📚 Quick Reference Handbook of Formulas and Theorems for CIE Pre-U Physics | CIE Pre-U 物理公式定理速查手册
This handbook provides a concise summary of the essential formulas, theorems, and constants needed for the CIE Pre-U Physics examination. Each section pairs an explanation in English with the corresponding Chinese translation, and key equations are highlighted. Use this guide to reinforce your understanding and as a quick reference during revision.
本手册简要总结了 CIE Pre-U 物理考试所需的核心公式、定理和常数。每个部分将英文解释与相应的中文翻译配对，关键方程突出显示。在复习过程中，可将本手册用作快速参考，以巩固理解。
1. Kinematics | 运动学
For constant acceleration a, the displacement s, initial velocity u, final velocity v and time t are linked by the SUVAT equations: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. In projectile motion, horizontal velocity is constant, while vertical motion is uniformly accelerated by g. The range on level ground is R = (u² sin 2θ)/g and the maximum height is H = (u² sin²θ)/(2g).
对于恒定加速度 a，位移 s、初速度 u、末速度 v 和时间 t 通过 SAT 方程关联：v = u + at, s = ut + ½at², v² = u² + 2as 以及 s = ½(u + v)t。在抛体运动中，水平分速度不变，竖直方向以 g 做匀变速运动。水平地面上的射程为 R = (u² sin 2θ)/g，最大高度为 H = (u² sin²θ)/(2g)。
2. Dynamics | 动力学
Newton's second law: the net force produces an acceleration directly proportional to the force and inversely proportional to the mass: F = ma. Linear momentum is p = mv. Impulse equals change in momentum: FΔt = Δp. In a closed system, total momentum is conserved.
牛顿第二定律：合外力产生与力成正比、与质量成反比的加速度：F = ma。线动量为 p = mv。冲量等于动量的变化：FΔt = Δp。在封闭系统中，总动量守恒。
Kinetic friction is fₖ = μₖN, where μₖ is the coefficient of kinetic friction. The maximum static friction is fₛ ≤ μₛN. Hooke's law for a spring gives restoring force F = -kx, and the stored elastic potential energy is Eₚ = ½kx².
动摩擦力为 fₖ = μₖN，其中 μₖ 为动摩擦系数。最大静摩擦力为 fₛ ≤ μₛN。弹簧的胡克定律给出回复力 F = -kx，储存的弹性势能为 Eₚ = ½kx²。
3. Work, Energy and Power | 功、能与功率
Work done by a constant force is W = Fs cosθ. Kinetic energy KE = ½mv² and gravitational potential energy near the Earth's surface is GPE = mgh. The work–energy principle states that the net work equals the change in kinetic energy. Power is the rate of doing work: P = W/t = Fv. Efficiency is useful output power divided by input power.
恒力做功为 W = Fs cosθ。动能为 KE = ½mv²，地球表面附近的重力势能为 GPE = mgh。功能原理指出，合外力做功等于动能的变化量。功率是做功的速率：P = W/t = Fv。效率为有用输出功率与输入功率之比。
4. Circular Motion and Gravitation | 圆周运动与万有引力
For uniform circular motion, centripetal acceleration a = v²/r = rω² and centripetal force F = mv²/r = mrω². Angular velocity ω = 2π/T = 2πf. Newton's law of gravitation: F = -GMm/r². Gravitational field strength g = GM/r². Potential energy is U = -GMm/r. The orbital speed for a circular orbit is v = √GM/r, and the period satisfies T² ∝ r³ (Kepler's third law).
对于匀速圆周运动，向心加速度 a = v²/r = rω²，向心力 F = mv²/r = mrω²。角速度 ω = 2π/T = 2πf。牛顿万有引力定律：F = -GMm/r²。引力场强度 g = GM/r²。势能为 U = -GMm/r。圆轨道的轨道速度为 v = √GM/r，周期满足 T² ∝ r³（开普勒第三定律）。
5. Simple Harmonic Motion and Waves | 简谐运动与波
In SHM, displacement x = A cos(ωt + φ), and acceleration is proportional to displacement: a = -ω²x. Velocity can be expressed as v = ±ω√A² – x². The period of a mass–spring system is T = 2π√m/k, and for a simple pendulum T = 2π√l/g. Wave speed is v = fλ. For double-slit interference, fringe separation Δy = λD/s. The diffraction grating condition is d sinθ = nλ.
在简谐运动中，位移
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