Year 10 CIE Engineering: Formula and Theorem Quick Reference Handbook | Year 10 CIE 工程：公式定理速查手册

📚 Year 10 CIE Engineering: Formula and Theorem Quick Reference Handbook | Year 10 CIE 工程：公式定理速查手册

This handbook provides a concise compilation of essential formulas and theorems for Year 10 CIE Engineering. Mastery of these equations is fundamental to analysing mechanical, electrical, thermal, and structural systems. Each entry is paired with its Chinese translation to support bilingual learning. Use this as a quick reference during revision and problem-solving practice.

本手册汇编了 Year 10 CIE 工程学的核心公式与定理。掌握这些方程是分析机械、电气、热学及结构系统的基础。每条内容均配有中文翻译，以支持双语学习。复习和解题练习时可将本手册用作快速参考。

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1. Kinematics | 运动学

The first equation of motion relates final velocity (v), initial velocity (u), constant acceleration (a), and time (t):

v = u + a t

第一个运动方程将末速度 (v)、初速度 (u)、恒定加速度 (a) 和时间 (t) 联系起来：

Displacement (s) covered in time t, given initial velocity u and uniform acceleration a, is calculated by:

s = u t + ½ a t²

在初速度 u 和匀加速度 a 下，时间 t 内的位移 (s) 由下式计算：

To link final velocity, initial velocity, acceleration, and displacement without involving time, use:

v² = u² + 2 a s

将末速度、初速度、加速度和位移关联起来而不涉及时间，可使用：

The average velocity form gives displacement as:

s = ½ (u + v) t

平均速度形式的位移表达式为：

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2. Forces and Newton’s Laws | 力与牛顿定律

Newton’s Second Law states that the net force acting on a body equals its mass multiplied by its acceleration:

F = m a

牛顿第二定律指出，作用在物体上的合力等于其质量乘以加速度：

Weight is the gravitational force on a mass m, where g is the acceleration due to gravity (≈ 9.8 m/s² on Earth):

W = m g

重量是作用在质量 m 上的重力，g 为重力加速度（在地球上约为 9.8 m/s²）：

For an elastic spring, the extension (x) is proportional to the applied force, up to the limit of proportionality (Hooke’s law):

F = k x

对于弹性弹簧，在比例极限内，伸长量 (x) 与施加的力成正比（胡克定律）：

When all forces acting on an object are balanced, the resultant force is zero; the object remains at rest or moves with constant velocity in a straight line.

当作用在物体上的所有力平衡时，合力为零；物体保持静止或沿直线匀速运动。

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3. Moments and Equilibrium | 力矩与平衡

A moment is the turning effect of a force about a pivot. It equals the product of the force and the perpendicular distance (d) from the line of action of the force to the pivot:

M = F × d

力矩是力对支点的转动效应，等于力与力作用线到支点的垂直距离 (d) 的乘积：

For rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same pivot:

Σ clockwise moments = Σ anticlockwise moments

对于转动平衡，绕同一支点的顺时针力矩之和等于逆时针力矩之和：

This principle is used to analyse levers, beams, and other simple machines when they are balanced.

该原理用于分析平衡状态下的杠杆、横梁及其他简单机械。

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4. Work, Energy and Power | 功、能与功率

Work done by a constant force acting in the direction of displacement (d) is:

W = F × d

恒力沿位移方向所做的功 (W) 为：

Kinetic energy of a moving object of mass m with velocity v:

KE = ½ m v²

质量为 m、速度为 v 的运动物体的动能 (KE) 为：

Gravitational potential energy gained by lifting a mass m through a vertical height h:

PE = m g h

将质量为 m 的物体垂直提升高度 h 所获得的重力势能 (PE) 为：

Power is the rate of doing work or energy transfer; it can be expressed as work done divided by time taken:

P = W / t

功率是做功或能量传递的速率，可表示为所做的功除以所用时间：

The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.

能量守恒原理指出，能量既不能创造也不能消灭，只能从一种形式转化为另一种形式。

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

Tensile or compressive stress (

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