body removing it (biological half-life Tb): 1/Te = 1/Tp + 1/Tb. A gamma camera has a lead collimator, a sodium iodide scintillator crystal, photomultiplier tubes and a computer. In therapy, high-energy (MeV) X-ray beams from a linear accelerator are aimed from many directions to meet at a tumour, or radioactive implants (brachytherapy) give a high dose right where it is needed. Each imaging method (X-ray, CT, ultrasound, MRI, gamma camera, PET) has its own strengths, costs and risks.
• Reflection of Light: Plane and Spherical Mirrors – Light bounces off a shiny surface so that the angle of incidence equals the angle of reflection. A plane mirror gives a virtual, upright, same-size image as far behind as the object is in front. A concave mirror can give real or virtual images depending on where the object is; a convex mirror always gives a virtual, upright, smaller image. The mirror formula 1/v + 1/u = 1/f and magnification m = −v/u (with the New Cartesian sign convention) let you find the image without drawing.
• Refraction of Light: Laws, Refractive Index and the Glass Slab – Light changes speed when it goes from one transparent medium to another, and so it bends at the boundary (unless it hits along the normal). Going into an optically denser medium it slows down and bends toward the normal; coming out it speeds up and bends away. For a pair of media, sin i / sin r stays constant (Snell's law); this constant is the refractive index, which also equals the ratio of the speeds of light, n = c/v. In a rectangular glass slab the emergent ray is parallel to the incident ray but shifted sideways (lateral displacement).
• Refraction Through a Prism, Dispersion of Light and the Rainbow – A glass prism bends light twice, both times towards its base; the total turn is the angle of deviation. Each colour in white light bends by a slightly different amount (violet most, red least), so a prism fans white light out into a spectrum, VIBGYOR. An upside-down second prism joins the colours back into white. Raindrops act like tiny prisms plus a mirror, which gives us the rainbow.
• Refraction, Total Internal Reflection and the Prism – Light bends when it crosses from one medium to another: n₁ sin i = n₂ sin r. Going from a denser to a rarer medium it bends away from the normal; beyond the critical angle C (sin C = 1/n) no light escapes and all of it reflects back: total internal reflection. Optical fibres use this to carry light. In a prism, r₁ + r₂ = A and deviation δ = i + e − A; at minimum deviation n = sin((A + δm)/2) / sin(A/2).
• Refraction: Snell's Law, Critical Angle and Total Internal Reflection – Refraction is the bending of light when it crosses from one medium into another, because its speed changes. The refractive index of a medium is n = c/v, where c = 3.00 × 10⁸ m/s. Snell's law links the angles, measured from the normal: n₁ sin θ₁ = n₂ sin θ₂. Going into a higher n the ray bends toward the normal; into a lower n it bends away. Frequency never changes at a boundary, so the wavelength shrinks: λ = λ₀/n. Going from high n to low n there is a critical angle, sin θc = n₂/n₁. Beyond it, total internal reflection happens, which is how optical fibres and diamonds work. Objects under water look shallower: apparent depth = real depth ÷ n (for near-normal viewing). Since n changes a little with colour, white light spreads into a spectrum (dispersion).
• Reinforced Concrete (RC) Structures – Concrete is strong when squeezed (compression) but weak when stretched (tension). Steel bars (rebar) placed where the stretching happens fix this. Together they make beams, columns, slabs and foundations. Concrete also protects the steel from rust and fire, and both expand almost equally with heat.
• Renewable Energy Sources – Non-renewable sources (coal, oil, gas, uranium) are used faster than nature makes them, and fossil fuels release CO₂. Renewable sources are refilled by nature: solar (photovoltaic cells and solar heating), wind (P ∝ v³), hydroelectric (P = η ρ g h Q), tidal, geothermal and biomass. Hydrogen fuel cells turn hydrogen and oxygen into electricity and water. Because sun and wind change, we need storage (batteries, pumped hydro) and a mix of sources. Every source has costs: land, materials, cost and effect on nature.
• Resistors in Series and Parallel – In series, resistors form one path: the same current flows through each, voltages add up and R_s = R₁ + R₂ + R₃. In parallel, each resistor gets its own branch: the voltage across each is the same, currents add up and 1/R_p = 1/R₁ + 1/R₂ + 1/R₃, so R_p is smaller than the smallest resistor.
• Resonance and Forced Vibration – Every object has a natural frequency at which it likes to vibrate. If a repeating push (the driver) has a different frequency, the object vibrates a little at the driver's frequency: forced vibration. If the push matches the natural frequency, the swing grows very large: resonance. Damping (friction) keeps the swing from growing forever.
• Road Safety: The Physics of Stopping and Staying Safe – A vehicle cannot stop at once. First the driver needs time to notice and react (reaction time, about 1 s). During this time the vehicle keeps moving: this is the thinking distance = speed × reaction time. Then the brakes slow it down: this is the braking distance = speed² ÷ (2 × deceleration). Stopping distance = thinking distance + braking distance. Double the speed and the braking distance becomes four times longer. Wet, icy or worn roads and tyres give less grip (friction), so braking is longer and bends are harder to take. In a crash, seat belts, helmets, airbags and crumple zones make the stop take longer, which makes the force on the body smaller. Pedestrians, cyclists, scooter riders and passengers all stay safer by following traffic rules, being seen, and never using a phone while moving.
