📚 Last-Minute Revision Notes for CIE A-Level Physics | CIE A-Level 物理考前冲刺笔记
As your CIE A-Level Physics exam approaches, these condensed revision notes highlight the essential concepts, key formulas, and common pitfalls. Designed for quick review, this guide covers the core topics across the syllabus to boost your confidence and memory before the test.
随着 CIE A-Level 物理考试的临近，这篇浓缩的复习笔记梳理了核心概念、关键公式和常见易错点，帮你高效回顾考纲重点，提升考前信心。
1. Mechanics: Kinematics & Dynamics | 运动学与动力学
For constant acceleration in a straight line, three equations of motion connect displacement, velocity, acceleration and time.
在匀加速直线运动中，三个运动方程建立了位移、速度、加速度和时间的关系。
v = u + at
s = ut + ½at²
v² = u² + 2as
Always choose a consistent sign convention (e.g. upward as positive) and apply it to all vector quantities.
务必规定统一的正方向（如向上为正），并将此用于全部矢量。
The total momentum of a system remains constant if no external resultant force acts. For two-dimensional collisions, resolve momenta into perpendicular components before applying conservation.
若系统不受外力的合力作用，总动量保持不变。在二维碰撞中，先将动量分解到两个垂直方向再运用守恒。
Impulse = FΔt = Δp
Impulse is a vector; the area under a force–time graph equals the impulse (and thus the change in momentum).
冲量为矢量；力–时间图下方的面积等于冲量，即动量的变化。
2. Forces, Energy and Power | 力、能量和功率
Work done by a constant force is W = Fd cosθ, where θ is the angle between force and displacement. Energy is transferred and can change between kinetic, potential, thermal, etc.
恒力所做的功为 W = Fd cosθ，θ 是力与位移的夹角。能量可以传递，能在动能、势能、内能等形式间转化。
K.E. = ½mv²
ΔG.P.E. = mgΔh
Elastic P.E. = ½kx²
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted.
能量守恒原理指出能量不会凭空产生或消失，只能传递或转换。
Power is the rate of doing work: P = W/t = Fv (for constant force in the direction of motion). Efficiency = useful output power / total input power.
功率是做功的速率：P = W/t = Fv（恒力沿运动方向）。效率 = 有用输出功率 / 总输入功率。
3. Circular Motion & Gravitation | 圆周运动与引力
An object moving in a circle at constant speed has a centripetal acceleration directed towards the centre: a = v²/r = rω². The centripetal force is F = mv²/r = mrω² and is always perpendicular to velocity.
匀速圆周运动的物体具有指向圆心的向心加速度：a = v²/r = rω²。向心力为 F = mv²/r = mrω²，方向始终与速度垂直。
Newton’s law of universal gravitation gives the force between point masses: F = GMm/r². The gravitational field strength at a point is g = GM/r², and gravitational potential is φ = −GM/r.
牛顿万有引力定律给出质点间的引力：F = GMm/r²。引力场强度为 g = GM/r²，引力势为 φ = −GM/r。
Escape speed: v = √(2GM/r)
Geostationary satellites orbit with a period of 24 hours in the equatorial plane; their orbital radius can be found using GMm/r² = mrω² and Kepler’s third law T² ∝ r³.
地球同步卫星周期为 24 小时，位于赤道平面内；利用 GMm/r² = mrω² 及开普勒第三定律 T² ∝ r³ 可求其轨道半径。
4. Oscillations & Waves | 振动与波动
Simple harmonic motion (SHM) requires a restoring force proportional to displacement: a = −ω²x. The period of a mass-spring system is T = 2π√(m/k) and of a simple pendulum T = 2π√(l/g) for small amplitudes.
简谐运动要求回复力与位移成正比：a = −ω²x。弹簧振子周期为 T = 2π√(m/k)，单摆在小振幅下周期为 T = 2π√(l/g)。
Wave speed is v = fλ. The intensity of a wave is proportional to the square of its amplitude. For coherent sources, double-slit interference gives fringe separation Δx = λD / a, where a is slit separation and D the distance to the screen.
波速为 v = fλ。波的强度与振幅的平方成正比。相干光源在双缝干涉中，条纹间距 Δx = λD / a，a 为缝距，D 为屏距。
Diffraction grating: d sinθ = nλ
Constructive interference occurs when the path difference is nλ, and destructive interference when it is (n+½)λ.
光程差为 nλ 时出现加强（亮纹），为 (n+½)λ 时出现减弱（暗纹）。
5. Electric Fields & Capacitance | 电场与电容
Coulomb’s law for two point charges: F = kQq/r², with k = 1/(4πε₀). Electric field strength E = F/q. In a uniform field between parallel plates, E = V/d and the force on a charge is F = qV/d.
