📚 Year 9 CAIE Engineering: Formula & Theorem Quick Reference Handbook | 9年级CAIE工程：公式定理速查手册
Welcome to your essential quick-reference guide for Year 9 CAIE Engineering. This handbook distils all the key formulas and theorems you need to recall, covering forces, energy, electricity, materials, and more. Use it for revision, homework, and in-class problem-solving to build confidence in applying engineering principles.
欢迎使用这本9年级CAIE工程核心速查手册。本手册凝练了你需要掌握的所有关键公式和定理，涵盖力、能量、电学、材料等主题。可用于复习、作业和课堂解题，帮助你自信地应用工程原理。
1. Forces and Newton's Laws | 力与牛顿定律
A force is a push or a pull that can change the motion of an object. Newton's laws of motion describe how forces affect motion. Newton’s first law (inertia) explains that objects resist changes to their state of motion. Newton’s second law gives the quantitative link between force, mass, and acceleration.
力是能改变物体运动的推或拉。牛顿运动定律描述了力如何影响运动。牛顿第一定律（惯性）说明物体倾向于保持运动状态不变。牛顿第二定律给出了力、质量和加速度之间的定量关系。
F = m × a
Net force (F) in newtons equals mass (m) in kilograms times acceleration (a) in m/s². When forces are balanced, acceleration is zero; unbalanced forces produce acceleration.
净力（F）以牛顿为单位，等于质量（m，千克）乘以加速度（a，米每二次方秒）。力平衡时加速度为零；非平衡力产生加速度。
Newton’s third law: For every action, there is an equal and opposite reaction. This means forces always occur in pairs acting on different bodies.
牛顿第三定律：每作用力都有一个大小相等、方向相反的反作用力。力总是成对出现并作用在不同的物体上。
Common force calculations also involve weight: W = m × g, where g ≈ 9.8 m/s² on Earth.
常见的力计算还包括重力：W = m × g，地球上g ≈ 9.8 米每二次方秒。
2. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot. The size of the moment depends on the force applied and the perpendicular distance from the pivot. The principle of moments states that for a system in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
力矩是力绕支点的转动效应。力矩大小取决于施加的力和力的作用线到支点的垂直距离。力矩原理指出，平衡系统中，顺时针力矩之和等于逆时针力矩之和。
Moment = F × d
Where moment (M) is measured in newton-metres (Nm), F is the force in newtons, and d is the perpendicular distance from the pivot in metres. This formula is essential for designing levers and analysing balance.
式中力矩（M）的单位是牛顿·米（N·m），F是力（牛顿），d是从支点到力作用线的垂直距离（米）。该公式对设计杠杆和分析平衡至关重要。
Levers are classified into three classes based on the relative positions of effort, load, and fulcrum. The mechanical advantage of a lever can be increased by moving the effort further from the fulcrum.
杠杆根据施力点、负载和支点的相对位置分为三类。将施
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