• Safety and Risk: How We Protect the Body – In a crash, force depends on how fast you stop. A longer stopping distance means a smaller force. Crumple zones, seat belts, airbags and helmets add distance and time. Risk analysis rates a danger as chance x effect, so we can fix the biggest risks first.
• Satellites and Optical Fibre: Long-Distance Links – Radio waves cannot bend round the round Earth, so far links use a relay in space or a glass thread. A satellite receives microwaves from the ground (uplink) and sends them down again (downlink). An optical fibre guides pulses of light by total internal reflection and carries huge amounts of data with little loss.
• Save Electricity at Home: Audit and Saving Plan – A home electricity audit lists every appliance with its power in watts and the hours it runs per day. Energy = power × time, shown in kilowatt-hours (units). The tallest energy bars show where to save first. Switch to efficient devices, run them for less time and cut standby use, then work out the new bill to see the saving.
• Scalars and Vectors for Motion in a Plane (Class 11) – A scalar has only size; a vector has size and direction. Vectors are equal if their size and direction match. Multiplying by a number changes the length (a negative number flips it). Vectors add tail-to-head (triangle or parallelogram law); A − B = A + (−B). Any vector in a plane is A = Ax î + Ay ĵ with Ax = A cos θ, Ay = A sin θ. A·B = AB cos θ is a scalar; A×B has size AB sin θ and is perpendicular to both.
• Second Law of Thermodynamics, Heat Engines and Refrigerators – The first law says energy is conserved; the second law says which way heat and energy can go. Heat flows by itself only from hot to cold (Clausius). No engine can turn all the heat it takes into work; some must be thrown into a colder body (Kelvin–Planck). A heat engine takes Q₁ from a hot source, does work W and rejects Q₂: efficiency η = W/Q₁ = 1 − Q₂/Q₁. A refrigerator uses work W to move Q₂ from cold to hot: COP α = Q₂/W. The best possible engine, the Carnot engine, has η = 1 − T₂/T₁.
• Seismic Design of Buildings – In an earthquake the ground moves and a building's mass resists, so it feels an inertia force F = m × a, pushed sideways, bigger for heavier floors and higher floors. Damage comes from weak storeys (soft storey), short columns, pounding, twisting, poor joints and brittle materials. Seismic design gives the building strength, stiffness, ductility and a regular shape, with shear walls, bracing or base isolation. Old buildings are strengthened by seismic retrofit: adding walls or braces, wrapping columns and fixing connections.
• Seismic Technology for Buildings – An earthquake shakes the ground and the building tries to stay behind, so it sways. There are three ways to protect a building: make it strong and stiff with walls and braces (seismic resistance), put rubber bearings under it so the shaking is not passed up (base isolation), or add dampers that absorb the swaying energy (vibration control). Old houses can be made safer by retrofitting.
• Semiconductors and the p-n Junction Diode – A semiconductor has a small energy gap (about 1 eV), so a little heat frees some electrons. Pure silicon is intrinsic (electrons = holes). Adding a 5-valence atom makes n-type; a 3-valence atom makes p-type. Joining p and n makes a junction with a depletion layer and a barrier (about 0.7 V for Si). The diode conducts in forward bias, almost not in reverse bias, so it can change AC into one-way DC (rectifier).
• Ship Design – A ship is designed so that its weight equals the weight of the water it pushes aside (displacement), so that the water resists it as little as possible, so that a propeller can push it, and so that its hull is strong enough for waves.
• Ship Equipment – A ship is a floating workshop and home. Its equipment has six groups: steering, engine and radio; mooring and cargo gear; stores; safety and sanitary items; fishing gear; and freezing and cold storage. Each group does one clear job.
• Ship Handling – Ship handling means controlling a ship's speed and direction safely. The rudder turns the ship, but a ship is heavy and keeps gliding, so it turns slowly and stops slowly. Wind and waves push it sideways. In heavy weather the crew slow down and meet waves from the bow. In an emergency, quick, calm, trained steps save lives.
• Ship Management: Inspection and Repair – A ship must be checked by inspectors at set times and must hold valid certificates to sail. When a check finds damage, the ship is repaired, often in a dry dock where the water is pumped out so the hull can be worked on.
• Ship Operation – Running a boat well needs six things: know the hull, deck and fittings; steer with the rudder and engine; read the compass and chart; understand weather and sea; plan the voyage (route, time, fuel, safe harbours); and know how to act in heavy weather so that accidents are avoided.
• Ship Operation and Security – A ship is run by a crew in departments (deck, engine, catering) under the captain. Its hull is split into watertight compartments, so one flooded space does not sink it. Fixed equipment, safety drills, international sea rules (such as red port and green starboard lights) and clear standard English on the radio keep everyone safe.
• Ship Propulsion Systems – A ship moves because its engine turns a shaft, the shaft turns a propeller, and the propeller pushes water backward, so the water pushes the ship forward. A rudder at the stern steers by bending the water stream. Other systems (twin screws, controllable pitch, azimuth pods, water jets) do the same job in different ways. Needed power grows roughly with the cube of speed, so going slower saves a lot of fuel.
• Ship Radio Practice: Range, Morse Code, Distress Calls and Wavelength – Boats talk to the shore by VHF radio, near 156 MHz. VHF goes in straight lines, so range ≈ 4.12 × (√h1 + √h2) km with antenna heights in metres. Morse sends letters with dots (1 unit) and dashes (3 units); SOS is three dots, three dashes, three dots. A Mayday call has five parts in order. Wavelength = 300 ÷ frequency in MHz, in metres.
