📚 Formula Cheat Sheet for IGCSE OCR Physics | IGCSE OCR 物理公式速查手册
This comprehensive cheat sheet compiles all essential formulas you need for the IGCSE OCR Physics examination. It is organised by topic for quick revision, featuring clear English explanations followed by their Chinese counterparts. Use it to memorise relationships, practise rearrangements, and build confidence in applying equations under exam conditions.
这份全面的速查手册汇总了 IGCSE OCR 物理考试所需的所有核心公式。手册按主题编排，方便快速复习，每一条公式都配有清晰的英文解释和对应的中文说明。用它来记忆关系、练习变形，并在考试条件下自信地应用方程式。
1. Motion and Kinematics | 运动学
These equations describe motion with constant acceleration. Always check the sign convention before substituting values.
以下方程描述匀加速直线运动。代入数值前务必检查正负号的规定。
v = u + a⋅t
Final velocity v equals initial velocity u plus acceleration a multiplied by time t.
末速度 v 等于初速度 u 加上加速度 a 与时间 t 的乘积。
s = u⋅t + ½⋅a⋅t²
Displacement s is given by the product of initial velocity and time plus one-half times acceleration times the square of time.
位移 s 等于初速度与时间的乘积，加上加速度与时间平方乘积的一半。
v² = u² + 2⋅a⋅s
This equation relates final velocity squared to initial velocity squared, acceleration, and displacement, eliminating time.
该方程把末速度的平方与初速度的平方、加速度和位移联系起来，消去了时间。
average speed = distance travelled / time taken
Average speed is the total distance divided by total time, a scalar quantity.
平均速率是总距离除以总时间，是一个标量。
average velocity = displacement / time
Average velocity is displacement (a vector) divided by time, and its direction is that of displacement.
平均速度是位移（矢量）除以时间，方向与位移相同。
2. Forces, Pressure and Momentum | 力、压强与动量
Newton’s laws are the foundation. Here are the key force-related equations.
牛顿定律是基础。以下是关键的与力相关的方程式。
F = m⋅a
Resultant force F equals mass m times acceleration a. This is Newton’s second law.
合力 F 等于质量 m 乘以加速度 a，即牛顿第二定律。
W = m⋅g
Weight W is the force due to gravity on a mass m, with gravitational field strength g (9.8 N/kg on Earth).
重力 W 是质量为 m 的物体由于引力场强度 g（地球约 9.8 N/kg）所受到的力。
p = F / A
Pressure p is force per unit area. For liquids, it is also given by p = h⋅ρ⋅g where h is depth and ρ is density.
压强 p 是单位面积上的力。对于液体，也可表示为 p = h⋅ρ⋅g，其中 h 是深度，ρ 是密度。
momentum = m⋅v
Momentum is mass times velocity; it is conserved in collisions and explosions when no external resultant force acts.
动量等于质量乘以速度；在没有外部合力作用时，碰撞和爆炸过程中动量守恒。
F = Δp / Δt
Force equals the rate of change of momentum. It links impulse and safety features like crumple zones.
力等于动量的变化率。它把冲量与诸如缓冲吸能区的安全设计联系起来。
moment of force = F × d
Moment of a force (torque) is force multiplied by perpendicular distance from the pivot. Moments are balanced when clockwise = anticlockwise.
力矩等于力乘以力到支点的垂直距离。当顺时针力矩等于逆时针力矩时，杠杆平衡。
3. Energy, Work and Power | 能量、功与功率
Energy is transferred through work and heating. Use these relationships to link mechanics with energy conservation.
能量通过做功和加热传递。用这些关系将力学与能量守恒联系起来。
W = F⋅d
Work done (energy transferred) is force times distance moved in the direction of the force.
功（能量转移）等于力乘以沿力方向移动的距离。
Eₚ = m⋅g⋅h
Gravitational potential energy stored when raising a mass m through height h against gravity.
重力势能是将质量 m 的物体克服重力举升高度 h 所储存的能量。
Eₖ = ½⋅m⋅v²
Kinetic energy depends on mass and the square of speed. It is valid for translation only.
