KS3 CAIE Engineering: Formula & Theorem Quick Reference Handbook | KS3 CAIE 工程：公式定理速查手册

📚 KS3 CAIE Engineering: Formula & Theorem Quick Reference Handbook | KS3 CAIE 工程：公式定理速查手册

This handbook brings together the most critical formulas and theorems you will encounter in KS3 CAIE Engineering, from basic electricity to mechanics and machine systems. Use it as a quick reference to check definitions, units, and rearrangements before exams.

本手册汇集了 KS3 CAIE 工程课程中最关键的公式和定理，涵盖基础电学、力学和机械系统。可作为考前快速查阅定义、单位与公式变换的工具。

1. Ohm’s Law | 欧姆定律

Ohm’s Law is fundamental to understanding electrical circuits, linking voltage, current, and resistance.

欧姆定律是理解电路的基础，它将电压、电流和电阻联系在一起。

V = I × R

Voltage (V) is measured in volts (V), current (I) in amperes (A), and resistance (R) in ohms (Ω).

电压 (V) 的单位是伏特 (V)，电流 (I) 的单位是安培 (A)，电阻 (R) 的单位是欧姆 (Ω)。

To find current: I = V ÷ R. To find resistance: R = V ÷ I. Always ensure the units are consistent when using these formulas.

求电流：I = V ÷ R。求电阻：R = V ÷ I。使用公式时确保单位一致。

In a series circuit, the total resistance is the sum of individual resistances: R_total = R₁ + R₂ + …

在串联电路中，总电阻等于各电阻之和：R_total = R₁ + R₂ + …。

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2. Mechanical Advantage (MA) of Levers | 杠杆的机械效益

Mechanical advantage tells us how many times a lever multiplies the input force. It is the ratio of load to effort.

机械效益表示杠杆将输入力放大了多少倍，是负载与施力之比。

MA = Load (L) / Effort (E)

Load is the force being moved or overcome, measured in newtons (N). Effort is the force applied, also in newtons (N). MA has no unit since it is a ratio.

负载是需移动或克服的力，单位为牛顿 (N)。施力是施加的力，单位也是牛顿 (N)。机械效益是比值，无单位。

For a first-class lever (e.g. seesaw), the MA can also be calculated by effort arm divided by load arm, if friction is ignored.

对于第一类杠杆（如跷跷板），如忽略摩擦，机械效益也可由施力臂除以负载臂计算。

A lever with MA > 1 makes work easier by reducing the effort needed; MA < 1 increases the distance or speed of the load.

MA > 1 的杠杆可省力；MA < 1 则增大负载的移动距离或速度。

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3. Moment of a Force (Torque) | 力矩（扭矩）

The moment of a force measures the turning effect about a pivot. It depends on the force and the perpendicular distance from the pivot.

力矩测量力绕支点产生的转动效应，取决于力的大小与力到支点的垂直距离。

Moment (M) = Force (F) × Distance (d)

Moment is measured in newton-metres (N m). Force (F) is in newtons (N) and distance (d) is in metres (m).

力矩的单位是牛顿·米 (N m)。力 (F) 以牛顿 (N) 计，距离 (d) 以米 (m) 计。

For equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about a pivot: Σ M_clockwise = Σ M_anticlockwise.

平衡时，绕支点的顺时针力矩之和等于逆时针力矩之和：Σ M_clockwise = Σ M_anticlockwise。

If a force is applied at an angle, only the perpendicular component contributes to the moment. The distance used must be the perpendicular distance from the line of action to the pivot.

若力以角度施加，仅垂直分量产生力矩。所用距离必须是力作用线到支点的垂直距离。

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4. Pressure | 压强

Pressure measures how much force acts on a given area. It is crucial in hydraulic systems and structural design.

压强测量单位面积上作用的力，在液压系统和结构设计中至关重要。

Pressure (P) = Force (F) / Area (A)

Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². Force is in newtons (N) and area in square metres (m²).

压强单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。力以牛顿 (N) 计，面积以平方米 (m²) 计。

Larger area with the same force gives lower pressure, which explains why snowshoes stop you sinking.

同等力下面积越大压强越低，这解释了雪鞋防陷的原理。

In hydraulic systems, pressure is transmitted equally throughout an enclosed fluid, allowing force multiplication: F₁/A₁ = F₂/A₂.

在液压系统中，封闭液体等值传递压强，可放大作用力：F₁/A₁ = F₂/A₂。

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5. Density | 密度

Density describes how much mass is packed into a certain volume. It helps select materials for lightweight or heavy-duty applications.

密度描述单位体积内所含的质量，有助于选择轻质或重型应用的材料。

Density (ρ) = Mass (m) / Volume (V)

Density is measured in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³). Mass is in kg or g, volume in m³ or cm³.

密度单位是千克每立方米 (kg/m³) 或克每立方厘米 (g/cm³)。质量单位为 kg 或 g，体积单位为 m³ 或 cm³。

Water has a density of 1000 kg/m³ (1 g/cm³). Objects with density less than water float; those with higher density sink.

水的密度为 1000 kg/m³ (1 g/cm³)。密度小于水的物体会浮起，大于水的则会下沉。

Engineers use density to calculate the weight of structures and choose materials with the right balance of strength and mass.

工程师利用密度计算结构重量，并选择强度与质量平衡的材料。

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6. Work Done | 做功

Work is done when a force moves an object through a distance. It represents the transfer of energy.

力使物体移动一段距离时即做功

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