• Ship Stability and Safety Equipment – A ship stays upright when its weight (pulling down at G) and the water's upward push (buoyancy, at B) form a pair that turns it back after a tilt. Heavy cargo placed high lifts G and can make the ship roll over. Life jackets, life rings and lifeboats keep people afloat and safe.
• Shipbuilding – A ship is built by drawing the real-size plan, cutting steel plates, welding plates into blocks, joining the blocks into one hull, launching the hull into water, and then fitting engines and equipment and painting it.
• Significant Figures and Errors in Measurement – No measurement is perfect. Significant figures are the digits we trust plus the first doubtful digit. Errors tell how far a reading may be from the true value: absolute error Δa, relative error Δa/a and percentage error (Δa/a) × 100. When we add or subtract, absolute errors add. When we multiply or divide, percentage errors add. For a power aⁿ, the percentage error becomes n times.
• Simple Harmonic Motion (SHM) – A motion that repeats after a fixed time is periodic. If the object goes to and fro about a middle point and the force pulling it back is proportional to its distance from the middle (F = −kx), the motion is simple harmonic. Its position is x = A sin(ωt + φ), with ω = 2π/T = 2πf. Speed is largest in the middle, acceleration is largest at the ends, and total energy ½kA² stays constant.
• Small Boat Engines: Handling, Care and Faults – A small boat engine burns fuel to turn a propeller. Good handling means checking fuel, oil, cooling water and the propeller before starting, watching gauges while running, and stopping properly. Care means changing oil, cleaning filters and rinsing the engine. When it fails, stay calm, make the boat safe, then check fuel, filter, cooling and propeller one by one.
• Soil Mechanics – Soil mechanics explains how soil behaves under loads and water. Soil is solids, water and air. Water seeps through it (Darcy law), loads squeeze it slowly (consolidation), it resists sliding with friction and cohesion (τ = c + σ tan φ), and it pushes sideways on walls (earth pressure).
• Solar Energy: From the Sun to Your Plug – The Sun makes energy by nuclear fusion: hydrogen nuclei join to make helium, and a little mass becomes a lot of energy (E = mc²). The hot surface (about 5800 K) radiates mostly visible light (Wien's law), and its total power grows as T⁴ (Stefan's law). About 1361 W reaches each square metre facing the Sun at the top of the atmosphere; about 1000 W/m² reaches the ground on a clear day. Sunlight hitting at a slant spreads over more area, which explains latitude and seasons. Solar cells turn light into electricity: P = intensity × area × efficiency × cos(angle). Solar water heaters turn light into heat.
• Sound – Sound is made by vibrating objects. It travels through a medium (air, water, solids) as a longitudinal wave: particles move back and forth, making crowded parts (compressions) and spread-out parts (rarefactions). Frequency (Hz) sets the pitch, amplitude sets the loudness, and speed v = f × λ. Sound cannot travel in vacuum. Humans hear 20 Hz to 20,000 Hz; below is infrasound, above is ultrasound. Reflected sound gives echoes, used and controlled in buildings.
• Space Exploration – Space exploration means sending rockets, satellites, probes and people beyond Earth's air. Rockets rise by pushing gas down (action–reaction). At about 7.9 km/s sideways a craft keeps falling around Earth in orbit; at 11.2 km/s it escapes. Since 1957 space has been a place of rivalry and cooperation, and it gives us weather forecasts, navigation, communication and new science.
• Space Velocity of Stars – A star moves through space with one real velocity, but we see it in two parts. The radial part is along our line of sight and is found from the Doppler shift of its light. The tangential part is across the sky and is found from proper motion μ with vt = 4.74 μ d (μ in arcsec per year, d in parsecs, vt in km/s). The space velocity is v = √(vr² + vt²).
• Space Weather and Near-Earth Asteroids – Space weather is the changing conditions in space caused by the Sun. Flares and coronal mass ejections (CMEs) send charged particles at 400 to 2000 km/s, reaching Earth in about 1 to 4 days. Earth's magnetic field shields us and makes aurora near the poles, but strong storms can upset satellites, GPS, radio and power grids. Near-Earth asteroids are rocks whose orbits pass close to Earth's path; they are tracked for years so any danger is known early.
• Special Relativity – Special relativity (Einstein, 1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in a vacuum, c ≈ 3.00 × 10⁸ m/s, is the same for every observer. It follows that moving clocks run slow (t = γt₀), moving objects are shorter along their motion (L = L₀/γ), and mass is a form of energy (E = mc²), with γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1, so Newton's mechanics works; near c it fails.
• Specific Heat Capacity and Heat Balance – Different materials need different amounts of energy to warm up. The specific heat capacity c of a material is the energy needed to raise the temperature of 1 kg of it by 1 °C (or 1 K). Its unit is J/(kg·°C) or J/(kg·K). The energy needed to heat any amount is Q = m × c × ΔT. Water has a very high c (about 4200 J/(kg·°C)), so it heats and cools slowly. When a hot and a cold body touch and nothing is lost, the heat given by the hot body equals the heat taken by the cold body (heat balance). A calorimeter uses this idea to measure c.
• Spherical Lenses: Images, Lens Formula and Power – A convex lens is thick in the middle and bends parallel light to meet at its focus; a concave lens is thin in the middle and spreads light out as if from its focus. With two simple rays (one parallel to the axis, one through the optical centre) you can find the image for any object position. A convex lens gives real, inverted images when the object is beyond F₁ and a virtual, erect, enlarged image inside F₁; a concave lens always gives a virtual, erect, diminished image. The lens formula 1/v − 1/u = 1/f, magnification m = v/u and power P = 1/f (in metres, unit dioptre) let you solve lens numericals.
