📚 IGCSE Cambridge Engineering: Formula & Theorem Quick Reference Handbook | IGCSE 剑桥工程：公式定理速查手册
This quick reference handbook brings together the most important formulas, definitions and theorem-style relationships for Cambridge IGCSE Engineering. Use it when solving calculation questions on mechanics, materials, electronics and energy. The focus is on core relationships that appear in written papers and practical problem-solving.
本速查手册汇总了剑桥 IGCSE 工程课程中最重要的公式、定义和定理式关系，可用于解答力学、材料、电子和能量相关的计算题。内容聚焦于笔试和实际问题解决中反复出现的核心关系。
1. SI Units and Prefixes | 国际单位制与词头
Every engineering calculation must use SI base units unless the question states otherwise. The common base units are metre (m), kilogram (kg), second (s), ampere (A), kelvin (K) and mole (mol). Derived units such as the newton (N), joule (J), watt (W), pascal (Pa) and ohm (Ω) are built from these base units.
除非题目另有说明，所有工程计算都应使用国际单位制基本单位。常见基本单位包括米（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）等导出单位均由这些基本单位组合而成。
Prefixes such as kilo, mega and milli convert very large or very small values into convenient numbers. Remember that a prefix must be converted back to its base value before substitution into a formula. For example, 1 kN = 1000 N and 1 mA = 0.001 A.
词头如 kilo、mega、milli 可以将很大或很小的数值转换为易读数字。代入公式前，必须先将词头还原为基本单位。例如，1 kN = 1000 N，1 mA = 0.001 A。
| Prefix | Symbol | Factor |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | μ | 10⁻⁶ |
2. Force, Mass and Acceleration | 力、质量与加速度
Newton’s second law states that the net force acting on an object is equal to the product of its mass and acceleration. This relationship is central to dynamics, motion analysis and structural load calculations.
牛顿第二定律指出，作用在物体上的合力等于质量与加速度的乘积。这是动力学、运动分析和结构载荷计算的核心关系。
F = ma
Weight is a special force caused by gravity acting on a mass. Near the Earth’s surface, the gravitational field strength g is approximately 9.8 m/s², so weight can be calculated directly from mass.
重量是重力对质量产生的一种特殊力。在地球表面附近，重力场强度 g 约为 9.8 m/s²，因此重量可以直接由质量计算得出。
W = mg
3. Moments and Equilibrium | 力矩与平衡
A moment is the turning effect of a force about a pivot. It is calculated by multiplying the force by the perpendicular distance from the pivot to the line of action of the force. The distance must be perpendicular, not simply the straight-line distance.
力矩是力绕支点的转动效应，等于力乘以支点到力作用线的垂直距离。该距离必须是垂直距离，而不是简单的直线距离。
M = Fd
For an object in static equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments about that pivot. In addition, the total upward force equals the total downward force. These two conditions are used to solve beam, lever and framework problems.
对于处于静力平衡的物体，绕任意支点的顺时针力矩之和等于逆时针力矩之和。此外，向上的合力等于向下的合力。这两个条件常用于求解梁、杠杆和框架问题。
Σ clockwise moments = Σ anticlockwise moments
4. Pressure and Hydraulics | 压强与液压
Pressure is defined as the force acting normally per unit area. A small force can create a large pressure if it acts on a small area, which is the principle behind cutting tools and hydraulic systems.
压强定义为单位面积上垂直作用的力。若力作用在很小的面积上，可以产生很大的压强，这正是切削工具和液压系统的原理。
P = F / A
In a hydraulic system, pressure applied to an enclosed fluid is transmitted equally in all directions. For two connected pistons, the ratio of force to area is the same on both sides. This allows a small effort to lift a large load.
在液压系统中，施加于密闭流体的压强会向各个方向等量传递。对于两个相连的活塞，两侧的力与面积之比相同。这样就可以用较小的力举起较大的负载。
F₁ / A₁ = F₂ / A₂
5. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application in the direction of the force. Energy is the capacity to do work. Both work and energy are measured in joules (J).
