📚 Year 8 CIE Physics: Formulas and Theorems Quick Reference | 公式定理速查手册
This quick reference handbook covers the essential formulas and key theorems you need to memorise for Year 8 CIE Physics. Every topic is broken down into clear definitions, balanced explanations in English and Chinese, and formulae centred for easy recall. Use this guide to support your homework, revision and Checkpoint examination preparation.
这本速查手册涵盖了 Year 8 CIE 物理必须记忆的核心公式和关键定理。每个主题都分解为清晰的定义、中英双语对照讲解以及居中排版的公式，便于快速记忆。使用本手册辅助你的家庭作业、复习和 Checkpoint 备考。
1. Speed | 速度
Speed tells us how fast an object is moving. Average speed is found by dividing the total distance travelled by the total time taken. If an object covers 100 m in 10 s, its speed is 10 m/s.
速度表示物体运动的快慢。平均速度由总路程除以总时间求得。如果一个物体在 10 s 内移动了 100 m，其速度为 10 m/s。
average speed = total distance / total time
The SI unit of speed is metres per second (m/s). Distance is measured in metres (m) and time in seconds (s). In everyday life, speed is also given in kilometres per hour (km/h).
速度的国际单位是米每秒（m/s）。距离以米（m）为单位，时间以秒（s）为单位。日常生活中，速度也常用千米每小时（km/h）表示。
Always check that the units match. To convert m/s to km/h, multiply by 3.6. For constant speed, the same formula applies directly.
请务必检查单位是否匹配。将 m/s 换算为 km/h 时，乘以 3.6。对于匀速运动，直接套用同一公式即可。
2. Density | 密度
Density measures how tightly matter is packed into a substance. A material with high density has more mass in a given volume. It is a property that helps identify materials.
密度衡量物质内质量的紧密程度。密度高的材料在给定体积内含有更多的质量。这一性质有助于识别材料。
density = mass / volume
Mass is recorded in kilograms (kg) or grams (g), volume in cubic metres (m³) or cubic centimetres (cm³). The standard unit is kg/m³, but g/cm³ is also common. The density of pure water is 1.0 g/cm³ or 1000 kg/m³.
质量使用千克（kg）或克（g），体积为立方米（m³）或立方厘米（cm³）。标准单位是 kg/m³，g/cm³ 也常使用。纯水的密度是 1.0 g/cm³ 或 1000 kg/m³。
To find the density of an irregular solid, measure its mass on a balance and its volume by displacement in a measuring cylinder, then apply the formula.
要测量不规则固体的密度，先用天平测质量，用量筒排水法测体积，再代入公式计算。
3. Pressure | 压强
Pressure describes how concentrated a force is over an area. A sharp knife cuts easily because it concentrates the force onto a tiny area, producing high pressure.
压强描述力在面积上的集中程度。锋利的刀易于切割，因为它将力集中在极小的面积上，产生很大的压强。
pressure = force / area
ascal (Pa), where 1 Pa = 1 N/m². Larger forces over smaller areas create larger pressures.
力以牛顿（N）为单位，面积以平方米（m²）为单位。压强单位是帕斯卡（Pa），1 Pa = 1 N/m²。力越大、面积越小，压强就越大。
This formula explains why boots with wide soles prevent sinking into soft ground: they spread the weight over a larger area, reducing pressure.
该公式解释了为何宽底靴子不会陷入软泥中：它们将体重分散到较大的面积上，降低了压强。
4. Moment of a Force | 力矩
A moment is the turning effect of a force about a pivot. It depends on two factors: the size of the force and the perpendicular distance from the pivot to the line of action of the force.
力矩是力对支点的转动效应。它取决于两个因素：力的大小以及支点到力作用线的垂直距离。
moment = force × perpendicular distance from pivot
Moment is measured in newton metres (N m). To increase the turning effect, you can either apply a larger force or increase the distance from the pivot. A spanner with a long handle makes it easier to turn a nut.