库仑定律：F = kQq/r²，其中 k = 1/(4πε₀)。电场强度 E = F/q；平行板间的匀强电场中 E = V/d，点电荷受力 F = qV/d。
Capacitance C = Q/V. The energy stored in a capacitor is given by E = ½QV = ½CV² = ½Q²/C. For a discharging capacitor through a resistor, the charge decays exponentially: Q = Q₀ exp(−t/RC), and the time constant is τ = RC.
电容 C = Q/V。电容器储存的能量为 E = ½QV = ½CV² = ½Q²/C。对电阻放电时，电荷指数衰减：Q = Q₀ exp(−t/RC)，时间常数为 τ = RC。
In series, the total capacitance 1/C_total = 1/C₁ + 1/C₂ + …; in parallel, C_total = C₁ + C₂ + ….
串联时总电容满足 1/C_total = 1/C₁ + 1/C₂ + …；并联时 C_total = C₁ + C₂ + …。
6. Current Electricity & Circuits | 电流与电路
Ohm’s law for an ohmic conductor at constant temperature: V = IR. Resistance arises from collisions between electrons and the lattice; resistivity ρ = RA/l, so R = ρl/A.
欧姆定律（恒温下欧姆导体）：V = IR。电阻源于电子与晶格的碰撞；电阻率 ρ = RA/l，因此 R = ρl/A。
A source of emf ε has internal resistance r, so the terminal potential difference is V = ε − Ir. In a potential divider, the output voltage from a resistor R₁ in series with R₂ is V_out = [R₁/(R₁+R₂)] × ε.
电动势为 ε 的电源有内阻 r，端电压为 V = ε − Ir。在分压电路中，串联电阻 R₁ 与 R₂ 的输出电压为 V_out = [R₁/(R₁+R₂)] × ε。
Power: P = IV = I²R = V²/R
Kirchhoff’s first law: total current entering a junction equals total current leaving. Kirchhoff’s second law: the sum of emfs around any closed loop equals the sum of potential differences.
基尔霍夫第一定律：流入节点的电流之和等于流出电流之和；第二定律：闭合回路中电动势的代数和等于各段电位降的代数和。
7. Magnetic Fields & Electromagnetic Induction | 磁场与电磁感应
Force on a current-carrying conductor in a magnetic field: F = BIL sinθ, where θ is the angle between the current and the B-field. On a moving charge, the force is F = Bqv sinθ.
磁场对电流的作用力：F = BIL sinθ，θ 为电流与磁场的夹角；对运动电荷的作用力为 F = Bqv sinθ。
Magnetic flux Φ = BA cosθ; flux linkage = NΦ. Faraday’s law states that the induced emf is proportional to the rate of change of flux linkage: ε = −d(NΦ)/dt. The negative sign indicates Lenz’s law: the induced current opposes the change causing it.
磁通量 Φ = BA cosθ；磁链 = NΦ。法拉第定律指出感应电动势与磁链变化率成正比：ε = −d(NΦ)/dt，负号代表楞次定律：感应电流的效应阻碍引起它的变化。
Transformer: Vₚ / Vₛ = Nₚ / Nₛ
A charged particle moving perpendicular to a uniform B-field follows a circular path of radius r = mv/(Bq). The Hall voltage is V_H = BI/(nqt), allowing measurement of magnetic field or charge carrier density.
带电粒子垂直于匀强磁场运动时做匀速圆周运动，半径 r = mv/(Bq)。霍尔电压为 V_H = BI/(nqt)，可用于测量磁场或载流子浓度。
8. Thermal Physics & Ideal Gases | 热物理与理想气体
Temperature is a measure of the average random kinetic energy of particles. Absolute zero is 0 K (−273 °C). Internal energy is the sum of the random kinetic and potential energies of the particles in a system.
温度是粒子无规则运动平均动能的量度；绝对零度为 0 K (−273 °C)。内能是系统内所有粒子随机动能与势能之和。
Q = mcΔθ (specific heat capacity) Q = mL (specific latent heat)
Ideal gas equation: pV = nRT = NkT. The kinetic theory model assumes perfectly elastic collisions, negligible volume of particles, no intermolecular forces, and that average kinetic energy ∝ T.
理想气体状态方程：pV = nRT = NkT。分子运动论假设：完全弹性碰撞、分子自身体积忽略、无分子间作用力，且平均动能与 T 成正比。
Average KE per molecule = (3/2)kT
First law of thermodynamics: ΔU = Q + W (using the sign convention: Q positive when added to the system, W positive when work is done ON the system). For an adiabatic change, pV^γ = constant, where γ = Cₚ/Cᵥ.
热力学第一定律：ΔU = Q + W（符号约定：系统吸热 Q 为正，外界对系统做功 W 为正）。绝热过程满足 pV^γ = 常数，γ = Cₚ/Cᵥ。
9. Quantum & Nuclear Physics | 量子与核物理
The photoelectric effect demonstrates the
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