📚 Year 12 Edexcel Engineering: Formula & Theorem Quick Reference Guide | 工程公式定理速查手册
This quick reference guide brings together the essential formulas and theorems you need to master for the Year 12 Edexcel Engineering course. Covering mechanics, materials, electrical principles, thermodynamics and more, each section presents the key equations in a clear, bilingual format. Use it for revision, problem-solving, and as a handy checklist before assessments.
这本快速参考手册汇总了Year 12 Edexcel工程课程必须掌握的核心公式和定理。内容涵盖力学、材料、电学原理、热力学等领域，每个部分以清晰的双语形式呈现关键方程。可用于复习、解题和考前快速核查。
1. Kinematic Equations | 运动学公式
These equations describe uniformly accelerated motion in a straight line. They relate initial velocity (u), final velocity (v), acceleration (a), displacement (s) and time (t).
这些方程描述匀加速直线运动，关联初速度(u)、末速度(v)、加速度(a)、位移(s)和时间(t)。
| Formula / 公式 | Description / 说明 |
|---|---|
| v = u + at | Velocity-time relation / 速度-时间关系 |
| s = ut + ½at² | Displacement with acceleration / 含加速度的位移公式 |
| v² = u² + 2as | Velocity-displacement relation / 速度-位移关系 |
| s = ½(u + v)t | Average velocity displacement / 平均速度位移 |
2. Newton’s Laws and Momentum | 牛顿定律与动量
Newton’s three laws form the foundation of classical mechanics. Momentum (p) and impulse help analyse collisions and variable forces. Weight is the gravitational force on a mass.
牛顿三定律是经典力学的基础。动量(p)和冲量用于分析碰撞与变力问题。重量是作用在质量上的重力。
| Formula / 公式 | Description / 说明 |
|---|---|
| F = ma | Newton’s second law / 牛顿第二定律 |
| W = mg | Weight / 重量 |
| p = mv | Momentum / 动量 |
| I = FΔt = Δp | Impulse equals change in momentum / 冲量等于动量的变化 |
3. Moments and Equilibrium | 力矩与平衡
A moment is the turning effect of a force about a pivot. For a body in static equilibrium, both resultant force and resultant moment must be zero.
力矩是力绕支点的转动效应。物体处于静力平衡时，合力与合力矩都必须为零。
| Formula / 公式 | Description / 说明 |
|---|---|
| M = Fd | Moment = force × perpendicular distance / 力矩 = 力 × 垂直距离 |
| ΣF = 0 | Equilibrium of forces / 力的平衡 |
| ΣM = 0 | Equilibrium of moments / 力矩的平衡 |
4. Work, Energy and Power | 功、能与功率
Work is done when a force moves its point of application. Energy is the capacity to do work, and power is the rate of doing work. Efficiency compares useful output to input.
力使作用点移动时做功。能量是做功的能力，功率是做功的速率。效率比较有用输出与输入。
| Formula / 公式 | Description / 说明 |
|---|---|
| W = Fs cosθ | Work done by a constant force / 恒力做功 |
| KE = ½mv² | Kinetic energy / 动能 |
| PE = mgh | Gravitational potential energy / 重力势能 |
| P = W/t = Fv | Power / 功率 |
| η = (Pout/Pin) × 100% | Efficiency / 效率 |
5. Stress, Strain and Young’s Modulus | 应力、应变与杨氏模量
Stress and strain describe how materials respond to external loads. Young’s modulus measures stiffness and is valid in the elastic (linear) region before permanent deformation.
应力和应变描述材料在外部载荷下的响应。杨氏模量衡量刚度，在永久变形前的弹性（线性）区域内有效。
| Formula / 公式 | Description / 说明 |
|---|---|
| σ = F/A | Stress (tensile or compressive) / 应力（拉伸或压缩） |
| ε = ΔL/L₀ | Strain / 应变 |
| E = σ/ε | Young’s modulus / 杨氏模量 |
| U = ½FΔL | Elastic strain energy / 弹性应变能 |
6. DC Circuit Fundamental Formulas | 直流电路基本公式
Ohm’s law and resistance calculations are at the heart of circuit analysis. Power in a resistor can be expressed in three equivalent forms, and combined resistance depends on series or parallel arrangements.
欧姆定律和电阻计算是电路分析的核心。电阻器上的功率有三种等效表达式，总电阻取决于串联或并联结构。
| Formula / 公式 | Description / 说明 |
|---|---|
| V = IR | Ohm’s law / 欧姆定律 |
| R = ρL/A | Resistance of a uniform wire / 均匀导线的电阻 |
| P = IV = I²R = V²/R | Electrical power / 电功率 |
| Rtotal = R₁ + R₂ + … | Resistors in series / 串联电阻 |
| 1/Rtotal = 1/R₁ + 1/R₂ + … | Resistors in parallel / 并联电阻 |
7. Kirchhoff’s Laws | 基尔霍夫定律
Kirchhoff’s current and voltage laws provide a systematic way to analyse more complex circuits with multiple loops and branches. They are based on conservation of charge and energy.
基尔霍夫电流定律和电压定律为分析多回路、多支路的复杂电路提供了系统方法。它们基于电荷守恒和能量守恒。
| Formula / 公式 | Description / 说明 |
|---|---|
| ΣIin = ΣIout | Kirchhoff’s current law (junction rule) / 基尔霍夫电流定律（节点） |
| ΣV = 0 (closed loop) | Kirchhoff’s voltage law (loop rule) / 基尔霍夫电压定律（回路） |
8. Trigonometry and Vectors | 三角学与向量
Engineers use trigonometry and vectors to resolve forces, velocities and other quantities into components. The sine and cosine rules extend beyond right-angled triangles.
工程师利用三角学和向量将力、速度等物理量分解为分量。正弦定理和余弦定理超越了直角三角形的限制。
| Formula / 公式 | Description / 说明 |
|---|---|
| sin θ = opposite/hypotenuse | Sine, cosine, tangent definitions / 正弦、余弦、正切定义 |
| a/sin A = b/sin B = c/sin C | Sine rule / 正弦定理 |
| a² = b² + c² − 2bc cos A | Cosine rule / 余弦定理 |
| Fx = F cos θ, Fy = F sin θ | Resolving a vector / 向量分解 |
| |F| = √(Fx² + Fy²) | Magnitude of resultant / 合力大小 |
9. Fluid Mechanics Basics | 流体力学基础
Hydrostatic pressure increases with depth, and continuity links area and velocity in a flow. Bernoulli’s equation expresses energy conservation along a streamline for inviscid, steady flow.
流体静压随深度增加，连续性方程关联流动中的截面积和速度。伯努利方程表达了无黏性稳定流沿流线的能量守恒。
| Formula / 公式 | Description / 说明 |
|---|---|
| p = ρgh | Hydrostatic pressure / 静水压强 |
| Q = Av | Vol
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