Year 13 CCEA Engineering: Formulae and Theorems Quick Reference | CCEA A2 工程公式定理速查手册

📚 Year 13 CCEA Engineering: Formulae and Theorems Quick Reference | CCEA A2 工程公式定理速查手册

This handbook compiles the essential formulae and theorems across the core topics of the Year 13 CCEA Engineering specification: mechanics, materials, thermodynamics, fluid dynamics, electrical circuits and control systems. Each entry is presented with a brief English explanation followed by its Chinese translation to facilitate rapid revision and bilingual concept reinforcement.

本手册汇集了 CCEA A2（Year 13）工程课程核心课题中的关键公式与定理，涵盖力学、材料、热力学、流体力学、电路与控制系统。每个条目均先用英文说明，再提供中文翻译，以便快速复习并强化双语概念理解。

---

1. Linear & Rotational Motion | 直线与旋转运动

This section covers the fundamental kinematic equations for linear and angular motion, as well as the relationships between torque, moment of inertia and angular acceleration.

本节涵盖直线与角运动的基本运动学方程，以及扭矩、转动惯量和角加速度之间的关系。

The four SUVAT equations for constant linear acceleration are:

匀加速直线运动的四个 SUVAT 方程为：

v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t

where u = initial velocity, v = final velocity, a = constant acceleration, t = time, s = displacement.

其中 u = 初速度，v = 末速度，a = 恒加速度，t = 时间，s = 位移。

Rotational analogues are obtained by replacing linear quantities with angular ones (θ for s, ω for v, α for a):

旋转运动的对应关系通过将线量替换为角量 (θ 代替 s，ω 代替 v，α 代替 a) 得到：

ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ

ω₀ is initial angular velocity (rad/s).

ω₀ 为初角速度（弧度/秒）。

Torque τ is the product of force and perpendicular distance: τ = F r. For a rigid body with moment of inertia I, Newton’s second law for rotation gives:

扭矩 τ 为力与垂直距离的乘积：τ = F r。对于转动惯量为 I 的刚体，转动形式的牛顿第二定律给出：

τ = I α

Kinetic energy exists in both linear and rotational forms. Power during rotation is given by torque times angular speed.

动能同时具有线动能和转动动能形式。旋转过程中的功率等于扭矩乘以角速度。

K = ½ m v², K_rot = ½ I ω², P = τ ω

Moment of inertia for a point mass: I = m r². For compound bodies, I is found by integration or standard tables.

点质量的转动惯量：I = m r²。对于组合体，转动惯量可通过积分或查阅标准表格求得。

---

2. Circular Motion & Simple Harmonic Motion | 圆周运动与简谐运动

Objects moving in a circular path experience centripetal acceleration directed towards the centre. Simple harmonic motion (SHM) occurs when restoring force is proportional to displacement.

沿圆周运动的物体受到指向圆心的向心加速度。当回复力与位移成正比时，物体作简谐运动 (SHM)。

Centripetal acceleration can be expressed in terms of tangential speed v or angular velocity ω:

向心加速度可用切向速度 v 或角速度 ω 表示：

a = v² / r = ω² r

The centripetal force required is:

所需向心力为：

F = m a = m v² / r = m ω² r

In SHM the acceleration is always opposite to the displacement from equilibrium:

在简谐运动中，加速度始终与离开平衡位置的位移方向相反：

a = −ω² x

The angular frequency ω for a mass–spring system is ω = √(k / m), and the period T is:

对于弹簧–质量系统，角频率 ω = √(k／m)，周期 T 为：

T = 2π / ω = 2π √(m / k)

Displacement, velocity and acceleration as functions of time (with zero initial phase) are:

位移、速度和加速度随时间变化的表达式（初相为零）为：

x = A sin(ωt), v = ωA cos(ωt), a = −ω²A sin(ωt)

Maximum speed v_max = ωA, maximum acceleration a_max = ω²A. The total mechanical energy is constant:

最大速度 v_max = ωA，最大加速度 a_max = ω²A。系统总机械能守恒：

更多咨询请联系16621398022（同微信）