China 高二 Physics
Chapters: 9
1. Selective 1 Ch.1 Momentum
Momentum; impulse; momentum theorem · Conservation of momentum · Elastic and inelastic collisions; recoil, rockets
- 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.
- 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.
2. Selective 1 Ch.2 Oscillations
Simple harmonic motion · Pendulum; measuring g · Forced oscillation; resonance
- 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.
- 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.
- 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.
3. Selective 1 Ch.3 Mechanical waves
Formation and description of waves · Reflection, refraction, diffraction, interference · Doppler effect
- 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.
- 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.
- 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.
- 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).
4. Selective 1 Ch.4 Light
Refraction; refractive index · Total internal reflection; optical fibre · Interference; double-slit wavelength · Diffraction; polarisation; lasers
- 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, 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).
- 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.
- 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.
5. Selective 2 Ch.1 Ampère and Lorentz forces
Force on current-carrying wire · Force on moving charges; circular motion in B · Mass spectrometer and cyclotron
- 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.
- 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).
6. Selective 2 Ch.2 Electromagnetic induction
Lenz's law · Faraday's law · Eddy currents; mutual and self-induction
- 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).
- 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.
7. Selective 2 Ch.3 Alternating current
AC and its description · Transformers · Power transmission
- 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.
- 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.
- 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).
8. Selective 2 Ch.4 EM oscillations and waves
LC oscillation; Maxwell's theory · Transmission and reception of radio waves · EM spectrum
- 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.
- 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.
- 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.
9. Selective 2 Ch.5 Sensors
Sensors and simple automatic control
- Sensors: How Machines Sense the World – A sensor turns a physical quantity (light, temperature, distance, moisture, sound, pressure) into an electrical signal. Analogue sensors give a smooth voltage; an ADC turns it into a number the computer can use. A controller compares the number with a threshold and switches an actuator, often through a relay. Readings taken at regular times are data logging. Good sensors have the right range, sensitivity, accuracy and response time.