📚 KS3 CAIE Physics: Quick Reference Handbook of Formulas and Theorems | KS3 CAIE 物理：公式定理速查手册
This article provides a concise yet complete compilation of all essential formulas and theorems covered in the KS3 CAIE Physics syllabus. Each equation is paired with a clear explanation, worked examples where helpful, and a bilingual presentation to support learners who study in both English and Chinese.
本文为 KS3 CAIE 物理课程中所有核心公式和定理提供了一份简明而完整的速查手册。每一个方程都配有清晰的解释，并在适当处加入示例，采用中英双语对照的形式，帮助双语学习者更好地掌握知识要点。
1. Motion and Speed | 运动与速度
Speed is the distance travelled per unit time. If an object moves at a constant speed, the formula is simple and direct.
速度是单位时间内通过的路程。如果物体匀速运动，公式便非常直接。
speed = distance ÷ time v = d / t
The SI unit of speed is metres per second (m/s). When distance is given in metres and time in seconds, speed will be in m/s. For average speed over a journey with varying speed, the same relationship holds using total distance and total time.
速度的国际单位是米每秒（m/s）。当距离以米为单位、时间以秒为单位时，速度单位即为 m/s。对于速度变化的全程，平均速度同样用总距离除以总时间计算。
Acceleration is the rate of change of velocity. It tells us how quickly an object speeds up, slows down or changes direction.
加速度表示速度变化的快慢。它描述了物体加速、减速或改变方向的快慢程度。
acceleration = change in velocity ÷ time taken a = (v − u) / t
Here, u is initial velocity, v is final velocity and t is the time taken. The unit is m/s². A negative acceleration is often called deceleration.
其中 u 为初速度，v 为末速度，t 为所用时间。单位为 m/s²。负的加速度常称为减速度。
2. Forces and Newton’s Laws | 力与牛顿定律
A force is a push or a pull, measured in newtons (N). Forces can change the speed, direction or shape of an object.
力是推或拉，单位为牛顿（N）。力可以改变物体的速度、运动方向或形状。
weight = mass × gravitational field strength W = m g
On Earth, g ≈ 9.8 N/kg, often rounded to 10 N/kg at KS3. Mass is measured in kilograms (kg) and weight in newtons (N). Never confuse mass and weight.
在地球上，g 约为 9.8 N/kg，KS3 阶段常取 10 N/kg。质量以千克（kg）为单位，重量以牛顿（N）为单位。切勿混淆质量和重量。
Newton’s Second Law links force, mass and acceleration. It is one of the most important relationships in physics.
牛顿第二定律将力、质量和加速度联系在一起，是物理学中最重要的关系式之一。
force = mass × acceleration F = m a
The unit of force is the newton, where 1 N is the force needed to accelerate 1 kg by 1 m/s². When multiple forces act, the net force is used.
力的单位是牛顿，1 N 是使 1 kg 物体产生 1 m/s² 加速度所需的力。当多个力作用时，应使用合外力进行计算。
3. Density | 密度
Density is the mass per unit volume of a substance. It helps to identify materials and predict whether objects will float or sink.
密度是物质单位体积的质量，常用于鉴别材料以及判断物体沉浮。
density = mass ÷ volume ρ = m / V
The SI unit is kg/m³, but g/cm³ is also common at KS3. To convert: 1 g/cm³ = 1000 kg/m³. A substance with density less than that of water (1 g/cm³) will float.
国际单位为 kg/m³，KS3 中也常用 g/cm³。换算关系：1 g/cm³ = 1000 kg/m³。密度小于水（1 g/cm³）的物体会浮在水面上。
4. Pressure | 压强
Pressure measures how concentrated a force is over a given area. A sharp knife exerts high pressure because the force is spread over a tiny area.
压强表示力在作用面上的集中程度。锋利的刀之所以能轻易切割，正是因为力集中在很小的面积上，产生了很大的压强。
pressure = force ÷ area P = F / A
Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². A larger area reduces pressure (e.g., snowshoes), while a smaller area increases it.
压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。增大受力面积可以减小压强（如雪鞋），减小受力面积则可增大压强。
5. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force. It depends on both the size of the force and the distance from the pivot.
力矩是力的转动效应，其大小取决于力的大小以及力到支点的垂直距离。
moment = force × perpendicular distance from pivot M = F d
The unit is newton-metre (N m). When an object is balanced, the total clockwise moments equal the total anticlockwise moments (the principle of moments).
力矩的单位是牛顿·米（N·m）。当物体平衡时，顺时针力矩之和等于逆时针力矩之和，这就是力矩平衡原理。
6. 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. Energy is the capacity to do work, measured in joules (J).
当力使物体沿力的方向移动时就做了功。能量是做功的能力，单位为焦耳（J）。
work done = force × distance moved in the direction of force W = F d
Kinetic energy and gravitational potential energy are two key forms. The gain in gravitational potential energy when an object is lifted is given by:
动能和重力势能是两种关键能量形式。物体被抬高时增加的重力势能可用下式计算：
ΔEₚ = m g Δh (change in gravitational potential energy = mass × g × change in height)
Power is the rate at which work is done or energy is transferred.
