📚 Year 13 CCEA Physics: Quick-Reference Formula and Theorem Handbook | CCEA Year 13 物理公式定理速查手册
This handbook presents the essential formulas and theorems required for Year 13 CCEA AS Physics. Every key relationship is stated clearly in symbols, accompanied by concise explanations in English and Chinese to aid dual-language revision.
本手册列出 CCEA Year 13 AS 物理所需的核心公式和定理。每个重要的关系式都用符号清晰表达，并配有简短的中英双语说明，方便双语复习。
1. Kinematics Equations | 运动学方程
For motion with constant acceleration a, the following equations link initial velocity u, final velocity v, displacement s, and time t. They apply only when acceleration is uniform.
对于恒定加速度 a 的运动，以下方程联系了初速度 u、末速度 v、位移 s 和时间 t。它们仅在加速度恒定时适用。
v = u + at – The final velocity equals the initial velocity plus the change due to acceleration over time.
v = u + at – 末速度等于初速度加上加速度与时间的乘积。
s = ut + ½at² – Displacement is the product of initial velocity and time plus half the acceleration multiplied by the square of the time.
s = ut + ½at² – 位移等于初速度乘时间加上加速度乘以时间平方的一半。
v² = u² + 2as – Relates final velocity and displacement without involving time.
v² = u² + 2as – 将末速度与位移联系起来，不显含时间。
2. Newton's Laws and Dynamics | 牛顿定律与动力学
Newton's three laws govern the motion of objects when forces act. The resultant force F produces an acceleration a proportional to the mass m.
牛顿三定律支配着物体受力时的运动。合力 F 产生与质量 m 成反比的加速度 a。
First Law: A body remains at rest or in uniform motion unless acted upon by a resultant force.
第一定律: 若无合力作用，物体保持静止或匀速直线运动状态。
F = ma – Second Law: resultant force equals mass times acceleration. Always use the resultant force in the direction of acceleration.
F = ma – 第二定律：合力等于质量乘以加速度。必须取加速度方向上的合力。
Third Law: If body A exerts a force on body B, then B exerts an equal and opposite force on A.
第三定律: 若物体 A 对 B 施加力，则 B 对 A 施加大小相等、方向相反的力。
3. Work, Energy and Power | 功、能与功率
Work done by a force is the product of the force and the displacement in the direction of the force. Energy is the capacity to do work; it is conserved in isolated systems.
力做的功是力与沿力方向的位移的乘积。能量是做功的本领；在孤立系统中能量守恒。
W = F s cos θ – Work done by a constant force F moving through displacement s, where θ is the angle between F and s.
W = F s cos θ – 恒力 F 通过位移 s 做的功，θ 为力与位移的夹角。
Eₖ = ½mv² – Kinetic energy of an object of mass m moving at speed v.
Eₖ = ½mv² – 质量为 m、速度为 v 的物体的动能。
Eₚ = mgh – Gravitational potential energy near Earth's surface (uniform g).
Eₚ = mgh – 近地面重力势能（均匀重力场 g）。
P = W/t = Fv – Power is the rate of doing work; for a constant force, it equals force times velocity.
P = W/t = Fv – 功率是做功的速率；对于恒力，功率等于力乘以速度。
4. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity. In the absence of external forces, total momentum is conserved. Impulse equals the change in momentum.
动量是质量与速度的乘积。无外力时，总动量守恒。冲量等于动量的变化量。
p = mv – Linear momentum.
p = mv – 线动量。
FΔt = Δp – Impulse–momentum theorem: the impulse of the resultant force equals the change in momentum.
FΔt = Δp – 冲量-动量定理：合力的冲量等于动量的变化。
Conservation of momentum: Σ p before = Σ p after for an isolated system.
动量守恒: 孤立系统内，碰撞前后的总动量相等。
5. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
When a solid is stretched, it experiences stress and strain. Hooke's law applies up to the limit of proportionality. Young modulus measures stiffness.
固体被拉伸时产生应力和应变。胡克定律在比例极限内成立。杨氏模量衡量材料的刚度。
σ = F/A – Tensile stress: force per unit cross-sectional area.
σ = F/A – 拉伸应力：单位横截面积上的力。
ε = ΔL/L₀ – Tensile strain: extension divided by original length.
ε = ΔL/L₀ – 拉伸应变：伸长量除以原长。
E = σ/ε – Young modulus, valid within the elastic limit. Also expressed as E = (FL₀)/(AΔL).
E = σ/ε – 杨氏模量，在弹性极限内成立。也可写作 E = (FL₀)/(AΔL)。
Elastic potential energy: E = ½FΔL = ½k(ΔL)² where k is the spring constant.