当力使其作用点沿力的方向移动时，力做功。能量是做功的能力。功和能量的单位都是焦耳（J）。
W = Fs
Gravitational potential energy is the energy stored by an object raised above a reference level. Kinetic energy is the energy of a moving object. Power is the rate of doing work or transferring energy, measured in watts (W).
重力势能是物体被抬升至参考面以上所储存的能量。动能是运动物体具有的能量。功率是做功或转移能量的速率，单位为瓦特（W）。
Eₚ = mgh Eₖ = ½mv² P = W / t
6. Efficiency and Mechanical Advantage | 效率与机械利益
Efficiency compares useful energy or power output with the total input. It is usually expressed as a percentage. No real machine can be 100% efficient because some energy is always lost as heat, sound or friction.
效率将有用的能量或功率输出与总输入进行比较，通常以百分比表示。任何真实机械都无法达到 100% 效率，因为总有一部分能量以热、声或摩擦形式损失。
Efficiency = (useful output / total input) × 100%
Mechanical advantage compares the load force to the effort force in a machine or mechanism. Velocity ratio compares the distance moved by the effort to the distance moved by the load. For an ideal machine with no losses, efficiency equals mechanical advantage divided by velocity ratio.
机械利益比较机械中的负载力与施力。速度比比较施力移动的距离与负载移动的距离。对于没有损耗的理想机械，效率等于机械利益除以速度比。
MA = load / effort VR = distance moved by effort / distance moved by load
Efficiency = (MA / VR) × 100%
7. 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. Strain measures extension per unit original length. Strain has no units because it is a ratio of two lengths. Stress is measured in pascals (Pa) or newtons per square metre (N/m²).
应力是材料内部单位面积上的力。应变是单位原长的伸长量。应变没有单位，因为它是两个长度的比值。应力的单位是帕斯卡（Pa）或牛顿每平方米（N/m²）。
Stress σ = F / A Strain ε = ΔL / L
Young modulus describes the stiffness of a material in the elastic region of its stress-strain graph. It is the gradient of the straight-line part of the stress-strain curve. A stiffer material has a higher Young modulus.
杨氏模量描述材料在应力-应变图中弹性范围内的刚度，是应力-应变曲线直线部分的斜率。刚度越大的材料，杨氏模量越高。
E = σ / ε = FL / (AΔL)
8. Electrical Quantities and Ohm’s Law | 电学量与欧姆定律
Current is the rate of flow of electric charge. Voltage is the energy transferred per unit charge. Resistance is the opposition to current flow in a circuit. These three quantities are linked by Ohm’s law for ohmic conductors at constant temperature.
电流是电荷流动的速率。电压是每单位电荷转移的能量。电阻是电路中对电流的阻碍。对于恒定温度下的欧姆导体，这三个量由欧姆定律联系起来。
I = Q / t V = IR
Electrical power is the rate at which electrical energy is converted into other forms. It can be calculated from voltage and current, or from current and resistance, or from voltage and resistance.
电功率是电能转换为其他形式的速率。它可以通过电压和电流、电流和电阻、或电压和电阻来计算。
P = IV = I²R = V² / R
9. Resistors in Series and Parallel | 串联与并联电阻
In a series circuit, the current is the same through all components and the total resistance is the sum of individual resistances. Adding more resistors in series therefore increases the total resistance.
在串联电路中，通过所有元件的电流相同，总电阻等于各电阻之和。因此，串联更多电阻会增加总电阻。
Rtotal = R₁ + R₂ + R₃ + …
In a parallel circuit, the voltage across each branch is the same and the reciprocal of total resistance is the sum of the reciprocals of individual resistances. Adding more resistors in parallel decreases the total resistance.
在并联电路中，各支路两端的电压相同，总电阻的倒数等于
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