China 高一 Physics
Chapters: 13
1. Compulsory 1 Ch.1 Describing motion
Particle, reference frame, time, displacement · Velocity · Acceleration
- 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.
2. Compulsory 1 Ch.2 Uniformly accelerated motion
v–t and x–t relations · Free fall
- 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.
3. Compulsory 1 Ch.3 Forces
Gravity, elastic force, Hooke's law · Friction · Newton's third law · Composition and resolution of forces · Equilibrium of concurrent forces
- 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.
- 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.
- 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.
- 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.
- 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.
4. Compulsory 1 Ch.4 Force and motion
Newton's first and second laws · SI mechanical units · Overweight and weightlessness
- 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.
- 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.
- 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.
5. Compulsory 2 Ch.5 Projectile motion
Curvilinear motion; composition of motion · Projectile motion
- 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.
- 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.
6. Compulsory 2 Ch.6 Circular motion
Circular motion; centripetal force and acceleration; centrifugal effects
- 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)].
7. Compulsory 2 Ch.7 Gravitation and spaceflight
Planetary motion · Law of gravitation and its achievements · Spaceflight; cosmic velocities · Relativity and limits of Newtonian mechanics
- 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.
- 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).
- 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).
- 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.
8. Compulsory 2 Ch.8 Conservation of mechanical energy
Work and power · Gravitational PE · Kinetic energy theorem · Conservation of mechanical energy
- 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.
- 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.
9. Compulsory 3 Ch.9 Electrostatics
Charge; Coulomb's law · Electric field · Uses and prevention of static
- 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.
- 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).
- 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.
10. Compulsory 3 Ch.10 Energy in electrostatic fields
Potential energy, potential, potential difference · Capacitance · Charged particles in fields
- 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.
- 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.
11. Compulsory 3 Ch.11 Circuits
Current; resistance; resistivity · Series and parallel · Using a multimeter
- 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.
- 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.
- 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.
12. Compulsory 3 Ch.12 Electric energy
Energy in circuits; Joule heating · Closed-circuit Ohm's law; EMF and internal resistance · Energy and sustainable development
- 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.
- 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.
- Minerals and Energy Resources – Minerals are natural substances found in rocks. They are metallic (ferrous or non-ferrous), non-metallic, or energy minerals. Energy comes from conventional sources like coal, petroleum, natural gas and electricity, and from non-conventional sources like sun, wind, nuclear, biogas, tides and heat from the Earth. Both minerals and energy must be conserved.
13. Compulsory 3 Ch.13 Electromagnetic induction and waves (intro)
Magnetic field; flux · Electromagnetic induction · Electromagnetic waves · Energy quantisation
- 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.
- 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 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.