弹性势能: E = ½FΔL = ½k(ΔL)²，其中 k 为弹簧常数。
6. Direct Current Circuits (Basic Laws) | 直流电路（基本定律）
Ohm's law and resistivity govern the behaviour of circuit components. Kirchhoff's laws ensure conservation of charge and energy within a circuit.
欧姆定律和电阻率描述电路元件的行为。基尔霍夫定律保证电路中电荷与能量的守恒。
V = IR – Ohm's law: potential difference across a resistor equals current times resistance.
V = IR – 欧姆定律：电阻两端的电势差等于电流乘以电阻。
ρ = RA/L – Resistivity: R depends on conductor length L, cross-sectional area A, and material property ρ.
ρ = RA/L – 电阻率：电阻 R 取决于导体长度 L、横截面积 A 和材料特性 ρ。
Series: Rtotal = R₁ + R₂ + ... ; Parallel: 1/Rtotal = 1/R₁ + 1/R₂ + ...
串联: Rtotal = R₁ + R₂ + ... ; 并联: 1/Rtotal = 1/R₁ + 1/R₂ + ...
KCL (Junction rule): Sum of currents entering a node equals sum leaving. KVL (Loop rule): Algebraic sum of p.d.s around any closed loop is zero.
基尔霍夫电流定律 (KCL): 流入节点的电流总和等于流出总和。 基尔霍夫电压定律 (KVL): 沿任意闭合回路，电势差的代数和为零。
7. EMF and Internal Resistance | 电动势与内阻
Real cells have internal resistance r that reduces the terminal potential difference when current is drawn. The emf ε is the energy supplied per unit charge.
实际电池具有内阻 r，当有电流时端电压会降低。电动势 ε 是每单位电荷提供的能量。
ε = I(R + r) – The emf is distributed across the external load R and internal resistance r.
ε = I(R + r) – 电动势分配在外电路负载 R 和内阻 r 上。
V = ε – Ir – Terminal p.d. equals emf minus the 'lost volts' across the internal resistance.
V = ε – Ir – 端电压等于电动势减去内阻上损失的电压。
8. Wave Basics and Refraction | 波的基本性质与折射
Waves transfer energy without transferring matter. The wave equation links speed, frequency, and wavelength. Refraction occurs when waves pass from one medium to another.
波传递能量而不传递物质。波动方程联系波速、频率和波长。当波从一种介质进入另一种介质时发生折射。
v = fλ – Wave speed equals frequency times wavelength. This holds for all waves.
v = fλ – 波速等于频率乘以波长，适用于所有波。
n = c/v – Absolute refractive index of a medium: ratio of speed of light in vacuum to speed in the medium.
n = c/v – 介质的绝对折射率：真空中光速与介质中光速之比。
n₁ sin θ₁ = n₂ sin θ₂ – Snell's law: relates angles of incidence and refraction at a boundary.
n₁ sin θ₁ = n₂ sin θ₂ – 斯涅耳定律：联系入射角和折射角。
sin C = n₂/n₁ (n₂ < n₁) – Critical angle for total internal reflection.
sin C = n₂/n₁ (n₂ < n₁) – 全反射的临界角。
9. Lenses | 透镜
Converging and diverging lenses form images by refraction. The lens equation and magnification formula are essential for ray optics.
会聚透镜和发散透镜通过折射成像。透镜方程和放大率公式是几何光学的基础。
1/f = 1/u + 1/v – Lens equation: f is focal length, u object distance, v image distance. Sign conventions must be applied consistently (e.g. real-is-positive).
1/f = 1/u + 1/v – 透镜方程：f 为焦距，u 为物距，v 为像距。必须一致使用符号约定（如实正虚负）。
m = v/u – Linear magnification: ratio of image height to object height. Negative m indicates an inverted image.
m = v/u – 线放大率：像高与物高之比。负值表示倒立的像。
10. Superposition, Interference and Diffraction | 叠加、干涉与衍射
When two or more waves overlap, the resultant displacement is the vector sum of individual displacements. Stable interference patterns reveal wavelength.
当两个或多个波叠加时，合位移是个别位移的矢量和。稳定的干涉图样可以揭示波长。
Δy = λD/d – Fringe spacing in Young's double-slit experiment: λ is wavelength, D distance to screen, d slit separation.
Δy = λD/d – 杨氏双缝干涉条纹间距：λ 为波长，D 为缝到屏幕距离，d 为缝间距。
d sin θ = nλ – Diffraction grating equation: n is the order number (0, 1, 2, ...), d is the grating spacing.
d sin θ = nλ – 衍射光栅方程：n 为级次 (0, 1, 2, ...)，d 为光栅常数。
Condition for constructive interference: path difference = nλ; destructive: path difference = (n + ½)λ.
相长干涉条件: 波程差 = nλ；相消干涉: 波程差 = (n + ½)λ。
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