📚 A2 Physics: Last-Minute Revision Notes | A2 物理考前冲刺笔记
This article provides a concise, formula-packed summary of the most important A2 Physics topics. Use it to quickly refresh your memory before the exam, focusing on definitions, equations, graphs and common pitfalls.
本文整理了 A2 物理最核心的概念、公式与图像，是考前快速回顾的冲刺笔记。读一遍，重点公式和易错点就清楚了。
1. Circular Motion | 圆周运动
Angular velocity ω = Δθ/Δt, measured in rad s⁻¹. Linear speed v and radius r are linked by v = ωr.
角速度 ω = Δθ/Δt，单位 rad s⁻¹。线速度 v 与半径 r 满足 v = ωr。
Centripetal acceleration always points towards the centre: a = v²/r = ω²r.
向心加速度始终指向圆心：a = v²/r = ω²r。
The net force producing circular motion is the centripetal force: F = mv²/r = mω²r. It is not a new kind of force; it can be tension, gravity, friction or a normal reaction.
产生圆周运动的合力是向心力：F = mv²/r = mω²r。它不是新的力，可以是张力、引力、摩擦力或支持力。
Centripetal force is always perpendicular to the velocity, so it does no work and does not change speed.
向心力始终垂直于速度，因此不做功，不改变速率。
2. Gravitational Fields | 引力场
Newton’s law of gravitation: F = G m₁ m₂ / r². G = 6.67 × 10⁻¹¹ N m² kg⁻².
牛顿万有引力定律：F = G m₁ m₂ / r²。G = 6.67 × 10⁻¹¹ N m² kg⁻²。
Gravitational field strength g = F/m = GM / r². Near the Earth’s surface g ≈ 9.81 N kg⁻¹.
引力场强度 g = F/m = GM / r²。地球表面附近 g ≈ 9.81 N kg⁻¹。
Gravitational potential V = -GM/r (scalar). Escape velocity from a planet of mass M and radius R: vesc = √(2GM/R) = √(2gR).
引力势 V = -GM/r（标量）。从质量为 M、半径为 R 的行星逃逸的速度：vesc = √(2GM/R) = √(2gR)。
For circular orbits, Kepler’s third law: T² ∝ r³. Geostationary satellites have T = 24 h and orbit above the equator.
对于圆形轨道，开普勒第三定律：T² ∝ r³。地球同步卫星的周期 T = 24 h，轨道位于赤道上方。
3. Simple Harmonic Motion | 简谐运动
SHM is defined by a = -ω²x. The restoring force F = -kx, and ω = √(k/m).
简谐运动的定义是 a = -ω²x。回复力 F = -kx，且 ω = √(k/m)。
Displacement: x = A cos(ωt + φ). Velocity: v = -Aω sin(ωt + φ). Maximum speed vmax = ωA.
位移：x = A cos(ωt + φ)。速度：v = -Aω sin(ωt + φ)。最大速度 vmax = ωA。
Period: for a mass-spring system T = 2π √(m/k), for a simple pendulum T = 2π √(l/g).
周期：弹簧振子 T = 2π √(m/k)，单摆 T = 2π √(l/g)。
Total energy Etotal = ½ m ω² A². Kinetic energy Ek = ½ m ω² (A² – x²), potential energy Ep = ½ m ω² x².
总能量 Etotal = ½ m ω² A²，动能 Ek = ½ m ω² (A² – x²)，势能 Ep = ½ m ω² x²。
Resonance occurs when the driving frequency matches the natural frequency, giving maximum amplitude. Light damping slightly reduces the resonant frequency.
当驱动频率等于固有频率时发生共振，振幅最大。轻阻尼会使共振频率略为降低。
4. Thermal Physics and Ideal Gases | 热物理与理想气体
Temperature is proportional to the average translational kinetic energy of particles. The internal energy of an ideal gas depends only on its temperature.
温度与分子平均平动动能成正比。理想气体的内能仅取决于温度。
Specific heat capacity: Q = mcΔθ. Specific latent heat: Q = mL.
比热容：Q = mcΔθ；潜热：Q = mL。
Ideal gas equation: pV = nRT = NkT, where k = 1.38 × 10⁻²³ J K⁻¹ and NA = 6.02 × 10²³ mol⁻¹.
理想气体状态方程：pV = nRT = NkT，其中 k = 1.38 × 10⁻²³ J K⁻¹，NA = 6.02 × 10²³ mol⁻¹。
Mean kinetic energy of a gas molecule: ½ m ⟨c²⟩ = (3/2) kT. The root-mean-square speed crms = √(3kT/m).
气体分子平均动能：½ m ⟨c²⟩ = (3/2) kT。方均根速率 crms = √(3kT/m)。
For a fixed mass of ideal gas, pV/T = constant. The three gas laws (Boyle, Charles, pressure law) follow from this.
一定质量理想气体，pV/T = 常数。由此可导出三大气体定律。
5. Electric Fields | 电场
Coulomb’s law: F = k Q₁ Q₂ / r², where k = 1/(4πε₀). Electric field strength E = F/q, a vector.
库仑定律：F = k Q₁ Q₂ / r²，其中 k = 1/(4πε₀)。电场强度 E = F/q，是矢量。
For a point charge, E = k Q / r². For a uniform field between parallel plates, E = V/d.
点电荷电场 E = k Q / r²；平行板间匀强电场 E = V/d。
Electric potential V = k Q / r is a scalar. The work done moving a charge q between two potentials is ΔW = q ΔV.
电势 V = k Q / r 是标量。移动电荷 q 经过电势差所作的功 ΔW = q ΔV。
A charged particle moving in a uniform electric field follows a parabolic path. Horizontal motion is uniform, vertical acceleration a = qE/m.
带电粒子在匀强电场中运动轨迹为抛物线，水平方向匀速，竖直加速度 a = qE/m。
6. Capacitance | 电容
Capacitance C = Q/V, unit Farad (F). For a parallel plate capacitor, C = ε₀ A / d. With a dielectric, C = εᵣ ε₀ A / d.
电容定义 C = Q/V，单位法拉 (F)。平行板电容器 C = ε₀ A / d；有介质时 C = εᵣ ε₀ A / d。
Energy stored in a capacitor: W = ½ Q V = ½ C V² = ½ Q² / C.
电容器储存的能量：W = ½ Q V = ½ C V² = ½ Q² / C。
Charging: Q = Q₀ (1 – e-t/RC), V
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