📚 A-Level CIE Physics: Formula Summary Handbook | A-Level CIE 物理：公式汇总手册
This article provides a comprehensive summary of essential formulas for the CIE A-Level Physics syllabus, covering mechanics, thermal physics, waves, electricity, fields, nuclear physics and more. Each section includes key equations, definitions of symbols, and brief notes to support revision and problem-solving.
本文为 CIE A-Level 物理教学大纲提供全面的公式汇总，涵盖力学、热学、波动、电学、场、核物理与量子物理等模块。每个小节列出核心方程、符号定义与简要说明，便于复习和解题参考。
1. Kinematics | 运动学
Kinematics describes the motion of objects without considering its causes. For uniformly accelerated motion along a straight line, the SUVAT equations are used, where u = initial velocity, v = final velocity, a = constant acceleration, s = displacement, and t = time.
运动学描述物体的运动而不涉及运动的原因。对于匀加速直线运动，使用 SUVAT 方程，其中 u = 初速度，v = 末速度，a = 恒定加速度，s = 位移，t = 时间。
v = u + a t
This equation gives the final velocity after a time t of constant acceleration.
该方程给出恒定加速度下经过时间 t 后的末速度。
s = u t + ½ a t²
Displacement as a function of time, including the contribution of acceleration.
位移作为时间的函数，包含加速度的贡献。
v² = u² + 2 a s
Relates velocity and displacement without involving time directly.
将速度与位移联系起来，不直接包含时间。
s = ½ (u + v) t
Displacement equals average velocity multiplied by time.
位移等于平均速度乘以时间。
For free fall under gravity, replace a with g (acceleration of free fall, ≈ 9.81 m s⁻²) and consider vertical displacement. Projectile motion can be analysed by resolving initial velocity into horizontal and vertical components.
对于自由落体，用 g（自由落体加速度，约 9.81 m s⁻²）代替 a，并考虑垂直位移。抛体运动可通过将初速度分解为水平分量和竖直分量来分析。
2. Dynamics & Forces | 动力学与力
Dynamics links forces to changes in motion. Newton’s laws provide the foundation.
动力学将力与运动的变化联系起来。牛顿定律提供了基础。
Σ F = m a
Newton’s second law: the net force acting on a body equals its mass times acceleration.
牛顿第二定律：作用在物体上的合力等于质量乘以加速度。
F = Δ p / Δ t
Force as the rate of change of momentum (p = m v). For constant force, impulse = F Δ t = Δ p.
力等于动量的变化率（p = m v）。对于恒力，冲量 = F Δ t = Δ p。
W = m g
Weight is the gravitational force on a mass m in a gravitational field of strength g.
重量是质量为 m 的物体在引力场强度为 g 时所受的重力。
The principle of conservation of momentum: in a closed system with no external forces, total momentum before collision equals total momentum after collision.
动量守恒定律：在无外力的封闭系统中，碰撞前的总动量等于碰撞后的总动量。
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
For a perfectly elastic collision, kinetic energy is also conserved.
对于完全弹性碰撞，动能也守恒。
3. Work, Energy & Power | 功、能与功率
Work and energy are scalar quantities measured in joules (J). Power is the rate of doing work.
功和能是标量，单位为焦耳 (J)。功率是做功的速率。
W = F s cos θ
Work done by a constant force F acting over a displacement s at an angle θ to the force.
恒力 F 在位移 s 上做的功，其中 θ 为力与位移的夹角。
Eₖ = ½ m v²
Kinetic energy of a body of mass m moving with speed v.
质量为 m、速度为 v 的物体的动能。
Δ Eₚ = m g Δ h
Change in gravitational potential energy near the Earth’s surface.
地表附近重力势能的变化。
Eₑ = ½ k x²
Elastic potential energy stored in a spring of force constant k stretched or compressed by x.
劲度系数为 k 的弹簧被拉伸或压缩 x 时储存的弹性势能。
P = W / t = F v
Power: work done per unit time, also given by force × velocity when force is parallel to motion.