• Spherical Mirrors and the Mirror Formula – A spherical mirror is a piece cut from a shiny ball. Its focal length is half its radius of curvature (f = R/2). With the Cartesian sign convention, the object distance u, image distance v and focal length f are linked by 1/v + 1/u = 1/f, and the magnification is m = h′/h = −v/u. Concave mirrors have negative f; convex mirrors have positive f.
• Sports Biomechanics – Biomechanics is the physics of the moving body. Movement happens in three planes (sagittal, frontal, transverse) around three axes. Bones, joints and muscles work as levers: a pivot, an effort and a load. Most body levers are third class: they give little force but fast, wide movement. Newton's three laws explain starting, speeding up and pushing off the ground; friction gives grip. Stability depends on the centre of gravity, the base of support and the line of gravity. Turning movements follow the same ideas: torque starts a spin, and with no outside torque angular momentum stays the same, so pulling the arms in makes you spin faster. A thrown ball, javelin or jumper is a projectile: speed, angle and release height set the distance. Air and water push back with drag; spin and shape can create lift (the Magnus effect).
• Star Clusters: Open, Globular and How We Find Their Age – A star cluster is a group of stars born together from one gas cloud, so they share the same age and almost the same chemical make-up. Open clusters are loose, young and blue; globular clusters are dense, old and reddish. Plot each star's brightness against its colour and you get a main-sequence curve; the point where it bends away (the turn-off) tells the cluster's age: lower turn-off means older cluster.
• Stars and Galaxies: From Starlight to the Big Bang – Everything we know about stars comes from their light. Splitting starlight into a spectrum shows dark lines that tell us which elements a star has; the colour tells us its temperature (blue = hot, red = cool) and stars are sorted into classes O B A F G K M. The H-R diagram plots true brightness against temperature: most stars, including the Sun, lie on the main sequence, with giants top right and white dwarfs bottom left. A star is born in a nebula and its mass decides its life: a Sun-like star becomes a red giant and then a white dwarf; a star of more than about 8 solar masses becomes a supergiant, explodes as a supernova and leaves a neutron star or black hole. Stars gather in galaxies, which are spiral, elliptical or irregular. Distances are huge, so we use the astronomical unit, the light-year and the parsec. Galaxies are moving apart, faster when farther (Hubble's law), which together with the cosmic microwave background supports the Big Bang about 13.8 billion years ago.
• Stars: Colour, Brightness, Distance and the H-R Diagram – A star is a huge ball of hot gas that shines by nuclear fusion. Its colour shows its surface temperature: red stars are cool, blue stars are hot (Wien's law: λmax × T = 2.9 × 10⁻³ m K). Stars are sorted into spectral classes O B A F G K M, hottest to coolest. How bright a star looks (apparent magnitude) depends on its real power (luminosity) and its distance, because light weakens as 1/d². Nearby distances are found by parallax: d (pc) = 1/p (arcsec). Luminosity depends on size and temperature (L = 4πR²σT⁴). The H-R diagram plots luminosity against temperature and shows the main sequence, giants and white dwarfs.
• State Changes in the Kitchen – The kitchen is full of changes of state. Butter melting is solid to liquid. Boiling water and drying clothes are liquid to gas. Steam on a cold lid is gas to liquid. Water in an ice tray is liquid to solid. When heat goes into a substance it melts or becomes a gas. When heat comes out, it freezes or condenses. These changes are physical: the substance stays the same. Cooking an egg or baking bread makes new substances, so that is a chemical change, not a state change.
• Static Electricity – Rubbing two different materials moves electrons from one to the other. The one that gains electrons becomes negative; the one that loses them becomes positive. Charge is never made or destroyed, only moved. Like charges repel and unlike charges attract. A charged object can pull a neutral one by induction. Earthing lets extra charge flow safely away.
• Steel Structures – Steel is strong in both pulling and pushing, so thin and light parts can carry big loads. Beams are shaped like an H so the steel sits where bending is largest. Parts are made in a factory and joined by bolts or welds. Weak points: slim columns buckle, steel softens in fire, and it can rust, so it needs fireproof and paint coats.
• Stellar Nucleosynthesis: How Stars Make the Elements – The Big Bang made almost only hydrogen and helium. Stars fuse hydrogen into helium and, in big stars, build heavier atoms up to iron. A supernova and colliding neutron stars make still heavier ones and scatter them into space. The Sun and Earth were formed from this recycled star material.
• Strength of Materials: Stress, Strain and Shape – Stress = force ÷ area (MPa). Strain = extra length ÷ original length (no unit). Up to the elastic limit a part springs back; beyond the yield point it stays stretched (plastic); at the ultimate stress it breaks. E = stress ÷ strain. Safety factor = ultimate stress ÷ working stress. Sharp corners raise stress, so designers round them.
• Structural Design: Beams, Trusses and Rigid Frames – Structural design means choosing the shape and size of parts so that they carry loads safely. Engineers compare load with capacity and keep a safety factor above 1. A beam resists bending (depth matters most), a truss uses triangles so every bar only pushes or pulls, and a rigid frame uses stiff corners so it keeps its shape under side push.
• Structural Materials – Structural materials carry loads in bridges, cars, planes and machines. Steel and cast iron are strong and cheap, light metals save weight, ceramics are hard but brittle, engineering plastics are light and tough, and composites mix two materials to get the best of both.