功率是做功或能量转移的速率。
power = work done ÷ time taken P = E / t or P = W / t
The unit of power is the watt (W), where 1 W = 1 J/s. A more powerful machine does the same work in less time.
功率的单位是瓦特（W），1 W = 1 J/s。功率越大的机器，做同样的功所需时间越短。
7. Wave Properties | 波的性质
Waves transfer energy without transferring matter. The relationship between wave speed, frequency and wavelength is fundamental for both transverse and longitudinal waves.
波传递能量而不传递物质。波速、频率和波长之间的关系对所有横波和纵波都成立。
wave speed = frequency × wavelength v = f λ
Frequency is measured in hertz (Hz), wavelength in metres (m) and wave speed in m/s. For light, v = c ≈ 3.0 × 10⁸ m/s in vacuum.
频率以赫兹（Hz）为单位，波长以米（m）为单位，波速单位为 m/s。真空中光速 c ≈ 3.0 × 10⁸ m/s。
8. Electric Current and Voltage | 电流与电压
Electric current is the flow of electric charge. Voltage (potential difference) provides the ‘push’ that drives current around a circuit.
电流是电荷的定向流动。电压（电势差）则为电路中电流的流动提供“推动力”。
current = charge ÷ time I = Q / t
Current is measured in amperes (A), charge in coulombs (C) and time in seconds (s). 1 A = 1 C/s.
电流用安培（A）计量，电荷用库仑（C），时间以秒（s）为单位。1 A = 1 C/s。
Voltage is the energy transferred per unit charge. It is measured in volts (V).
电压是单位电荷转移的能量，单位为伏特（V）。
V = E / Q (potential difference = energy transferred ÷ charge)
9. Resistance and Ohm’s Law | 电阻与欧姆定律
Resistance is a measure of how much a component opposes the flow of current. It is the ratio of voltage to current for a conductor at constant temperature.
电阻是衡量元件对电流阻碍作用大小的物理量。对于恒温下的导体，电阻为电压与电流的比值。
resistance = voltage ÷ current R = V / I
The unit is the ohm (Ω). Ohm’s law states that, provided temperature stays constant, the current through a metal conductor is proportional to the voltage across it.
电阻的单位为欧姆（Ω）。欧姆定律指出，在温度不变的条件下，通过金属导体的电流与其两端的电压成正比。
10. Electrical Power and Energy | 电功率与电能
Electrical power is the rate at which electrical energy is transferred by a circuit component. It depends on both current and voltage.
电功率是电路元件传递电能的速率，由电流和电压共同决定。
power = current × voltage P = I V
Using Ohm’s law, this formula can also be written as P = I²R or P = V²/R for components that obey Ohm’s law.
结合欧姆定律，对于遵守欧姆定律的元件，该公式还可写为 P = I²R 或 P = V²/R。
The total energy transferred is power multiplied by time. The unit of electrical energy used in households is often the kilowatt-hour (kWh).
总的电能传递为功率乘以时间。家庭用电中常用的电能量单位为千瓦时（kWh）。
energy = power × time E = P t
11. Magnetism and Electromagnetism | 磁与电磁
The region around a magnet where a magnetic force is experienced is called a magnetic field. Field lines run from north to south outside the magnet.
磁体周围能感受到磁力的区域称为磁场。磁体外部的磁感线从北极指向南极。
Electromagnets are created by passing current through a coil of wire (solenoid). The strength of an electromagnet can be increased by increasing the current, adding more turns to the coil, or inserting a soft iron core.
电磁铁是通过对螺线管（线圈）通电产生的。增大电流、增加线圈匝数或插入软铁芯都可增强电磁铁的磁性。
There is no single core equation for magnetism at KS3, but the relationship F = B I L for a current-carrying wire in a magnetic field is sometimes introduced for extension.
KS3 阶段磁学没有单一的核心公式，但在拓展内容中有时会引入载流导线在磁场中受力公式 F = B I L。
12. Energy Conservation and Efficiency | 能量守恒与效率
Energy cannot be created or destroyed, only transferred or transformed from one form to another. This is the principle of conservation of energy.
能量既不能被创造也不能被消灭，只能从一种形式转移或转化为另一种形式，这就是能量守恒原理。
total energy input = useful energy output + wasted energy
Efficiency measures the fraction of energy supplied that is transferred to useful forms. It can be expressed as a percentage.
效率衡量供给能量中转化为有用形式的比例，可以用百分比表示。
efficiency = (useful output energy / total input energy) × 100%
High efficiency means less energy is dissipated as heat or sound; low efficiency means more energy is wasted. Efficiency is always less than or equal to 100% for real devices.
高效率意味着较少能量以热或声音等形式耗散；低效率则浪费更多能量。实际装置的效率总是≤100%。
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