📚 IGCSE Physics Formula Handbook | IGCSE 物理：公式汇总手册
Mastering the essential formulas is key to success in IGCSE Physics. This handbook brings together all the core equations from the syllabus, organised by topic, with clear explanations of symbols, SI units, and typical applications. Use it regularly for revision, and always check that you substitute values in consistent units before solving.
掌握核心公式是 IGCSE 物理成功的关键。本手册将大纲中所有核心方程按主题归纳，清楚说明每个符号的含义、国际单位及典型应用。请经常使用以作复习，并务必在代入数值前确认单位一致。
1. Motion | 运动学
For an object moving with constant acceleration, we use the SUVAT equations. Here u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (s), s = displacement (m).
对于匀加速运动，我们使用 SUVAT 方程。其中 u = 初速度（m/s），v = 末速度（m/s），a = 加速度（m/s²），t = 时间（s），s = 位移（m）。
v = u + a t
Used to find final velocity when acceleration is constant. No displacement is involved.
用于求匀加速运动的末速度，不涉及位移。
s = ut + ½ a t²
Displacement when initial velocity and constant acceleration are known.
已知初速度和恒定加速度时位移的计算式。
v² = u² + 2 a s
Used when time is not given. Links velocity, acceleration and displacement.
当未知时间时使用，连接速度、加速度和位移。
average speed = total distance / total time
For non-uniform motion, average speed is the total distance travelled divided by the total time taken.
对于非匀速运动，平均速率 = 总路程 / 总时间。
2. Forces and Momentum | 力与动量
Newton’s second law relates resultant force, mass and acceleration. Momentum is the product of mass and velocity.
牛顿第二定律给出了合力、质量与加速度的关系。动量是质量与速度的乘积。
F = m a
Resultant force F in newtons (N), mass m in kilograms (kg), acceleration a in m/s². Direction of acceleration is the same as the resultant force.
合力 F 单位为牛顿（N），质量 m 单位为千克（kg），加速度 a 单位为 m/s²。加速度方向与合力方向相同。
p = m v
Momentum p (kg m/s) is a vector quantity. It is conserved in collisions and explosions when no external resultant force acts.
动量 p（kg m/s）是矢量。在没有外合力作用的碰撞和爆炸中，动量守恒。
F = Δp / Δt
The resultant force equals the rate of change of momentum. This explains how safety features like airbags reduce the force by increasing impact time.
合力等于动量的变化率。这解释了为何安全气囊等通过延长碰撞时间来减小作用力。
3. Work, Energy and Power | 功、能与功率
Energy can be transferred by doing work. Power is the rate at which work is done or energy is transferred.
通过做功可以转移能量。功率是做功或能量转移的速率。
W = F d cos θ
When force F (N) and displacement d (m) are in the same direction, θ = 0 and W = F d. Work is measured in joules (J).
当力 F（N）与位移 d（m）方向相同时，θ = 0，W = F d。功的单位是焦耳（J）。
Eₖ = ½ m v²
Kinetic energy depends on mass and the square of speed. A small increase in speed causes a large increase in kinetic energy.
动能取决于质量和速度的平方。速度的小幅增加会引起动能的大幅增加。
Eₚ = m g h
Gravitational potential energy is the energy stored due to an object’s height above a reference level. g = 9.8 m/s² on Earth.
重力势能是因物体相对参考平面的高度而储存的能量。地球上 g = 9.8 m/s²。
P = W / t = E / t
Power P in watts (W) equals work done or energy transferred divided by time. 1 W = 1 J/s.
功率 P 单位为瓦特（W），等于做功或能量转移量除以时间。1 W = 1 J/s。
efficiency = useful output energy / total input energy × 100%
Efficiency can also be expressed as useful power output / total power input. Always less than 100% due to thermal dissipation.
效率也可表示为有用输出功率 / 总输入功率。因热量耗散，效率始终小于100%。
4. Pressure | 压强
Pressure measures how concentrated a force is. It is higher when the same force acts on a smaller area.
