Year 13 CIE Physics Formula and Theorem Quick Reference Handbook | Year 13 CIE 物理：公式定理速查手册

📚 Year 13 CIE Physics Formula and Theorem Quick Reference Handbook | Year 13 CIE 物理：公式定理速查手册

This quick reference handbook compiles essential formulas, theorems, and key relationships for CIE A Level Physics (Year 13). Each section presents core concepts with their mathematical expressions, ideal for last-minute revision.

本速查手册汇编了 CIE A Level 物理（Year 13）的核心公式、定理和关键关系。每一部分都给出了核心概念及其数学表达式，非常适合考前最后复习。

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1. Circular Motion | 圆周运动

When an object moves in a circle at constant speed, its velocity direction changes continuously, resulting in a centripetal acceleration directed towards the centre.

当物体以恒定速率做圆周运动时，速度方向不断变化，产生指向圆心的向心加速度。

Angular velocity: ω = Δθ/Δt. Linear speed: v = rω.

角速度：ω = Δθ/Δt。线速度：v = rω。

Centripetal acceleration: a = v²/r = rω².

向心加速度：a = v²/r = rω²。

Centripetal force: F = mv²/r = mrω².

向心力：F = mv²/r = mrω²。

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2. Gravitational Fields | 引力场

Newton’s law of gravitation describes the attractive force between two point masses.

牛顿万有引力定律描述了两个质点之间的吸引力。

Gravitational force: F = G m₁ m₂ / r².

引力：F = G m₁ m₂ / r²。

Gravitational field strength: g = F/m = GM/r².

引力场强度：g = F/m = GM/r²。

Gravitational potential: V = -GM/r (zero at infinity).

引力势：V = -GM/r（无穷远处为零）。

Orbital speed for a satellite: v = √(GM/r); for near-surface orbit v = √(gR).

卫星的轨道速度：v = √(GM/r)；近地轨道速度 v = √(gR)。

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3. Simple Harmonic Motion | 简谐运动

Simple harmonic motion (SHM) occurs when the restoring force is proportional to the displacement and directed towards equilibrium.

简谐运动发生在回复力与位移成正比且指向平衡位置时。

Defining equation: a = -ω²x.

定义方程：a = -ω²x。

Displacement: x = x₀ sin(ωt) or x = x₀ cos(ωt).

位移：x = x₀ sin(ωt) 或 x = x₀ cos(ωt)。

Velocity: v = ±ω√(x₀² – x²); maximum speed v_max = ωx₀.

速度：v = ±ω√(x₀² – x²)；最大速率 v_max = ωx₀。

Period of mass-spring system: T = 2π√(m/k); simple pendulum: T = 2π√(l/g).

弹簧振子的周期：T = 2π√(m/k)；单摆周期：T = 2π√(l/g)。

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4. Thermal Physics & Ideal Gases | 热物理与理想气体

The ideal gas equation and kinetic theory link macroscopic properties to microscopic behaviour.

理想气体状态方程和分子动理论将宏观性质与微观

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