功率：单位时间做的功，当力与运动方向平行时也可表示为力乘速度。
efficiency = useful output power / input power
Efficiency is the ratio of useful output to total input, often expressed as a percentage.
效率为有用输出与总输入的比值，通常以百分比表示。
4. Circular Motion & Gravitation | 圆周运动与引力
An object moving in a circle at constant speed has an acceleration directed towards the centre.
以恒定速率做圆周运动的物体具有指向圆心的加速度。
ω = 2 π f = 2 π / T
Angular velocity ω related to frequency f and period T.
角速度 ω 与频率 f 和周期 T 的关系。
v = r ω
Linear speed v at radius r from the centre.
离中心半径 r 处的线速度 v。
a = r ω² = v² / r
Centripetal acceleration towards the centre.
向心加速度。
F = m r ω² = m v² / r
Centripetal force required to keep a mass m in circular motion.
维持质量为 m 的物体做圆周运动所需的向心力。
Newton’s law of gravitation:
牛顿万有引力定律：
F = G M m / r²
Gravitational force between two point masses M and m separated by distance r; G is the universal gravitational constant.
两个质点 M 和 m 之间距离 r 时的引力；G 为万有引力常量。
g = G M / r²
Gravitational field strength at a distance r from a point mass M.
距离点质量 M 为 r 处的引力场强度。
U = – G M m / r
Gravitational potential energy in a radial field (zero at infinity).
径向场中的引力势能（无穷远处为零）。
T² ∝ r³
Kepler’s third law: for planets orbiting the same central mass, the square of the orbital period is proportional to the cube of the orbital radius.
开普勒第三定律：对于绕同一中心天体的行星，轨道周期的平方与轨道半径的立方成正比。
5. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when the acceleration is directly proportional to the displacement from equilibrium and is always directed towards the equilibrium position.
当加速度与偏离平衡位置的位移成正比且总指向平衡位置时，物体做简谐运动。
a = – ω² x
Defining equation for SHM, where ω is the angular frequency.
简谐运动的定义方程，其中 ω 为角频率。
x = A cos(ω t)
Displacement–time equation starting from maximum displacement A (amplitude).
从最大位移 A（振幅）开始的位移–时间方程。
v = ± ω √(A² – x²)
Velocity as a function of displacement. Maximum speed is v_max = ω A.
速度随位移变化的关系。最大速度为 v_max = ω A。
T = 2 π / ω
Period of oscillation. For a mass–spring system: T = 2 π √(m / k). For a simple pendulum: T = 2 π √(l / g) (small angles).
振动周期。对于弹簧振子：T = 2 π √(m / k)；对于单摆（小角度）：T = 2 π √(l / g)。
E_total = ½ m ω² A²
Total mechanical energy (constant) in an undamped SHM system.
无阻尼简谐运动系统的总机械能（常量）。
6. Thermal Physics | 热学
Thermal physics deals with temperature, heat transfer, kinetic theory of gases and the laws of thermodynamics.
热学研究温度、热传递、气体动理论以及热力学定律。
p V = n R T
Ideal gas equation: pressure × volume = number of moles × molar gas constant × absolute temperature.
理想气体状态方程：压强 × 体积 = 摩尔数 × 摩尔气体常量 × 绝对温度。
N = 1/3 N m ⟨c²⟩ / V ??
A better representation: p V = 1/3 N m ⟨c²⟩ or p = 1/3 ρ ⟨c²⟩. We’ll use: p = 1/3 ρ ⟨c²⟩ where ρ is density and ⟨c²⟩ is the mean square speed.
气体压强微观表达式：p = 1/3 ρ ⟨c²⟩，其中 ρ 为密度，⟨c²⟩ 为均方速率。
Eₖ_avg = (3/2) k T
Average translational kinetic energy of a molecule in an ideal gas, where k is Boltzmann’s constant.
理想气体分子的平均平移动能，k 为玻尔兹曼常数。
Δ U = q + W
First law of thermodynamics: increase in internal energy equals thermal energy added plus work done on the system (sign conventions may vary).
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