📚 Cambridge IGCSE Physics Formula & Theorem Quick Reference | 剑桥 IGCSE 物理公式定理速查手册
This article provides a rapid recall guide for Year 11 Cambridge IGCSE Physics students, covering essential formulas, core laws, and key relationships organised by topic. Use it to reinforce memory, support exam preparation, and build confidence with quantitative problem-solving.
本文为 Year 11 剑桥 IGCSE 物理学生提供一份快速回忆指南，按主题整理必背公式、核心定律与关键关系，帮助巩固记忆、助力备考，提升定量解题的信心。
1. Motion | 运动学
Average speed is the total distance travelled divided by the total time taken. It measures how fast an object moves on average during a journey.
平均速率等于总路程除以总时间，描述物体在行程中的平均快慢。
average speed = total distance / total time
v = s / t
For uniformly accelerated motion in a straight line, the final speed, initial speed, acceleration and time are linked without involving displacement.
对于匀加速直线运动，末速度、初速度、加速度和时间的关系不包含位移。
v = u + a t
The distance travelled under uniform acceleration can be found from the average speed multiplied by time.
匀加速运动的位移可以用平均速度乘以时间求得。
s = (u + v) t / 2
Acceleration is defined as the rate of change of velocity. A negative value indicates deceleration.
加速度定义为速度的变化率，负值表示减速。
a = (v − u) / t
The gradient of a distance–time graph gives speed. The gradient of a speed–time graph gives acceleration, and the area under a speed–time graph gives distance travelled.
距离–时间图斜率表示速率；速度–时间图斜率表示加速度，图线下面积表示走过的距离。
2. Forces and Newton's Laws | 力与牛顿定律
Newton's first law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a resultant external force.
牛顿第一定律指出，若无净外力作用，物体将保持静止或匀速直线运动状态。
Newton's second law relates resultant force, mass and acceleration. It explains that acceleration is directly proportional to force and inversely proportional to mass.
牛顿第二定律将合外力、质量和加速度联系在一起，加速度与力成正比，与质量成反比。
F = m a
Weight is the gravitational force acting on an object and depends on the local gravitational field strength.
重量是作用在物体上的重力，取决于当地的重力场强度。
W = m g
th, g ≈ 9.8 m/s², but 10 m/s² is commonly used in Cambridge exams unless stated otherwise.
地球上 g ≈ 9.8 m/s²，但剑桥考试中通常取 10 m/s²，除非题目另有说明。
Newton's third law states that for every action force there is an equal and opposite reaction force. These forces act on different objects.
牛顿第三定律指出，每个作用力都有一个大小相等、方向相反的反作用力，且作用在不同物体上。
Hooke's law describes the extension of a spring within its elastic limit, where the extension is proportional to the applied load.
胡克定律描述弹簧在弹性限度内的伸长量与所加载荷成正比。
F = k x
Friction is a force that opposes motion. It can be useful (e.g. walking) or problematic (e.g. causing wear).
摩擦力阻碍运动，既可以是需要的（如行走），也可能带来问题（如磨损）。
3. Momentum | 动量
Momentum is the product of mass and velocity. It is a vector quantity and its direction follows the direction of velocity.
动量是质量与速度的乘积，为矢量，方向与速度方向一致。
p = m v
The principle of conservation of momentum states that in the absence of external forces, total momentum before a collision or explosion equals total momentum after.
动量守恒定律指出，在没有外力作用时，碰撞或爆炸前后的总动量保持不变。
total momentum before = total momentum after
Impulse is the change in momentum and also equals the product of force and the time during which it acts.
冲量等于动量的变化量，也等于力与其作用时间的乘积。
F t = Δp = m v − m u
Car safety features such as seat belts, airbags and crumple zones increase the impact time, reducing the average force on occupants.
安全带、安全气囊和溃缩区等汽车安全装置通过延长碰撞时间，降低乘员所受平均力。
4. Energy, Work and Power | 能量、功与功率
Work is done when a force moves an object in the direction of the force. It transfers energy mechanically.
力使物体沿力的方向移动时做功，实现机械能的转移。
W = F d
Gravitational potential energy depends on mass, gravitational field strength and vertical height above a reference level.
重力势能取决于质量、重力场强和相对于参考面的竖直高度。
Eₚ = m g h
Kinetic energy is the energy possessed by an object due to its motion. It increases with the square of the speed.
动能是物体因运动而具有的能量，与速度的平方成正比。
Eₖ = ½ m v²
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed.