• Structural Mechanics for Civil Engineering – A structure must stay still while loads push on it. So the forces must balance: sum of vertical forces = 0 and sum of moments = 0. For a simply supported beam these two rules give the support reactions. Then we find the bending moment, and finally the stress σ = force ÷ area to check that the member is strong enough.
• Structures and Forces – A structure is anything that holds a shape and carries a load: a bridge, a chair, a bone, an egg. There are three main types: solid (one heavy mass), frame (bars joined together) and shell (a thin curved skin). Loads cause forces inside the parts: compression squeezes, tension stretches, bending does both, shear slides, torsion twists. Triangles keep frames rigid. A structure is stable when the line down from its centre of gravity stays inside its base; it is strong when its material, shape and joints can carry the load without breaking.
• Superposition, Reflection and Standing Waves – When waves overlap, their displacements add (superposition). A wave reflected from a fixed end comes back upside down; from a free end it comes back upright. A wave and its reflection make a standing wave with nodes (no motion) and antinodes (most motion). A string fixed at both ends allows fₙ = n·v/2L (all harmonics). An open pipe allows fₙ = n·v/2L; a pipe closed at one end allows only odd harmonics, fₙ = n·v/4L (n = 1, 3, 5…).
• Surface Tension, Angle of Contact and Capillary Rise – Molecules at a liquid's surface are pulled inward by their neighbours, so the surface behaves like a stretched skin. The extra energy stored per unit area of surface is the surface energy, and it equals the surface tension S (force per unit length, N/m). Where a liquid meets a solid, the angle of contact θ tells whether it wets the solid (θ < 90°, like water on glass) or not (θ > 90°, like mercury). Curved surfaces have extra pressure inside: 2S/r for a drop or air bubble in liquid, 4S/r for a soap bubble. In a thin tube the liquid rises (or falls) by h = 2S cosθ / (rρg).
• Telescopes and Detectors – Stars send out light, radio waves, X-rays and even ghostly particles. A telescope is a collector: a wide mirror or dish gathers more radiation than an eye, and a detector records it. Light gathering grows with the area (width squared). The air blocks UV, X-rays and most infrared, so those telescopes fly in space. Neutrino and gravitational-wave detectors catch signals that are not light at all.
• Temperature – Temperature tells us how hot or cold something is. Inside every object, tiny particles are always moving; temperature measures their average kinetic energy (how fast they jiggle on average). We measure it with a thermometer, in degrees Celsius (°C), kelvin (K, the SI unit) or degrees Fahrenheit (°F). K = °C + 273 and °F = 9/5 × °C + 32. The lowest possible temperature is absolute zero, 0 K = −273 °C. When a hot and a cold object touch, heat flows from hot to cold until both have the same temperature (thermal equilibrium).
• The Discovery of the Electron – In low-pressure discharge tubes, rays came from the cathode. These cathode rays travel in straight lines, carry negative charge and are bent by electric and magnetic fields. In an electron gun a hot filament releases electrons by thermionic emission and an anode voltage V accelerates them: eV = ½mv². J. J. Thomson balanced an electric field against a magnetic field so the beam went straight: v = E/B. Then e/m = v² ÷ 2V ≈ 1.76 × 10¹¹ C kg⁻¹, about 1800 times the value for a hydrogen ion, showing the particle was very light and the same in every metal. Millikan balanced charged oil drops between plates (QV/d = mg) and found every charge was a whole-number multiple of e = 1.6 × 10⁻¹⁹ C: charge is quantised.
• The Diving Environment – Under water the world changes. Pressure rises by about 1 atm for every 10 m, so air shrinks (Boyle's law). It gets colder and darker, and red light vanishes first. Things look closer, and sound travels fast so direction is hard to tell. Buoyancy decides if a diver floats or sinks. Currents can push divers, and some sea animals can sting or bite.
• The Doppler Effect – The Doppler effect is the change in the frequency we hear (or detect) when the source of a wave and the observer move toward or away from each other. Moving closer squeezes the crests together: shorter wavelength, higher frequency, higher pitch. Moving apart stretches them: longer wavelength, lower frequency. For sound, f′ = f × (v ± vo) ÷ (v ∓ vs), using the upper signs when they approach. It is used in speed guns, weather radar, ultrasound scans of blood flow, bat echolocation and in astronomy (red shift and blue shift of light).
• The Electromagnetic Spectrum – Electromagnetic (EM) waves are transverse waves of changing electric and magnetic fields. They need no medium and all travel at 3 × 10⁸ m/s in a vacuum. In order of falling wavelength (rising frequency and energy) they are radio, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Speed = frequency × wavelength (c = fλ). Each type has uses; the high-energy ones (UV, X-rays, gamma) are ionising and can harm living cells.
• The Greenhouse Effect – The Sun heats Earth with visible light. About 30% is reflected straight back to space (albedo ≈ 0.30). The rest warms the ground, which gives off infrared radiation. Greenhouse gases – water vapour, carbon dioxide, methane, nitrous oxide – let visible light through but absorb infrared and send part of it back down. Earth settles at the temperature where energy in equals energy out. Without greenhouse gases Earth would average about −18 °C; with them it is about +15 °C. Adding more CO₂ and CH₄ (from burning fuels, farming, landfills) strengthens the effect and warms the planet.