力矩的单位是牛顿米（N m）。要增大转动效果，可以施加更大的力，或增大与支点的距离。长柄扳手更容易转动螺母。
In equilibrium, the total clockwise moment equals the total anticlockwise moment. This principle is used to solve problems with levers and see-saws.
物体平衡时，顺时针力矩之和等于逆时针力矩之和。这一原理用于解决杠杆和跷跷板的问题。
5. Hooke's Law | 胡克定律
Hooke's Law describes the behaviour of springs and many elastic materials. It states that the extension of a spring is directly proportional to the force applied, provided the elastic limit is not exceeded.
胡克定律描述弹簧和许多弹性材料的行为。它指出，只要不超过弹性限度，弹簧的伸长量与所施加的力成正比。
F ∝ x (within the elastic limit)
re k is the spring constant. If too much force is applied, the spring deforms permanently.
此处 F 为施加的力，x 为伸长量。该关系也可写作 F = k x，k 为劲度系数。若施加的力过大，弹簧将发生永久变形。
A force-extension graph gives a straight line through the origin up to the limit of proportionality. The steeper the line, the stiffer the spring.
在比例限度内，力-伸长量图像为一条过原点的直线。直线越陡，弹簧越硬。
6. Work | 功
Work is done whenever a force moves an object in the direction of the force. Energy is transferred when work is done. If you push a box 3 m with a force of 5 N, you do 15 J of work.
只要力使物体沿力的方向移动，就做了功。做功能转移能量。若你用 5 N 的力将一个箱子推动 3 m，你做了 15 J 的功。
work = force × distance (moved in the direction of the force)
The unit of work is the joule (J). One joule is equal to one newton metre. No work is done if there is no movement, or if the movement is perpendicular to the force.
功的单位是焦耳（J）。1 J 等于 1 N m。如果没有移动，或移动方向与力垂直，均不做功。
Work is a scalar quantity; it does not depend on direction but on the path taken in the direction of the force.
功是标量，不依赖方向，而是取决于沿力方向移动的路径。
7. Power | 功率
Power measures how quickly work is done or how fast energy is transferred. A powerful machine does the same work in less time.
功率衡量做功或能量转移的快慢。大功率机器可以在更短时间内完成同样的功。
power = work done / time taken
ergy transferred / time. Power is measured in watts (W). One watt is one joule per second.
由于功等于转移的能量，也可以写作 power = energy transformed / time。功率单位是瓦特（W），1 W = 1 J/s。
For example, a 60 W lamp transfers 60 J of electrical energy into light and heat every second. High-power appliances include kettles and heaters, often quoted in kilowatts (kW).
例如，一盏 60 W 的灯每秒将 60 J 的电能转化为光能和热能。高功率电器如电水壶和取暖器常用千瓦（kW）表示。
8. Conservation of Energy and Efficiency | 能量守恒与效率
The law of conservation of energy states that energy cannot be created or destroyed. It can only be transferred from one store to another or transformed from one form to another. The total energy in a closed system remains constant.
能量守恒定律指出，能量既不能凭空产生也不能凭空消失，只能从一种储存转移到另一种或从一种形式转化为另一种形式。封闭系统中的总能量保持不变。
Efficiency measures how well a device converts input energy into useful output energy. No machine is 100% efficient because some energy is always dissipated as heat to the surroundings.
效率衡量装置将输入能量转化为有用输出能量的程度。由于总有部分能量以热的形式散失到环境中，没有机器能达到 100% 效率。
efficiency = (useful output energy / total input energy) × 100%
b that gives 10 J of light for 50 J of electrical input has an efficiency of (10/50) × 100% = 20%.
效率也可用小数表示。一个 LED 灯泡输入 50 J 电能，输出 10 J 光能，其效率为 (10/50) × 100% = 20%。
9. Electric Current and Charge | 电流与电荷
Electric current is a flow of electric charge. In a metal wire, the charge is carried by moving electrons. The size of the current depends on the amount of charge passing a point each second.