压强衡量力的集中程度。同样的力作用在更小的面积上，压强更大。
p = F / A
Pressure p in pascals (Pa) or N/m², force F in newtons (N), area A in m². Used to explain why sharp objects cut more easily.
压强 p 单位为帕斯卡（Pa）或 N/m²，力 F 为牛顿（N），面积 A 为 m²。可解释为何尖锐物体更容易切割。
p = ρ g h
Pressure due to a liquid column depends on liquid density ρ (kg/m³), gravitational field strength g (N/kg), and vertical height h (m). Does not depend on the shape of the container.
液柱产生的压强取决于液体密度 ρ（kg/m³）、重力场强度 g（N/kg）和垂直高度 h（m），与容器形状无关。
5. Thermal Physics and Gas Laws | 热学与气体定律
Temperature, internal energy, and the behaviour of ideal gases are linked by two key relationships. All temperatures must be in kelvin (K).
温度、内能与理想气体的行为通过两个关键关系相连。所有温度须使用开尔文（K）。
p V = constant (at constant temperature)
Boyle’s law: For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional. (p₁V₁ = p₂V₂)
波义耳定律：在温度不变时，一定质量气体的压强与体积成反比。（p₁V₁ = p₂V₂）
V / T = constant (at constant pressure)
Charles’s law: For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature. (V₁/T₁ = V₂/T₂)
查理定律：在压强不变时，一定质量气体的体积与绝对温度成正比。（V₁/T₁ = V₂/T₂）
p / T = constant (at constant volume)
Pressure law: For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature. (p₁/T₁ = p₂/T₂)
压强定律：在体积不变时，一定质量气体的压强与绝对温度成正比。（p₁/T₁ = p₂/T₂）
Q = m c Δθ
Thermal energy Q (J) required to change the temperature of mass m (kg) by Δθ (°C or K). c is specific heat capacity (J/(kg °C)).
改变质量为 m（kg）的物体的温度 Δθ（°C或K）所需的热量 Q（J），c 为比热容（J/(kg °C)）。
Q = m L
Thermal energy needed to change state at constant temperature. L is specific latent heat (J/kg), either of fusion or vaporisation.
在温度不变时改变物态所需的热量。L 为比潜热（J/kg），分为熔化潜热或汽化潜热。
6. Waves | 波
All waves obey the wave equation linking speed, frequency and wavelength. Reflection, refraction and diffraction are common behaviours.
所有波都遵循连接波速、频率与波长的波动方程。反射、折射和衍射是常见行为。
v = f λ
Wave speed v (m/s), frequency f (Hz), wavelength λ (m). For light in vacuum, v = c = 3.0 × 10⁸ m/s.
波速 v（m/s），频率 f（Hz），波长 λ（m）。真空中光速 v = c = 3.0 × 10⁸ m/s。
f = 1 / T
Frequency is the reciprocal of period T (s). If the period is 0.02 s, the frequency is 50 Hz.
频率是周期 T（s）的倒数。若周期为0.02 s，频率则为50 Hz。
refractive index n = sin i / sin r
For light passing from air into a medium, i is the angle of incidence and r is the angle of refraction, both measured from the normal. n is dimensionless.
光从空气射入介质时，i 为入射角，r 为折射角，均从法线量起。n 无量纲。
n = c / v
The refractive index also equals the speed of light in vacuum divided by the speed in the medium.
折射率也等于真空中光速除以介质中的光速。
7. Optics and Lenses | 光学与透镜
The thin lens equation and magnification formula describe image formation by converging and diverging lenses.
薄透镜方程和放大率公式描述会聚透镜与发散透镜的成像。
1/f = 1/u + 1/v
For a thin lens, f is focal length, u is object distance, v is image distance. Use real‑is‑positive sign convention: f is positive for converging lens, negative for diverging.
对于薄透镜，f 为焦距，u 为物距，v 为像距。使用实正符号法则：会聚透镜 f 为正，发散透镜为负。
magnification = image height / object height = v / u
Magnification has no units. A value greater than 1 means the image is larger than the object.