• The Human Eye: Parts, Accommodation and Defects of Vision – The eye is a camera made of living parts. The cornea and eye lens bend light to make a real, upside-down image on the retina. The ciliary muscles change the lens thickness so both far and near things look sharp (accommodation). When the eyeball is too long or too short, or the lens gets stiff, the image misses the retina; the right spectacle lens puts it back.
• The Interstellar Medium: Gas, Dust and Molecules Between the Stars – The interstellar medium (ISM) is the thin gas and dust that fills the space between stars. About 99% of it is gas (mostly hydrogen and helium) and about 1% is tiny solid dust grains. In cold, dense clouds atoms join into molecules such as H₂ and CO. Dust absorbs and scatters starlight, blue light more than red, so a star behind dust looks fainter (extinction) and redder (reddening).
• The Milky Way: Our Home Galaxy – The Milky Way is a barred spiral galaxy of about 100–400 billion stars, roughly 100,000 light-years across. It has a thin disc with spiral arms, a central bulge and bar, and a large faint halo with old globular clusters. The Sun sits about 26,000 light-years from the centre in the Orion Arm and orbits at about 230 km/s, once every 230 million years or so. Dust hides much of the disc, so astronomers map the arms using 21 cm radio waves from hydrogen. At the centre is a black hole, Sgr A*, of about 4 million solar masses. The flat rotation curve shows the galaxy holds much more mass than we can see: dark matter.
• The Particle Model of Matter – All matter is made of tiny particles that are always moving. In a solid they are close and only vibrate; in a liquid they are close but slide past each other; in a gas they are far apart and move fast in all directions. Heating gives particles more energy: either they move faster (temperature rises) or the forces between them are broken (the state changes while the temperature stays the same). Gas pressure comes from particles hitting the walls.
• The Photon Model of Light: Waves, Photons and Spectra – Light behaves like a wave with wavelength λ and frequency f (c = fλ), and also like a stream of packets called photons, each with energy E = hf = hc/λ. Short waves carry more energy per photon. The electromagnetic spectrum runs from radio to gamma rays, with visible light a small band. Atoms have fixed energy levels, so they absorb or emit photons only of energies equal to the gaps between levels, which gives each element its own line spectrum. A thin lens forms images by 1/v − 1/u = 1/f.
• The Quantum Idea: Energy Comes in Packets – A hot object glows, and the old physics could not explain its colours. In 1900 Max Planck guessed that energy is exchanged only in small packets. One packet of light of frequency f carries E = hf, where h = 6.63 × 10⁻³⁴ J s. Such a packet of light is a photon. This one guess fixed the puzzle and started quantum physics.
• The Solar System – The Solar System is the Sun and everything its gravity holds: 8 planets, their moons, dwarf planets, asteroids, comets and dust. The inner four planets (Mercury, Venus, Earth, Mars) are small and rocky. After the asteroid belt come the giants: gas giants Jupiter and Saturn, ice giants Uranus and Neptune. Gravity pulls planets towards the Sun while they move sideways, so they travel in orbits; closer planets move faster and have shorter years. It all formed about 4.6 billion years ago from a spinning cloud of gas and dust.
• The Sun: Our Star from Core to Corona – The Sun is a star: a huge ball of hot gas (plasma), about 73% hydrogen and 25% helium by mass. It is 1.39 million km wide (109 Earths), holds 99.86% of the Solar System's mass and is about 150 million km away, so its light takes about 8 minutes 20 seconds to reach us. Its surface (photosphere) is about 5500 °C; its core is about 15 million °C. In the core, nuclear fusion joins 4 hydrogen nuclei into 1 helium nucleus; the small mass lost becomes energy (E = mc²). The Sun turns about 4 million tonnes of mass into energy every second. Energy crawls out through the radiative zone (as light, over thousands of years), then rises by convection to the surface. Fusion also makes neutrinos, tiny particles that escape at once and prove fusion is happening. The Sun's magnetic field makes sunspots (cooler, darker patches), flares (sudden blasts) and coronal mass ejections. Activity rises and falls in an 11-year cycle. The solar wind and storms cause auroras and can disturb radio, GPS, satellites and power grids.
• The Uncertainty Principle and the Modern Atom Model – A particle is a wave, so it cannot have an exact position and an exact momentum together. The more sharply you fix where it is (small Δx), the less you know about its momentum (large Δp). The rule is Δx · Δp ≥ ħ/2. Because of this, the modern atom has no fixed orbits. Electrons live in orbitals, which are clouds showing where an electron is likely to be found.
• Thermal Equilibrium and the Zeroth Law – Two bodies in contact swap heat until their temperatures are equal. Then they are in thermal equilibrium and nothing changes any more. Zeroth law: if A and B are each in equilibrium with C, then A and B are in equilibrium with each other. This is why a thermometer works. A gas in equilibrium is described by state variables P, V, T and n, which are linked by an equation of state. For an ideal gas it is PV = nRT.
• Thermal Expansion, Specific Heat, Calorimetry and Latent Heat – Temperature tells how hot a body is; heat is energy that flows because of a temperature difference. Most things expand when heated: ΔL = αLΔT, ΔA = βAΔT, ΔV = γVΔT, with β = 2α and γ = 3α. Water is an exception between 0 °C and 4 °C, where it shrinks on heating, so it is densest at 4 °C. The heat needed to warm a body is Q = mcΔT, where c is the specific heat; gases have two, Cp > Cv, with Cp − Cv = R per mole. In calorimetry, heat lost by hot bodies equals heat gained by cold ones. During melting or boiling the temperature stays constant and heat Q = mL goes into changing the state.
