📚 Year 10 Cambridge Physics: Formula and Theorem Quick Reference | 十年级剑桥物理：公式定理速查手册
This quick reference guide brings together the essential formulas and theorems covered in Year 10 Cambridge IGCSE Physics. Use it as a handy revision tool to recall the equations for motion, forces, energy, waves, electricity, magnetism, nuclear physics and space.
本速查手册汇集了十年级剑桥 IGCSE 物理课程中的核心公式和定理。你可以将它作为便捷的复习工具，随时回顾运动、力、能量、波、电学、磁学、核物理和空间物理等专题的关键方程。
1. Kinematics: Motion in a Straight Line | 运动学：直线运动
For an object moving with constant acceleration a, the final velocity v is related to the initial velocity u and time t by v = u + a t.
对于以恒定加速度 a 运动的物体，末速度 v 与初速度 u 和时间 t 的关系为 v = u + a t。
The displacement s can be calculated using s = u t + ½ a t².
位移 s 可通过 s = u t + ½ a t² 计算。
When time is not known, use v² = u² + 2 a s.
当时间未知时，使用 v² = u² + 2 a s。
Average speed = total distance / total time. For uniform acceleration, average speed = (u + v) / 2.
平均速率 = 总路程 / 总时间。对于匀加速运动，平均速度 = (u + v) / 2。
The gradient of a distance–time graph gives speed; the gradient of a velocity–time graph gives acceleration, and the area under it gives displacement.
距离–时间图线的斜率表示速率；速度–时间图线的斜率表示加速度，其下的面积表示位移。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s second law states that the resultant force on an object equals its mass times its acceleration: F = m a.
牛顿第二定律指出，作用在物体上的合力等于质量乘以加速度：F = m a。
Weight is the gravitational force on a mass: W = m g, where g ≈ 9.8 m/s² on Earth.
重力是作用在质量上的引力：W = m g，地球上 g ≈ 9.8 m/s²。
Newton’s third law: if body A exerts a force on body B, then B exerts an equal and opposite force on A.
牛顿第三定律：如果物体 A 对物体 B 施加力，那么 B 会对 A 施加大小相等、方向相反的力。
Hooke’s law: the extension of a spring is directly proportional to the applied force, F = k x, within the limit of proportionality.
胡克定律：在弹性限度内，弹簧的伸长量 x 与施加的力成正比，F = k x。
The moment of a force about a pivot is M = F d, where d is the perpendicular distance from the pivot. For equilibrium, total clockwise moments = total anticlockwise moments.
力对支点的力矩为 M = F d，其中 d 是力到支点的垂直距离。平衡时，总顺时针力矩 = 总逆时针力矩。
3. Momentum | 动量
Momentum p is the product of mass and velocity: p = m v.
动量 p 是质量与速度的乘积：p = m v。
Impulse is the change in momentum and equals force multiplied by time: F Δt = Δp = m v – m u.
冲量是动量的变化量，等于力乘以时间：F Δt = Δp = m v – m u。
In a closed system, total momentum before a collision equals total momentum after: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂.
在封闭系统中，碰撞前的总动量等于碰撞后的总动量：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂。
4. Energy, Work and Power | 能量、功与功率
Work done by a constant force is W = F d, where d is the distance moved in the direction of the force.
恒力做的功为 W = F d，其中 d 是沿力方向移动的距离。
Gravitational potential energy change: ΔEₚ = m g Δh.
重力势能变化量：ΔEₚ = m g Δh。
Kinetic energy: Eₖ = ½ m v².
动能：Eₖ = ½ m v²。
Power is the rate of doing work: P = W / t = F v (for constant speed).
功率是做功的速率：P = W / t = F v（匀速时）。
Efficiency = (useful output energy / total input energy) × 100%.
效率 =（有用输出能量 / 总输入能量）× 100%。
5. Density and Pressure | 密度与压强
Density ρ = mass m / volume V (units: kg/m³).
密度 ρ = 质量 m / 体积 V（单位：kg/m³）。
Pressure due to a solid on a surface: p = F / A, where A is the area.