能量守恒定律表明，能量既不会凭空产生，也不会凭空消失，只能转移或转化。
Power is the rate of doing work or transferring energy.
功率是做功或转移能量的速率。
P = W / t = E / t
Efficiency compares useful output energy or power to total input. It can be expressed as a percentage.
效率比较有用输出能量或功率与总输入之比，可用百分比表示。
efficiency = (useful output / total input) × 100%
5. Pressure and Density | 压强与密度
Density is mass per unit volume. It determines whether an object will float or sink in a fluid.
密度是单位体积的质量，决定物体在流体中的沉浮。
ρ = m / V
Pressure is the force acting per unit area. It explains why a sharp knife cuts more easily than a blunt one.
压强是单位面积上所受的压力，解释了为何锋利的刀比钝刀更容易切割。
p = F / A
Pressure in a liquid increases with depth and density. It does not depend on the shape of the container.
液体压强随深度和密度增加而增大，与容器形状无关。
p = h ρ g
Atmospheric pressure can be measured using a barometer. It decreases with altitude.
大气压强可用气压计测量，随海拔升高而减小。
6. Thermal Physics | 热物理
Boyle's law relates pressure and volume of a fixed mass of gas at constant temperature; the product is constant.
波义耳定律描述一定质量气体在恒温下压强与体积成反比，乘积恒定。
p V = constant (for fixed m and constant T)
The pressure law (Gay-Lussac) links pressure and absolute temperature at constant volume.
盖-吕萨克定律（压力定律）表明一定质量气体在体积不变时，压强与绝对温度成正比。
p / T = constant (V constant)
Charles's law connects volume and absolute temperature at constant pressure.
查理定律在压强不变时，体积与绝对温度成正比。
V / T = constant (p constant)
Thermal energy transferred during heating or cooling depends on mass, specific heat capacity and temperature change.
加热或冷却过程中传递的热能取决于质量、比热容和温度变化。
Q = m c Δθ
Specific latent heat is the energy required to change the state of 1 kg of a substance without a change in temperature.
比潜热是使 1 kg 物质改变状态而不改变温度所需的能量。
Q = m L
Heat transfer occurs via conduction, convection and radiation. Conduction is dominant in solids, convection in fluids, and radiation can travel through a vacuum.
热传递有传导、对流和辐射三种方式。传导主要发生在固体中，对流在流体中，辐射可在真空中传播。
7. Waves | 波动
The wave equation links wave speed, frequency and wavelength. It applies to both transverse and longitudinal waves.
波速公式把波速、频率和波长联系起来，适用于横波和纵波。
v = f λ
Frequency is the number of complete waves passing a point per second; period is the time for one complete wave.
频率是每秒通过某点的完整波数，周期是一个完整波所需要的时间。
f = 1 / T
Reflection follows the law where the angle of incidence equals the angle of reflection, measured relative to the normal.
反射定律指出入射角等于反射角，均以法线为基准。
Refraction occurs when a wave changes speed at a boundary, causing a change in direction unless the wave hits normally.
当波在不同介质边界速度改变时发生折射，除非垂直入射，否则方向改变。
n = sin i / sin r (optional at IGCSE level, but commonly used)
In the electromagnetic spectrum, all waves travel at the same speed in a vacuum.
电磁波谱中，所有波在真空中传播速度相同。
c = 3.0 × 10⁸ m/s (in vacuum)
8. Electricity | 电学
Current is the rate of flow of charge. In metals, it is a flow of electrons.
电流是电荷的流动速率，金属导体中为电子流。
I = Q / t
Ohm's law states that for a metallic conductor at constant temperature, current is proportional to potential difference.
欧姆定律表明，在温度不变时，金属导体中的电流与电压成正比。
V = I R
Resistance depends on length (proportional), cross-sectional area (inversely proportional), and resistivity of the material. For IGCSE, the qualitative relationship is sufficient.
电阻与导体长度成正比，与横截面积成反比，并取决于材料电阻率。IGCSE 层次掌握定性关系即可。
Electrical power can be expressed in terms of voltage and current.
电功率可用电压和电流表示。
P = I V
Combined with Ohm's law, power can also be calculated as:
结合欧姆定律，功率也可表示为：
P = I² R = V² / R
Energy transferred by an electrical appliance is power multiplied by time.
用电器转移的电能等于功率乘以时间。
E = I V t
In series circuits, current is the same everywhere, while total voltage is shared. In parallel circuits, voltage across each branch is the same, while currents add up.