• Thermodynamic Processes: Isothermal, Adiabatic and More – A thermodynamic process takes a gas from one state to another; on a P–V graph it is a path. Isothermal: T fixed, PV = constant, W = nRT ln(V₂/V₁), ΔU = 0. Adiabatic: no heat in or out, PV^γ = constant, W = nR(T₁ − T₂)/(γ − 1), the gas cools when it expands. Isobaric: P fixed, W = PΔV. Isochoric: V fixed, W = 0. Reversible processes go slowly through equilibrium states; real, fast ones are irreversible. In a cyclic process the gas returns to its start, ΔU = 0 and net work = area of the loop.
• Thin Lenses: Lens Maker's Formula, Lens Formula and Power – At one curved surface, n₂/v − n₁/u = (n₂ − n₁)/R. Two such surfaces make a thin lens with 1/f = (n − 1)(1/R₁ − 1/R₂) (lens maker's formula). Object and image distances follow 1/v − 1/u = 1/f, magnification m = v/u, power P = 1/f (in dioptres when f is in metres), and thin lenses in contact add their powers: P = P₁ + P₂.
• Third Law, Conservation of Momentum and Equilibrium of Forces – Forces always come in pairs: if A pushes B, B pushes A with an equal and opposite force at the same instant (third law). The pair acts on different bodies. For a system with no net external force, the total linear momentum stays constant, which explains recoil, rockets and collisions. A particle is in equilibrium when all forces on it add to zero; three concurrent forces in equilibrium form a closed triangle.
• Timber Structures – A timber structure uses wooden posts and beams joined into a frame. Joints such as mortise and tenon connect the pieces. Diagonal braces stop wind from leaning the frame. Wood must be kept dry and off the ground to avoid rot, and a deep beam sags far less than a shallow one because stiffness grows with depth cubed.
• Torque, Angular Momentum and Equilibrium of Rigid Bodies – Torque is the turning effect of a force: τ = r × F, size rF sinθ, unit N m. Angular momentum is the turning version of momentum: L = r × p; for a body spinning about a fixed axis L = Iω. Torque changes angular momentum: τ = dL/dt. If the outside torque is zero, L stays constant, so pulling mass in makes a body spin faster. A rigid body is in equilibrium when the total force is zero (no sliding) and the total torque about any point is zero (no turning).
• Transmission and Reception of Radio Waves – Sound is a slow signal that cannot travel far on its own. A radio station puts it on a fast carrier wave by modulation: in amplitude modulation (AM) the carrier's height follows the sound. The wave leaves a transmitting antenna as a radio wave. At home, the antenna catches many stations at once; a tuned LC circuit with f = 1/(2π√LC) picks one. A diode and a filter then demodulate it, taking the sound back out of the carrier, and the speaker plays it.
• Turbine Engines: Steam Turbines and Gas Turbines – A turbine engine turns a fast-moving gas into spinning motion. A steam turbine gets hot steam from a boiler. A gas turbine compresses air, burns fuel in it, and sends the hot gas through a turbine. The spinning shaft drives a generator, a ship propeller or a jet. Efficiency = useful work out ÷ heat in.
• Types and Properties of Interior Materials – Interior materials fall in four families. Structural materials carry loads (concrete, timber). Functional materials do a job such as blocking heat, sound or fire (mineral wool, gypsum board). Finishing materials give the final look and wear (paint, tile). Unit materials come in pieces of fixed size (tiles, boards, bricks) and are counted. We choose by properties: strength, heat, fire, water and wear.
• Units and Measurement (Class 11) – To measure means to compare a quantity with a fixed, agreed amount called a unit. Result = number × unit. The world now uses the SI system with 7 base units: metre, kilogram, second, ampere, kelvin, mole and candela. Every other unit (like newton or joule) is a derived unit made by multiplying or dividing base units. Prefixes like kilo (10³) and milli (10⁻³) make very big or very small numbers easy.
• Using and Maintaining Household Appliances – Appliances turn electricity into heat, motion or light. Use them safely: dry hands, switch off before plugging, never overload a socket, keep cords undamaged. Care for them by cleaning and descaling. Only small, safe jobs are for children; electrical repairs are for a trained adult.
• Variable Stars and Cepheids – A variable star changes its brightness. A Cepheid pulsates: it swells and shrinks in a steady beat of 1 to 100 days. The longer the period P, the brighter the star really is (the period–luminosity law). So by timing the beat we learn the true brightness, compare it with how bright the star looks, and get its distance.
• Various Construction Works – A building needs many kinds of work: temporary works, foundation and ground work, structural frame, finishing, building services, seismic strengthening of old buildings, labour-saving methods such as prefab and machines, and careful demolition with recycling to protect the environment.
• Various Waveforms: Sine, Square, Triangle and Transients – A waveform is a graph of voltage or current against time. Mains AC is a sine wave, but circuits also carry square, triangle and saw waves (non-sinusoidal AC). Any such wave is a sum of sine waves. After a switch is closed, voltage in an RC circuit rises along a curve with time constant τ = RC; this short settling stage is the transient.
• Vehicle Ownership: How a Car Works and How to Look After It – A vehicle owner does not need to be a mechanic, but should know the basics. The powertrain (engine or motor, gearbox, axles, wheels) moves the car. Five fluids and parts under the bonnet need regular checks: oil, coolant, brake fluid, battery and washer fluid. Tyres need the right pressure and enough tread. Dashboard lights warn by colour. The owner’s manual gives the service schedule. Regular cleaning stops rust. In a breakdown or crash, a calm, ordered set of steps keeps people safe and meets the law.