动能取决于质量和速度的平方，仅适用于平动。
P = W / t
Power is the rate of doing work: energy transferred divided by time taken.
功率是做功的快慢：转移的能量除以所用时间。
efficiency = (useful energy output / total energy input) × 100%
Efficiency is the ratio of useful output to total input, often expressed as a percentage. It is never greater than 100%.
效率是有用输出与总输入的比值，通常用百分数表示，永远不会超过 100%。
4. Waves | 波
The wave equation links speed, frequency and wavelength. It applies to both longitudinal and transverse waves.
波速方程沟通了波速、频率和波长。它既适用于纵波，也适用于横波。
v = f⋅λ
Wave speed v equals frequency f multiplied by wavelength λ (lambda).
波速 v 等于频率 f 乘以波长 λ（拉姆达）。
f = 1 / T
Frequency is the reciprocal of period T. If a wave has a period of 0.02 s, its frequency is 50 Hz.
频率是周期 T 的倒数。若一个波的周期为 0.02 s，则其频率为 50 Hz。
refractive index n = c / v
The refractive index of a medium is the ratio of speed of light in vacuum c to its speed v in the medium.
介质的折射率是光在真空中的速度 c 与在该介质中的速度 v 之比。
n = sin i / sin r
Snell’s law: refractive index also equals the sine of the angle of incidence divided by the sine of the angle of refraction.
斯涅耳定律：折射率也等于入射角的正弦除以折射角的正弦。
sin c = 1 / n
The critical angle c for total internal reflection is found from the refractive index n. This applies when light goes from denser to less dense medium.
全反射的临界角 c 由折射率 n 用此式求得，适用于光从光密介质射向光疏介质的情况。
5. Electricity | 电学
Ohm’s law and power dissipation are central. Always use SI units: amperes, volts, ohms, watts.
欧姆定律和功率耗散是中心内容。始终使用国际单位：安培、伏特、欧姆、瓦特。
V = I⋅R
Potential difference across a resistor equals current times resistance (Ohm’s law for constant temperature).
电阻两端的电势差等于电流乘以电阻（恒温下的欧姆定律）。
P = I⋅V
Electric power is the product of current and voltage. It can also be written as P = I²R or P = V²/R using Ohm’s law.
电功率是电流与电压的乘积。利用欧姆定律还可写为 P = I²R 或 P = V²/R。
E = P⋅t = I⋅V⋅t
Energy transferred is power multiplied by time. This is often measured in joules or kilowatt-hours for domestic use.
转移的能量等于功率乘以时间。通常用焦耳计量，家庭用电常用千瓦时。
R = ρ⋅L / A
The resistance of a wire depends on its resistivity ρ, length L and cross-sectional area A.
导线的电阻取决于其电阻率 ρ、长度 L 和横截面积 A。
R_total = R₁ + R₂ + … (series)
Resistors in series add up directly; total resistance is greater than any individual resistor.
串联电阻直接相加；总电阻大于任何一个单独的电阻。
1/R_total = 1/R₁ + 1/R₂ + … (parallel)
For parallel resistors, the reciprocal of total resistance is the sum of the reciprocals; total resistance is less than the smallest individual resistance.
对于并联电阻，总电阻的倒数等于各电阻倒数之和；总电阻小于最小的单个电阻。
6. Magnetism and Electromagnetism | 磁与电磁
These equations describe the link between electricity and magnetism, including transformers and motor effect.
这些方程式描述了电与磁之间的联系，包括变压器和电动机效应。
F = B⋅I⋅L
Force on a current-carrying conductor in a magnetic field: F equals magnetic flux density B times current I times length L of wire in the field, when perpendicular.
磁场对载流导体的力：当导体与磁场垂直时，F 等于磁通量密度 B 乘以电流 I 乘以导线在磁场中的长度 L。
V_p / V_s = N_p / N_s
For an ideal transformer, the ratio of primary voltage to secondary voltage equals the ratio of turns on the primary coil to turns on the secondary coil.