串联电路中电流处处相等，总电压分配；并联电路中各支路电压相等，干路电流等于各支路电流之和。
9. Electromagnetism | 电磁学
A current-carrying conductor in a magnetic field experiences a force. This is the motor effect and is used in electric motors.
通电导体在磁场中会受到力的作用，即电动机效应，应用于电动机。
The magnitude of the force depends on magnetic flux density, current and length of conductor when the field is perpendicular.
当磁场与电流方向垂直时，力的大小取决于磁通密度、电流大小和导体长度。
F = B I L (when perpendicular)
Fleming' on of force: thuMb → Motion, First finger → Field, seCond finger → Current (conventional).
弗莱明左手定则给出力方向：拇指→运动，食指→磁场，中指→传统电流方向。
A changing magnetic field can induce a voltage across a conductor. This electromagnetic induction is the principle behind generators and transformers.
变化的磁场可在导体中感生电压，这一电磁感应原理是发电机和变压器的基础。
A simple transformer relies on alternating current. The voltage ratio equals the turns ratio for an ideal transformer.
简单变压器依赖交流电工作。理想变压器电压比等于匝数比。
Vₚ / Vₛ = Nₚ / Nₛ
For an ideal transformer, input power approximates output power, so:
理想变压器输入功率近似等于输出功率，因此：
Vₚ × Iₚ = Vₛ × Iₛ
10. Radioactivity and Atomic Physics | 放射性及原子物理
The atom consists of a nucleus containing protons and neutrons, surrounded by orbiting electrons. Proton number Z and nucleon number A identify isotopes.
原子由包含质子和中子的原子核以及绕核电子组成。质子数 Z 和质量数 A 用于标识同位素。
Alpha particles are helium nuclei (²⁴He), beta particles are fast electrons (⁰₋₁e), and gamma rays are electromagnetic waves of very high frequency.
α 粒子是氦核（⁴₂He），β 粒子是高速电子（⁰₋₁e），γ 射线是极高频率的电磁波。
Radioactive decay is a random process. The half-life is the time taken for half the nuclei in a sample to decay.
放射性衰变是随机过程。半衰期是样品中一半核发生衰变所需的时间。
Activity is the number of decays per second, measured in becquerels (Bq). It decreases over time following the same decay pattern.
活度是每秒衰变次数，单位为贝克勒尔（Bq），随时间按相同规律衰减。
Background radiation comes from natural sources such as cosmic rays and rocks, as well as artificial sources.
背景辐射来自宇宙射线、岩石等天然来源以及人工来源。
11. Key Constants and Useful Relationships | 重要常数与常用关系
Speed of light in vacuum: c = 3.0 × 10⁸ m/s. This is used in wave calculations and optics.
真空中光速：c = 3.0 × 10⁸ m/s，用于波动计算和光学。
Acceleration of free fall near Earth's surface: g ≈ 9.8 m/s² (use 10 m/s² if directed).
近地表自由落体加速度：g ≈ 9.8 m/s²（按指示可用 10 m/s²）。
needed for photon energy E = h f. This appears more frequently in the extended curriculum.
普朗克常数（考试可能会提供）：h = 6.63 × 10⁻³⁴ J·s，用于光子能量 E = h f，在拓展课程中更常见。
1 kilowatt-hour (kWh) = 3.6 × 10⁶ J, a practical unit of electrical energy consumption.
1 千瓦时 (kWh) = 3.6 × 10⁶ J，是实用的电能消耗单位。
between Celsius and Kelvin: T(K) = θ(°C) + 273. Always use kelvin in gas law calculations.
摄氏温度与开氏温度关系：T(K) = θ(°C) + 273，气体定律计算必须使用开氏温标。
12. Exam Tips and Common Mistakes | 应试提示与常见错误
Always write the formula before substituting numbers. Show unit conversions clearly; e.g., km/h to m/s by dividing by 3.6.
务必先写公式再代入数值。单位换算要清晰，例如 km/h 换算为 m/s 需除以 3.6。
Check that the direction of vectors is considered when using momentum and force equations. State the law or principle used, such as 'conservation of energy'.
使用动量和力方程时，注意矢量方向。陈述所用的定律或原理，比如“能量守恒”。
In circuit calculations, redraw the diagram if necessary. Identify whether resistors are in series or parallel before applying formulas.
电路计算时，必要时重绘电路图。先用串并联规则判断电阻连接方式，再应用公式。
When describing experimental methods, mention repeated readings and averaging to improve reliability, and refer to control of variables.
描述实验方法时，应提及多次测量取平均值以提高可靠性，并指出控制变量。
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