Year 11 CIE Engineering: Quick Reference Formula & Theorem Handbook | Year 11 CIE 工程：公式定理速查手册

📚 Year 11 CIE Engineering: Quick Reference Formula & Theorem Handbook | Year 11 CIE 工程：公式定理速查手册

This handbook compiles essential formulas and theorems required for the CIE IGCSE Engineering syllabus. It is designed as a revision tool to help you quickly recall key relationships across mechanics, materials, electricity and simple machines. Use it to supplement your exam preparation by testing yourself on each formula’s meaning and application.

本手册汇编了 CIE IGCSE 工程课程所需的基本公式和定理，旨在作为复习工具，帮助您快速回顾力学、材料、电学与简单机械中的关键关系。通过自测每个公式的含义和应用，配合试题练习，可有效巩固知识。

1. Kinematics and Newton’s Laws | 运动学与牛顿定律

For an object moving with uniform acceleration a, initial velocity u, final velocity v, displacement s, and time t, the three equations of motion are:

对于以匀加速度 a 运动的物体，初速度为 u，末速度为 v，位移为 s，时间为 t，三个运动学方程如下：

v = u + at: the final velocity equals the initial velocity plus the product of acceleration and time.

v = u + at：末速度等于初速度加上加速度与时间的乘积。

s = ut + ½at²: displacement is given by initial velocity times time plus one-half of acceleration times the square of time. (½ is half, t² is t squared)

s = ut + ½at²：位移等于初速度乘以时间加上二分之一的加速度乘以时间的平方。

v² = u² + 2as: the square of the final velocity equals the square of the initial velocity plus twice the product of acceleration and displacement.

v² = u² + 2as：末速度的平方等于初速度的平方加上两倍的加速度与位移的乘积。

These equations only apply when acceleration is constant and in a straight line.

这些方程仅适用于加速度恒定的直线运动。

Newton’s Second Law states that the resultant force F acting on an object is equal to the product of its mass m and acceleration a: F = m a. The force is measured in newtons (N) when mass is in kg and acceleration in m/s².

牛顿第二定律指出，作用在物体上的合力 F 等于其质量 m 与加速度 a 的乘积：F = m a。当质量以千克、加速度以米每二次方秒为单位时，力的单位为牛顿 (N)。

The weight W of an object is the gravitational force on its mass: W = m g, where g is the acceleration of free fall (~9.8 m/s² on the Earth’s surface).

物体的重量 W 是地球引力对其质量的作用：W = m g，其中 g 为自由落体加速度（地表约 9.8 m/s²）。

For dry sliding surfaces, the maximum static friction force F_max is proportional to the normal reaction N: F_max = μ N, where μ is the coefficient of static friction (dimensionless).

对于干燥接触面，最大静摩擦力 F_max 与正压力 N 成正比：F_max = μ N，其中 μ 为静摩擦系数（无量纲）。

2. Work, Energy and Power | 功、能与功率

Work done W by a constant force F acting over a displacement s in the direction of the force: W = F s. The SI unit of work is the joule (J).

恒力 F 沿位移 s 方向所做的功 W 为：W = F s，国际单位为焦耳 (J)。

Kinetic energy (KE) of an object of mass m moving with speed v: KE = ½ m v².

质量为 m、速度为 v 的物体的动能：KE = ½ m v²。

Gravitational potential energy (GPE) gained when raising a mass m through a vertical height h is: GPE = m g h.

将质量为 m 的物体提升垂直高度 h 所增加的重力势能：GPE = m g h。

Power P is the rate of doing work or transferring energy: Published by TutorHao | Year 11 工程 Revision Series | aleveler.com

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