放大率无单位。数值大于1表示像比物大。
8. Electricity | 电学
Current, voltage, resistance and power are linked by fundamental equations. Always check if components are in series or parallel.
电流、电压、电阻和功率由基本方程联系。务必判断元件是串联还是并联。
Q = I t
Charge Q (coulombs, C), current I (A), time t (s). One coulomb is the charge passing a point in one second when the current is 1 A.
电荷量 Q（库仑，C），电流 I（A），时间 t（s）。1 库仑是电流为1 A时1秒内通过某点的电荷量。
V = I R
Ohm’s law: The potential difference V (V) across a resistor is directly proportional to the current I (A) at constant temperature. R is resistance (Ω).
欧姆定律：在恒温下，电阻两端的电势差 V（V）与电流 I（A）成正比。R 为电阻（Ω）。
P = I V = I² R = V² / R
Electrical power dissipated in a component. Use P = I V for any component; use P = I² R only when all electrical energy is converted to heat.
元件中消耗的电功率。任意元件可用 P = I V；只有全部电能转化为热量时才用 P = I² R。
R series = R₁ + R₂ + …
In series, resistance adds up. The current is the same through all resistors.
串联时电阻相加，通过各个电阻的电流相同。
1/R parallel = 1/R₁ + 1/R₂ + …
In parallel, the reciprocal of total resistance equals the sum of reciprocals. Total resistance is always smaller than the smallest individual resistance.
并联时，总电阻的倒数等于各电阻倒数之和。总电阻始终小于最小的单个电阻。
9. Electromagnetism and Transformers | 电磁学与变压器
Electromagnetic induction and transformers rely on the link between changing magnetic fields and induced voltages.
电磁感应与变压器基于变化的磁场与感应电压之间的联系。
Vₚ / Vₛ = Nₚ / Nₛ
For an ideal transformer, the ratio of primary voltage Vₚ to secondary voltage Vₛ equals the ratio of turns in the primary Nₚ to turns in the secondary Nₛ. A step‑up transformer has Nₛ > Nₚ.
对于理想变压器，原线圈电压 Vₚ 与副线圈电压 Vₛ 之比等于原线圈匝数 Nₚ 与副线圈匝数 Nₛ 之比。升压变压器 Nₛ > Nₚ。
Pₚ ≈ Pₛ → Vₚ Iₚ = Vₛ Iₛ (ideal)
Power is approximately conserved. If voltage is stepped up, current is stepped down in the same ratio, assuming 100% efficiency.
功率近似守恒。若电压升高，电流则以相同比例降低（假设效率100%）。
10. Radioactivity and Nuclear Physics | 放射性及核物理
Radioactive decay is random and exponential. The decay constant and half‑life describe the rate of decay.
放射性衰变是随机的且呈指数规律。衰变常数和半衰期描述衰变的速率。
A = λ N
Activity A (becquerels, Bq) is the number of decays per second. λ is the decay constant (s⁻¹), N is the number of undecayed nuclei. Activity decreases over time.
活度 A（贝克勒尔，Bq）是每秒衰变次数。λ 为衰变常数（s⁻¹），N 为未衰变原子核数。活度随时间减小。
T₁/₂ = ln 2 / λ ≈ 0.693 / λ
Half‑life T₁/₂ is the time taken for half the radioactive nuclei in a sample to decay. It is constant for a given isotope.
半衰期 T₁/₂ 是样本中一半放射性原子核发生衰变所需的时间，对给定的同位素是常数。
In addition, the equivalence of mass and energy is given by Einstein’s famous equation:
此外，质量和能量的等价性由爱因斯坦著名的方程给出：
E = m c²
Energy released in a nuclear reaction equals the mass defect multiplied by the square of the speed of light in vacuum (c = 3.0 × 10⁸ m/s).
核反应中释放的能量等于质量亏损乘以真空中光速的平方（c = 3.0 × 10⁸ m/s）。
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