📚 GCSE Edexcel Engineering: Formula & Theorem Quick Reference Handbook | GCSE Edexcel 工程：公式定理速查手册
This quick reference handbook provides a condensed summary of the essential formulas and theorems required for the GCSE Edexcel Engineering course. It covers mechanics, materials, electricity, energy, fluid systems, and more. Each section presents key equations with explanations to support your revision.
本速查手册概括了GCSE Edexcel工程课程所需的核心公式和定理，涵盖力学、材料、电学、能量、流体系统等。每节都列出了关键方程并附有解释，助力高效复习。
1. Mechanics and Forces | 力学与力
Newton’s Second Law states that the net force F on an object is equal to its mass m multiplied by its acceleration a:
F = m × a
Force is measured in newtons (N).
牛顿第二定律：物体所受合力 F 等于质量 m 乘以加速度 a：
F = m × a
力的单位是牛顿 (N)。
Weight W is the gravitational force on a mass:
W = m × g
where g ≈ 9.8 m/s² on Earth.
重量 W 是质量所受的重力：
W = m × g
其中地球表面的 g 约 9.8 m/s²。
The moment of a force about a pivot is the force times the perpendicular distance:
M = F × d
For equilibrium, total clockwise moments = total anticlockwise moments.
力对支点的力矩等于力乘以垂直距离：
M = F × d
平衡时，顺时针力矩之和等于逆时针力矩之和。
Work done W when a force moves its point of application:
W = F × d (when force and motion are in the same direction)
功 W 是力在其作用点移动时做的功：
W = F × d (力与运动方向相同时)
Power P is the rate of doing work:
P = W / t or P = E / t
功率 P 是做功的速率：
P = W / t 或 P = E / t
2. Materials and Stress–Strain | 材料与应力–应变
Tensile stress σ is force per unit cross-sectional area:
σ = F / A
拉伸应力 σ 是单位横截面积上的力：
σ = F / A
Tensile strain ε is the extension per original length:
ε = ΔL / L₀
拉伸应变 ε 是伸长量除以原长：
ε = ΔL / L₀
Young’s modulus E measures stiffness:
E = σ / ε
杨氏模量 E 衡量材料的刚度：
E = σ / ε
Factor of safety is the ratio of ultimate stress to working stress:
Factor of safety = Ultimate stress / Working stress
安全系数是极限应力与工作应力的比值：
安全系数 = 极限应力 / 工作应力
3. Electricity and Circuits | 电学与电路
Ohm’s Law relates voltage V, current I, and resistance R:
V = I × R
欧姆定律将电压 V、电流 I 和电阻 R 联系起来：
V = I × R
Resistors in series:
Rtotal = R₁ + R₂ + R₃ + …
串联电阻：
R总 = R₁ + R₂ + R₃ + …
Resistors in parallel:
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
并联电阻：
1 / R总 = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
Electrical power:
P = I × V and P = I² × R
电功率：
P = I × V 以及 P = I² × R
Energy transferred in a circuit:
E = V × I × t
电路中的能量转换：
E = V × I × t
4. Energy, Work and Power | 能量、功与功率
Kinetic energy:
KE = ½ m v²
动能：
KE = ½ m v²
Gravitational potential energy:
PE = m g h
重力势能：
PE = m g h
Principle of conservation of energy: energy cannot be created or destroyed, only transferred. In a closed system, total energy is constant.
能量守恒定律：能量既不能被创造也不能被消灭，只能转移。在封闭系统中，总能量保持不变。
Efficiency of a system:
Efficiency = (Useful output energy / Total input energy) × 100%
系统效率：
效率 = (有用的输出能量 / 总输入能量) × 100%
Mechanical advantage (MA) of a machine:
MA = Load / Effort
机械利益：
MA = 负载 / 作用力
Velocity ratio (VR):
VR = Distance moved by effort / Distance moved by load
速度比：
VR = 作用力移动的距离 / 负载移动的距离
5. Fluid Pressure and Hydraulics | 流体压力与液压
Pressure is force per unit area:
p = F / A
压强是单位面积上的力：
p = F / A
Pascal’s principle: pressure applied to an enclosed fluid is transmitted equally in all directions.
帕斯卡原理：施加在密闭流体上的压强会大小不变地向各个方向传递。
For a hydraulic system:
F₁ / A₁ = F₂ / A₂
液压系统：
F₁ / A₁ = F₂ / A₂
Pressure due to a liquid column:
p = ρ g h
where ρ is density, g is gravitational field strength, and h is depth.
液柱产生的压强：
p = ρ g h
其中 ρ 是密度，g 是重力场强度，h 是深度。
6. Motion and Kinematics | 运动学
Average speed:
v = s / t
平均速度：
v = s / t
Acceleration:
a = (v − u) / t
where u is initial velocity, v is final velocity.