对于理想变压器，原边电压与副边电压之比等于原边线圈匝数与副边线圈匝数之比。
P_p = P_s (ideal transformer)
In an ideal transformer, input power equals output power, so I_p⋅V_p = I_s⋅V_s.
理想变压器中输入功率等于输出功率，因此 I_p⋅V_p = I_s⋅V_s。
e.m.f. = -N ΔΦ / Δt
Faraday’s law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. The minus sign indicates Lenz’s law direction.
法拉第定律：感应电动势与磁通量链的变化率成正比。负号表示楞次定律决定的方向。
7. Thermal Physics | 热物理
These relationships connect heat energy, temperature change, and changes of state.
这些关系式将热能、温度变化和物态变化联系起来。
ΔE = m⋅c⋅Δθ
Energy required to change temperature of mass m by Δθ is mass times specific heat capacity c times temperature change.
使质量为 m 的物体温度变化 Δθ 所需的能量等于质量乘以比热容 c 再乘以温度变化。
E = m⋅L
Energy to change state at constant temperature (latent heat) is mass times specific latent heat L. Use L_f for fusion and L_v for vaporisation.
恒温下改变物态所需的能量（潜热）等于质量乘以比潜热 L。熔化用 L_f，汽化用 L_v。
p⋅V = constant (Boyle’s law, constant T)
For a fixed mass of ideal gas at constant temperature, pressure is inversely proportional to volume.
对于一定质量的理想气体，在温度不变时，压强与体积成反比。
V/T = constant (Charles’s law, constant p)
At constant pressure, the volume of a gas is directly proportional to its absolute temperature (in kelvin).
在压强恒定时，气体的体积与其绝对温度（开尔文）成正比。
p/T = constant (Pressure law, constant V)
At constant volume, pressure of a fixed mass of gas is proportional to its absolute temperature.
在体积恒定时，一定质量气体的压强与绝对温度成正比。
8. Matter: Density and Gas Laws | 物质：密度与气体定律
Density is a fundamental property relating mass and volume. It is used in floatation and particle models.
密度是关联质量与体积的基本属性，用于浮力问题和粒子模型。
ρ = m / V
Density ρ (rho) is mass per unit volume. Units are kg/m³ or g/cm³.
密度 ρ（柔）是单位体积的质量。单位为 kg/m³ 或 g/cm³。
p₁V₁/T₁ = p₂V₂/T₂
The combined gas law for a fixed mass of gas, where p, V and T must be in kelvin.
适用于一定质量气体的联合气体定律，其中 p、V 和 T 必须使用开尔文温标。
p⋅V = n⋅R⋅T (ideal gas equation, extension)
The ideal gas equation is sometimes used as an extension: p is pressure, V volume, n number of moles, R molar gas constant, T absolute temperature.
理想气体状态方程有时作为拓展内容使用：p 为压强，V 为体积，n 为摩尔数，R 为摩尔气体常数，T 为绝对温度。
9. Radioactivity and Nuclear Physics | 放射性与核物理
Decay equations describe the random nature of radioactive decay. Half-life and activity are key.
衰变方程描述放射性衰变的随机性质。半衰期和活度是关键概念。
activity A = -dN/dt = λN
Activity (A) is the number of decays per second, proportional to the number of undecayed nuclei N, with decay constant λ.
活度 (A) 是每秒衰变的次数，与未衰变原子核数 N 成正比，比例常数为衰变常数 λ。
N = N₀ e^(-λt)
The exponential decay law relates remaining nuclei N to initial number N₀, decay constant and time.
指数衰变律将剩余核数 N 与初始核数 N₀、衰变常数和时间联系起来。
t½ = ln 2 / λ ≈ 0.693 / λ
Half-life is the time for half the radioactive nuclei to decay, and it is related to decay constant by this formula.
半衰期是一半放射性原子核衰变所需的时间，由该公式与衰变常数关联。
10. Topic-Specific Constants and Units | 专题常数与单位
Make sure you know common constants and unit conversions. These are often required in calculations without being given.