固体对表面的压强：p = F / A，其中 A 是受力面积。
Pressure at a depth h in a liquid: p = h ρ g, where ρ is the liquid density.
液体中深度 h 处的压强：p = h ρ g，ρ 为液体密度。
For a hydraulic system, pressure is transmitted equally: F₁ / A₁ = F₂ / A₂.
在液压系统中，压强等值传递：F₁ / A₁ = F₂ / A₂。
6. Thermal Physics | 热物理
Energy required to change temperature: Q = m c Δθ, where c is specific heat capacity.
改变温度所需能量：Q = m c Δθ，其中 c 是比热容。
Energy required for a change of state: Q = m L, where L is specific latent heat (fusion or vaporisation).
物态变化所需能量：Q = m L，L 是比潜热（熔化或汽化）。
Boyle’s law: for a fixed mass of gas at constant temperature, p V = constant, so p₁ V₁ = p₂ V₂.
波义耳定律：一定质量的气体在温度不变时，p V = 常量，即 p₁ V₁ = p₂ V₂。
Charles’s law: at constant pressure, V / T = constant, so V₁ / T₁ = V₂ / T₂ (T in kelvin).
查理定律：压强不变时，V / T = 常量，即 V₁ / T₁ = V₂ / T₂（T 用开尔文）。
Pressure law: at constant volume, p / T = constant, so p₁ / T₁ = p₂ / T₂.
压强定律：体积不变时，p / T = 常量，即 p₁ / T₁ = p₂ / T₂。
7. Waves: General Properties | 波的一般性质
The wave equation links speed v, frequency f and wavelength λ: v = f λ.
波速方程联系波速 v、频率 f 和波长 λ：v = f λ。
Period T is the reciprocal of frequency: T = 1 / f.
周期 T 是频率的倒数：T = 1 / f。
Reflection follows the law: angle of incidence i = angle of reflection r.
反射遵循：入射角 i = 反射角 r。
Refraction is described by Snell’s law: n = sin i / sin r, where n is the refractive index. Also, n = c / v, where c is the speed of light in vacuum.
折射由斯涅尔定律描述：n = sin i / sin r，n 为折射率。同时 n = c / v，c 是真空光速。
The critical angle θ꜀ for total internal reflection satisfies sin θ꜀ = 1 / n.
全反射的临界角 θ꜀ 满足 sin θ꜀ = 1 / n。
8. Light and Sound | 光与声
For a converging lens, the magnification M = image height / object height = v / u, where v is image distance and u is object distance.
对会聚透镜，放大率 M = 像高 / 物高 = v / u，其中 v 为像距，u 为物距。
The thin lens equation (extended) is 1 / f = 1 / u + 1 / v, with the real-is-positive sign convention.
薄透镜公式（拓展）为 1 / f = 1 / u + 1 / v，采用实正符号约定。
Sound waves also obey v = f λ. The speed of sound in air is about 340 m/s.
声波同样遵循 v = f λ。空气中的声速约为 340 m/s。
Echo location: distance to a reflector = (speed of sound × time) / 2.
回声定位：到反射面的距离 =（声速 × 时间）/ 2。
9. Electric Circuits and Charge | 电路与电荷
Electric charge Q is related to current I and time t: Q = I t.
电荷 Q 与电流 I 和时间 t 的关系：Q = I t。
Potential difference V is the work done per unit charge: V = W / Q.
电势差 V 是每单位电荷做的功：V = W / Q。
Ohm’s law gives the resistance R = V / I, valid at constant temperature.
欧姆定律给出电阻 R = V / I，在温度恒定时成立。
Resistors in series: Rₜₒₜₐₗ = R₁ + R₂ + …
串联电阻：Rₜₒₜₐₗ = R₁ + R₂ + …
Resistors in parallel: 1 / Rₜₒₜₐₗ = 1 / R₁ + 1 / R₂ + …
并联电阻：1 / Rₜₒₜₐₗ = 1 / R₁ + 1 / R
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