电流是电荷的流动。在金属导线中，电荷由自由电子的移动输送。电流的大小取决于每秒通过某点的电荷量。
current = charge / time (I = Q / t)
Current is measured in amperes (A), charge in coulombs (C), and time in seconds (s). An ammeter connected in series measures current. A current of 1 A means 1 C of charge flows past a point per second.
电流以安培（A）为单位，电荷以库仑（C）为单位，时间以秒（s）为单位。串联的安培计测量电流。1 A 的电流表示每秒有 1 C 的电荷通过某一点。
arranged: Q = I × t. This is useful for calculating how much charge flows in a given time.
电荷也可用 Q = I × t 表示，便于计算给定时间内流过的电荷量。
10. Voltage, Resistance and Ohm's Law | 电压、电阻与欧姆定律
Voltage (potential difference) is the energy transferred per unit charge. It tells us how much energy is given to or taken from each coulomb of charge as it moves through a component.
电压（电势差）是每单位电荷转移的能量。它表示每库仑电荷通过某一元件时获得或失去的能量。
voltage = energy / charge (V = E / Q)
Voltage is measured in volts (V). Resistance opposes the flow of current. Ohm's Law relates voltage, current and resistance in a simple way for many conductors at constant temperature.
电压单位是伏特（V）。电阻阻碍电流的流动。对于许多在恒温下的导体，欧姆定律用一种简单关系将电压、电流和电阻联系在一起。
resistance = voltage / current (R = V / I)
Resistance is measured in ohms (Ω). The law is only true if the temperature stays constant. Some components, like a filament lamp, do not follow Ohm's Law because their resistance increases with temperature.
电阻单位是欧姆（Ω）。该定律仅在温度恒定时成立。有些元件如白炽灯的灯丝不遵循欧姆定律，因为其电阻随温度升高而增大。
11. Resistors in Series | 串联电阻
When resistors are connected end-to-end, the same current passes through each one. The total (or equivalent) resistance is simply the sum of all individual resistances.
当电阻首尾相连时，每个电阻中流过的电流相同。总电阻（等效电阻）等于所有单个电阻之和。
Rtotal = R₁ + R₂ + R₃ + ...
For example, if a 2 Ω resistor, a 3 Ω resistor and a 5 Ω resistor are placed in series, the total resistance is 10 Ω. Adding more resistors in series always increases the total resistance.
例如，将 2 Ω、3 Ω 和 5 Ω 的电阻串联后，总电阻为 10 Ω。串联更多电阻总会增加总电阻。
This rule is used to design circuits that need a specific resistance value. The current drawn from the power supply decreases as total resistance increases.
该规则用于设计需要特定阻值的电路。随着总电阻增大，从电源汲取的电流会减小。
12. Wave Speed and the Law of Reflection | 波速与反射定律
A wave transfers energy from one place to another without transferring matter. The speed of a wave depends on the medium. It links frequency and wavelength through one simple equation.
波将能量从一处传递到另一处，并不传递物质。波速取决于介质，并通过一个简单方程联系频率和波长。
wave speed = frequency × wavelength (v = f λ)
Wave speed is in metres per second (m/s), frequency in hertz (Hz), and wavelength in metres (m). Frequency is the number of complete waves passing a point per second.
波速单位为米每秒（m/s），频率单位为赫兹（Hz），波长单位为米（m）。频率是每秒通过某点的完整波数。
When a wave strikes a smooth barrier, it obeys the law of reflection:
当波遇到光滑障碍物时，遵循反射定律：
angle of incidence = angle of reflection (i = r)
Both angles are measured between the ray direction and the normal line at right angles to the surface. This law applies to light, sound and water waves in ray diagrams.
两个角度均为射线方向与法线之间的夹角，法线垂直于表面。在光线图中，该定律适用于光、声和水波。
Knowing this equation and law helps predict the path of waves in mirrors, echoes and other reflections.
掌握该方程和定律，有助于预测波在镜面、回声及其他反射中的路径。
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