请确保自己熟悉常见常数和单位换算。这些常常在计算中需要但题目不提供。
| Quantity / 量 | Value / 数值 |
|---|---|
| Acceleration due to gravity, g | 9.8 m/s² (Earth); 1.6 m/s² (Moon) |
| Speed of light in vacuum, c | 3.0 × 10⁸ m/s |
| Speed of sound in air | 330–340 m/s (at room temperature) |
| Specific heat capacity of water, c | 4200 J/(kg·°C) |
| Specific latent heat of fusion of water | 3.34 × 10⁵ J/kg |
| Specific latent heat of vaporisation of water | 2.26 × 10⁶ J/kg |
| Planck constant, h | 6.63 × 10⁻³⁴ J·s |
| Elementary charge, e | 1.60 × 10⁻¹⁹ C |
11. Tips for Using Formulae in OCR Exams | OCR 考试中使用公式的技巧
Always show your working step by step. Write the formula, substitute values, calculate, and state the unit. Check if the question asks for a specific unit conversion (e.g. cm to m, minutes to seconds). Remember to rearrange equations correctly before substituting numbers.
务必逐步展示解题过程。写出公式，代入数值，进行计算，并写明单位。检查题目是否要求特定的单位换算（例如厘米转换为米，分钟转换为秒）。记住要在代入数字之前先正确变形方程。
If you are given a formula in a different form, such as ΔE = m c Δθ arranged for finding c, practise making any variable the subject. Using a formula triangle can help, but ensure you understand the underlying algebra.
如果题目给出的公式是另一种形式，比如将 ΔE = m c Δθ 变形求 c，务必要练习使任一变量成为公式的主语。使用公式三角形有助于记忆，但务必理解背后的代数关系。
In multi-step calculations, store intermediate results in your calculator rather than rounding too early. Only round your final answer to an appropriate number of significant figures, usually matching the least precise data given.
在多步计算中，应将中间结果储存在计算器里，不要过早进行舍入。最后只把最终答案舍入到合适的有效数字位数，通常要与所给数据中精度最低的数值相匹配。
For questions on series and parallel circuits, draw a diagram and label known quantities. For transformer equations, remember that the ideal transformer equation assumes 100% efficiency; if efficiency is given, apply it to the output power.
对于串并联电路的问题，绘制草图并标出已知量。对于变压器方程，记住理想变压器方程假设效率为 100%；若题目给出效率，就应用到输出功率上。
12. Quick Revision Checklist | 快速复习清单
- Can you write all motion equations from memory and choose the right one for a problem?
- 你能默写出所有运动学方程并根据问题选择合适的方程吗？
- Do you know the direction of forces in equilibrium and how to resolve vectors?
- 你是否了解平衡状态下力的方向以及如何分解矢量？
- Can you convert between joules and kilowatt-hours (1 kWh = 3.6 × 10⁶ J)?
- 你能在焦耳和千瓦时之间进行换算吗（1 kWh = 3.6 × 10⁶ J）？
- Have you practised rearranging the wave equation, the pressure equation, and the refractive index equations?
- 你练习过变形波速方程、压强方程和折射率方程吗？
- Can you describe the difference between series and parallel circuits in terms of current, voltage and resistance?
- 你能从电流、电压和电阻的角度描述串联电路和并联电路的区别吗？
- Do you understand the significance of the minus sign in Faraday’s law (Lenz’s law)?
- 你理解法拉第定律中负号的意义（楞次定律）吗？
- Can you sketch and interpret the magnetic field around a straight wire, a coil, and a solenoid?
- 你能画出并解释直导线、线圈和螺线管周围的磁场吗？
- Have you memorised the density of water (1000 kg/m³) and typical specific heat capacities?
- 你记住了水的密度（1000 kg/m³）和典型的比热容吗？
- Do you know the half-life graph shape and how to calculate half-life from data?
- 你知道半衰期图的形状以及如何根据数据计算半衰期吗？
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