United Grade 12 Physics
Chapters: 4
1. Forces and interactions
Newton's second law · Conservation of momentum · Designing collision-safety devices · Gravitation and Coulomb’s law · Electric currents and magnetic fields
- 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.
- 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.
- 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.
- 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).
- 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.
2. Energy
Computing energy changes in systems · Energy as motion and fields at the macro scale · Designing energy-conversion devices · Thermal energy transfer and the second law · Energy stored in fields
- 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.
- 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.
- 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.
3. Waves and electromagnetic radiation
Wave speed, frequency and wavelength · Digital information transmission · Wave and particle models of light · Effects of EM radiation on matter · Wave technologies
- 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.
- Data Representation: How Computers Store Numbers, Text, Images and Sound – Data is raw facts; information is data given meaning; knowledge is information we can use. A computer stores all data as bits (0 or 1). 8 bits make a byte, and 1 kB = 1000 bytes, 1 MB = 1000 kB, 1 GB = 1000 MB, 1 TB = 1000 GB. Numbers are stored in binary, where place values double: 1, 2, 4, 8 and so on. Text uses a character set: in ASCII 'A' is 65; Unicode covers every script. A bitmap image is a grid of pixels; size = width × height × colour depth. Sound is sampled: size = sample rate × bit depth × seconds. Vector images store shapes instead of pixels. Compression makes files smaller: lossless keeps every bit, lossy throws some detail away.
- 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.
- 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.
- 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.
4. Common course additions
1D and 2D kinematics · Circuits and Ohm’s law
- 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.
- 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.