加速度：
a = (v − u) / t
其中 u 是初速度，v 是末速度。
Equations of uniformly accelerated motion (suvat equations):
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = (u + v) t / 2
匀加速运动方程 ( suvat 方程)：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = (u + v) t / 2
7. Levers and Simple Machines | 杠杆与简单机械
For a lever in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments:
Effort × effort arm = Load × load arm
杠杆平衡时，顺时针力矩之和等于逆时针力矩之和：
作用力 × 作用力臂 = 负载 × 负载臂
Three classes of levers are identified by the relative positions of fulcrum, load, and effort. Mechanical advantage can be greater than, equal to, or less than 1.
杠杆根据支点、负载和作用力的相对位置分为三类。机械利益可大于、等于或小于 1。
Gear ratio (for meshing gears):
Gear ratio = Number of teeth on driven gear / Number of teeth on driving gear
齿轮比（啮合齿轮）：
齿轮比 = 从动齿轮齿数 / 主动齿轮齿数
Speed ratio is the inverse of gear ratio:
Speed ratio = Output speed / Input speed = Teeth on driver / Teeth on driven
转速比是齿轮比的倒数：
转速比 = 输出转速 / 输入转速 = 主动轮齿数 / 从动轮齿数
Pulley systems: ideal mechanical advantage equals the number of rope sections supporting the load (excluding the free end if pulling down changes the count – typically, for a simple pulley system, MA = number of load-bearing ropes).
滑轮系统：理想的机械利益等于支撑负载的绳段数（通常，简单滑轮系统的 MA = 承重绳的根数）。
8. Structures and Statics | 结构与静力学
For a body in static equilibrium, both the resultant force and the resultant moment must be zero:
ΣF = 0 and ΣM = 0
For coplanar forces, this often means resolving into perpendicular components and setting the algebraic sum of horizontal and vertical forces to zero.
物体处于静力平衡时，合外力与合外力矩都必须为零：
ΣF = 0 且 ΣM = 0
对于共面力系，通常需要正交分解，并使水平与竖直方向的代数和均为零。
For simple truss analysis using the method of joints, each joint is assumed to be in equilibrium, allowing calculation of member forces through vector triangles or resolution.
使用节点法分析简单桁架时，假定每个节点都处于平衡状态，通过矢量三角形或分解可求得杆件内力。
9. Thermodynamics and Heat | 热力学与热
Specific heat capacity c: energy required to raise the temperature of 1 kg of a substance by 1 °C:
Q = m c Δθ
比热容 c：使 1 kg 物质温度升高 1 °C 所需的能量：
Q = m c Δθ
In an ideal heat engine, thermal efficiency can be expressed as:
Efficiency = (Work output / Heat input) × 100%
理想热机中，热效率可表示为：
效率 = (输出的功 / 输入的热量) × 100%
Heat transfer occurs by conduction, convection, and radiation. While not always expressed as a single formula, Fourier’s law for steady-state conduction is Q/t = k A (ΔT / d) where k is thermal conductivity.
热传递通过传导、对流和辐射实现。稳态导热可用傅里叶定律表示：Q/t = k A (ΔT / d)，其中 k 为导热系数。
10. Electronics and Dividers | 电子与分压器
The potential divider rule for two resistors in series:
Vout = Vin × (R₂ / (R₁ + R₂))
串联电阻的分压公式：
Vout = Vin × (R₂ / (R₁ + R₂))
For a transistor used as a switch, the base current IB must be sufficient to saturate the transistor. The current gain β (or hFE) relates collector current to base current:
IC = β × IB
晶体管作为开关使用时，基极电流 IB 必须足够大以使晶体管饱和。电流增益 β (或 hFE) 将集电极电流与基极电流关联起来：
IC = β × IB
Logic gates (AND, OR, NOT, NAND, NOR) follow Boolean algebra; truth tables are used to define their operation. While no numerical formula applies, understanding their function in control circuits is essential.
逻辑门 (与、或、非、与非、或非) 遵循布尔代数；真值表用于定义其操作。虽无数值公式，但理解它们在控制电路中的作用至关重要。
11. Manufacturing Tolerances and Quality | 制造公差与品质
Tolerance is the permissible limit of variation in a dimension. It is defined as the difference between the upper and lower deviation:
Tolerance = Upper limit − Lower limit
公差是尺寸允许的变动量，定义为上偏差与下偏差之差：
公差 = 上极限尺寸 − 下极限尺寸
Clearance fit, interference fit, and transition fit are specified by the relationship between hole and shaft tolerances. Understanding these ensures proper assembly of components.
间隙配合、过盈配合和过渡配合由孔与轴的公差关系决定。理解这些配合可确保零件正确装配。
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