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

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

This handbook provides a concise summary of essential formulas and theorems for GCSE WJEC Engineering. Mastering these relationships is crucial for solving problems in mechanics, electronics, materials, and manufacturing. Keep this guide handy for quick revision.

本手册简要总结了 GCSE WJEC 工程学中的基本公式和定理。掌握这些关系对于解决力学、电子学、材料和制造问题至关重要。随身携带本指南，方便快速复习。

1. 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 its mass multiplied by its acceleration.

牛顿第二定律指出，作用在物体上的净力等于其质量乘以加速度。

F = m × a

On Earth, the weight of an object is the force due to gravity, where g is the gravitational field strength (approximately 9.8 m/s²).

在地球上，物体的重量是由重力引起的力，其中 g 是重力场强度（约为 9.8 m/s²）。

W = m × g

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2. Moments and Equilibrium | 力矩与平衡

The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action.

力绕支点的力矩是力与支点到力作用线的垂直距离的乘积。

M = F × d

For a system to be in rotational equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments.

为了使系统达到转动平衡，顺时针力矩之和必须等于逆时针力矩之和。

Σ clockwise moments = Σ anticlockwise moments

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

Tensile or compressive stress (σ) is defined as the applied force (F) divided by the original cross-sectional area (A).

拉伸或压缩应力（σ）定义为施加的力（F）除以原始横截面积（A）。

σ = F / A

Tensile or compressive strain (ε) is the change in length (ΔL) divided by the original length (L₀).

拉伸或压缩应变（ε）是长度变化量（ΔL）除以原始长度（L₀）。

ε = ΔL / L₀

Young’s modulus (E) describes the stiffness of a material and is the ratio of stress to strain within the elastic limit.

杨氏模量（E）描述材料的刚度，是在弹性极限内应力与应变之比。

E = σ / ε

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4. Mechanical Advantage and Efficiency | 机械利益与效率

Mechanical advantage (MA) is the ratio of the load to the effort for a machine or mechanism.

机械利益（MA）是机器或机构的负载与输入力之比。

MA = Load / Effort

Velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load in the same time.

速度比（VR）是输入力移动的距离与负载在同一时间内移动的距离之比。

VR = Distance moved by effort / Distance moved by load

Efficiency (η) is the ratio of useful output work to input work, often expressed as a percentage using MA and VR.

效率（η）是有用输出功与输入功之比，通常用机械利益和速度比以百分比表示。

η = (MA / VR) × 100%

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5. Kinematics Equations | 运动学方程

This equation calculates final velocity (v) when initial velocity (u), acceleration (a) and time (t) are known.

当已知初速度（u）、加速度

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