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

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

This quick reference handbook brings together the essential formulas and theorems needed for IGCSE WJEC Engineering. It covers mechanics, energy, materials, electricity, fluids and trigonometry, with each rule stated clearly for rapid revision and exam use.

本速查手册汇总了 IGCSE WJEC 工程所需的核心公式和定理。内容涵盖力学、能量、材料、电学、流体和三角学，每条规则均以清晰方式呈现，便于快速复习和考试使用。

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1. SI Units and Prefixes | 国际单位制与词头

In WJEC Engineering, all calculations should be carried out in SI units unless a question states otherwise. The base units are metre (m), kilogram (kg), second (s), ampere (A), kelvin (K) and mole (mol). Derived units such as newton (N), joule (J), watt (W), pascal (Pa) and ohm (Ω) appear frequently.

在 WJEC 工程考试中，除非题目另有说明，所有计算都应使用国际单位制。基本单位包括米 (m)、千克 (kg)、秒 (s)、安培 (A)、开尔文 (K) 和摩尔 (mol)。牛顿 (N)、焦耳 (J)、瓦特 (W)、帕斯卡 (Pa) 和欧姆 (Ω) 等导出单位也经常出现。

Prefix	Symbol	Value
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹

Always convert prefixes before substituting values into a formula. For example, 40 kN must be written as 40 × 10³ N.

在将数值代入公式之前，必须先换算词头。例如，40 kN 必须写成 40 × 10³ N。

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2. Motion and Force | 运动与力

The relationship between force, mass and acceleration is given by Newton’s second law.

力、质量和加速度之间的关系由牛顿第二定律给出。

F = m × a

Weight is the force caused by gravity acting on a mass, where g is the gravitational field strength, approximately 9.8 N/kg on Earth.

重量是重力作用在质量上产生的力，其中 g 为重力场强度，在地球上约为 9.8 N/kg。

W = m × g

Average speed, acceleration and uniformly accelerated motion equations are useful when analysing mechanisms and vehicles. The most common IGCSE forms are shown below.

平均速度、加速度和匀加速运动方程在分析机构和车辆时非常有用。IGCSE 最常见的形式如下。

v = u + a × t

s = (u + v) ÷ 2 × t

v² = u² + 2 × a × s

Here u is initial velocity, v is final velocity, a is acceleration, s is displacement and t is time.

其中 u 为初速度，v 为末速度，a 为加速度，s 为位移，t 为时间。

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3. Energy, Work and Power | 能量、功与功率

Work is done when a force moves its point of application in the direction of the force.

当力使其作用点沿力的方向移动时，就做了功。

W = F × d

Gravitational potential energy and kinetic energy are the two main mechanical energy stores in engineering problems.

重力势能和动能是工程问题中两种主要的机械能储存形式。

Eₚ = m × g × h

Eₖ = ½ × m × v²

Power is the rate of doing work or transferring energy.

功率是做功或传递能量的速率。

P = E ÷ t = W ÷ t

Efficiency compares useful output with total input and is often expressed as a percentage.

效率将有用输出与总输入进行比较，通常以百分比表示。

efficiency = useful output energy ÷ total input energy × 100%

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4. Moments and Equilibrium | 力矩与平衡

A moment is the turning effect of a force about a pivot. The distance used must be the perpendicular distance from the pivot to the line of action of the force.

力矩是力绕支点产生的转动效应。所用距离必须是支点到力作用线的垂直距离。

moment = F × d

For an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. This is the principle of moments.

对于处于转动平衡的物体，顺时针力矩之和等于逆时针力矩之和。这就是力矩原理。

Σ clockwise moments = Σ anticlockwise moments

When two equal and opposite parallel forces act on a body, they form a couple. The moment of a couple equals one force multiplied by the perpendicular separation between the forces.

当两个大小相等、方向相反的平行力作用在物体上时，就形成一个力偶。力偶矩等于其中一个力乘以两力之间的垂直距离。

couple moment = F × d

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5. Stress, Strain and Young Modulus | 应力、应变与杨氏模量

Stress measures the internal force per unit area within a material. It is measured in pascals (Pa).

应力衡量材料内部单位面积上的内力，其单位为帕斯卡 (Pa)。

σ = F ÷ A

Strain is the extension per unit original length. It has no units because it is a ratio of two lengths.

应变是单位原始长度的伸长量。它是两个长度的比值，因此没有单位。

ε = ΔL ÷ L₀

Young modulus describes the stiffness of a material in the elastic region, before permanent deformation occurs.

杨氏模量描述材料在弹性区域内的刚度，即在发生永久变形之前。

E = σ ÷ ε = F × L₀ ÷ (A × ΔL)

Within the limit of proportionality, Hooke’s law applies: extension is directly proportional to the applied force.

在比例极限内，胡克定律适用：伸长量与施加的力成正比。

F = k × x

Here k is the spring constant or stiffness, and x is the extension.

其中 k 为弹簧常数或刚度，x 为伸长量。

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6. Electrical Principles | 电学原理

Electric current is the rate of flow of charge. One ampere is one coulomb of charge passing a point per second.

电流是电荷流动的速率。一安培表示每秒通过某一点的电荷量为一库仑。

I = Q ÷ t

Potential difference is the energy transferred per unit charge.

电势差是每单位电荷传递的能量。

V = W ÷ Q

Ohm’s law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant.

欧姆定律表明，在温度保持不变的条件下，通过导体的电流与其两端的电势差成正比。

V = I × R

Electrical power can be calculated in three equivalent ways, depending on which quantities are known.

电功率可以根据已知量用三种等价方式计算。

P = V × I = I² × R = V² ÷ R

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7. Resistors in Series and Parallel | 电阻的串联与并联

In a series circuit, the current is the same through all components. The total resistance is the sum of the individual resistances.

在串联电路中，所有元件的电流相同。总电阻等于各个电阻之和。

R_total = R₁ + R₂ + R₃ + …

In a parallel circuit, the potential difference across each branch is the same. The reciprocal of total resistance is the sum of the reciprocals of the individual resistances.

在并联电路中，各支路两端的电势差相同。总电阻的倒数等于各电阻倒数之和。

1 ÷ R_total = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃ + …

For two resistors in parallel, the product-over-sum shortcut may be used.

对于两个并联电阻，可以使用积除以和的快捷公式。

R_total = R₁ × R₂ ÷ (R₁ + R₂)

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8. Materials and Density | 材料与密度

Density links mass and volume. It is a key property when selecting materials for lightweight or

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