• Ventilation and Smoke-Exhaust Installations – Ventilation replaces stale indoor air with fresh air, by natural openings or by fans. Flow is planned with air changes per hour (ACH = flow ÷ room volume). Heat-recovery units save energy by moving heat from outgoing to incoming air. Smoke-exhaust systems remove hot smoke from the ceiling in a fire, so a clear layer stays near the floor for escape.
• Viscosity, Stokes' Law and Bernoulli's Theorem – A moving fluid is like a stack of layers sliding over each other. The friction between layers is viscosity: F = ηA(dv/dx). A small ball falling through a fluid feels a drag F = 6πηrv (Stokes' law); when drag plus buoyancy balance the weight, it falls at a steady terminal velocity. Slow flow is streamline; above a critical velocity (Reynolds number about 2000) it becomes turbulent. For steady streamline flow, Av is constant (continuity) and P + ½ρv² + ρgh is constant (Bernoulli). So fast fluid has low pressure. This explains Torricelli's efflux speed √(2gh), the venturimeter, and the lift on wings and spinning balls.
• Water and Hot-Water Supply Installations – Water comes from a source (river, lake, reservoir or well), is cleaned at a treatment plant and sent through mains to buildings. A raised tank or pump gives the pressure: p = ρgh, about 9.81 kPa per metre of height. Pipes are sized so the water speed stays below about 2 m/s. A water heater warms the water for taps, using E = m × c × ΔT.
• Water Cycle and Water Resources: State Changes and Saving Water – The water cycle is a loop of state changes powered by the Sun. Sun heat evaporates liquid water from seas and rivers into vapour (liquid to gas, heat in). High in the cold air the vapour condenses into drops and forms clouds (gas to liquid, heat out). Drops fall as rain, or as snow or hail when it is cold (solid). Melted snow and rain flow back to the sea. Only about 2.5 per cent of Earth's water is fresh, and most of that is ice, so we must save water.
• Wave Phenomena: Reflection, Refraction, Diffraction and Interference – All waves (water, sound, light) do four things. They bounce off walls (reflection). They bend when their speed changes (refraction). They spread out after a gap or an edge (diffraction). And when two waves meet, they add up (superposition): crest + crest makes a bigger wave (constructive interference), crest + trough cancels (destructive interference). The rule: path difference = nλ gives a big wave; path difference = (n + ½)λ gives calm. For two slits, fringe spacing Δx = λD/d.
• Wavefronts and Huygens' Principle – A wavefront is a surface on which every point of a wave is in the same phase. A point source gives spherical wavefronts; a far source gives plane wavefronts; rays are at right angles to wavefronts. Huygens' principle: every point on a wavefront acts as a source of secondary wavelets, and the forward envelope of these wavelets is the new wavefront. Using it, reflection gives i = r and refraction gives sin i / sin r = v₁/v₂ = n₂/n₁.
• Waves at Boundaries, Polarisation and the Doppler Effect – When a wave reaches the end of its medium it reflects. At a fixed end the reflected pulse is upside down (a phase change of half a cycle); at a free end it stays upright. Where two media meet, part of the wave reflects and part is transmitted: the transmitted part is never inverted, and the reflected part is inverted only if the second medium is slower (denser). Frequency stays the same across a boundary, while speed and wavelength change. Polarisation means the vibrations of a transverse wave are in one direction only; a polariser passes half of unpolarised light, and a second polariser at angle θ passes I = I₀ cos²θ (Malus's law). Longitudinal waves such as sound cannot be polarised. The Doppler effect is the change in observed frequency when source or observer move: f' = f (v ± v_o)/(v ∓ v_s). These ideas power technologies like ultrasound scans, sonar, radar speed guns, optical fibres, LCD screens and digital communication.
• What Is Engineering? – Engineering is using science, maths and creativity to design and build useful things that solve real problems within limits of cost, safety, time and materials. Engineers follow a design process loop: identify the problem, research, generate ideas, build a prototype, test, and improve. From ancient irrigation and roads to today's chips and vaccines, engineering shaped civilisation. Its main branches are civil, mechanical, electrical, chemical, computer and biomedical, and modern problems join many of them together (convergent or STEAM engineering).
• Work, Energy and Power – Work is done when a force moves an object: W = F × s, measured in joules (J). Energy is the ability to do work. A moving body has kinetic energy ½mv²; a raised body has potential energy mgh. Energy is never made or destroyed, only changed from one form to another. Power is how fast work is done: P = W ÷ t, in watts. Simple machines like levers and pulleys let a small effort move a big load.
• Work, Kinetic Energy, Work–Energy Theorem and Power – Work is done when a force moves something along its direction: W = F·s = F s cos θ. For a changing force, work is the area under the F–x graph. A moving body has kinetic energy K = ½mv². The work–energy theorem says: net work done on a body = change in its kinetic energy. Power is how fast work is done: P = W/t = F·v.
• X-ray Imaging – X-rays are very short-wavelength electromagnetic waves. In an X-ray tube, electrons are sped up by a high voltage and hit a metal target, which gives out X-rays. Different body parts absorb X-rays by different amounts: the intensity falls as I = I₀e^(−μx). Bone absorbs much more than soft tissue, so it shows white on the image. Contrast media, image intensifiers and CT scanners make the pictures clearer and three-dimensional.