📚 Year 11 Edexcel Engineering: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook compiles the essential formulas, theorems, and constants required for the Year 11 Edexcel Engineering specification. Each entry is presented with a clear definition and contextual application to support problem‑solving in mechanics, materials, electronics, and systems. Use this guide alongside your practical work and past papers to build confidence and accuracy.
本手册汇编了 Year 11 Edexcel 工程课程所必需的核心公式、定理和常量。每个条目均附有清晰的定义及实际应用说明，以助力力学、材料、电子和系统领域的解题。请将本指南与你的实践作业和历年真题结合使用，从而增强信心、提升解题准确性。
1. SI Base Units and Prefixes | 国际单位制基本单位与词头
All quantities in engineering are expressed using the International System of Units (SI). Mastering base units and prefixes ensures correct dimension analysis and conversion.
工程中所有量均采用国际单位制 (SI) 表示。掌握基本单位与词头能保证量纲分析正确无误并顺利完成换算。
| Quantity | Unit (Symbol) | 中文名称 |
|---|---|---|
| Length | metre (m) | 米 |
| Mass | kilogram (kg) | 千克 |
| Time | second (s) | 秒 |
| Electric Current | ampere (A) | 安培 |
| Temperature | kelvin (K) or degree Celsius (°C) | 开尔文或摄氏度 |
Common prefixes: kilo (k, 10³), mega (M, 10⁶), milli (m, 10⁻³), micro (μ, 10⁻⁶).
常用词头：千 (k, 10³)、兆 (M, 10⁶)、毫 (m, 10⁻³)、微 (μ, 10⁻⁶)。
2. Hooke's Law | 胡克定律
F = k × x
The extension x of a spring is directly proportional to the applied force F, provided the elastic limit is not exceeded. The spring constant k (N/m) measures stiffness.
在不超过弹性极限的前提下，弹簧的伸长量 x 与施加的力 F 成正比。弹簧常数 k（N/m）衡量弹簧的劲度。
This law is fundamental for analysing springs in suspension systems, tensile testing, and any component that stores elastic potential energy.
该定律是分析悬架弹簧、拉伸测试及任何储存弹性势能的元件的基础。
3. Moments and Equilibrium | 力矩与平衡
M = F × d
A moment (torque) is the turning effect of a force. It is calculated as the product of the force F and the perpendicular distance d from the pivot to the line of action of the force. The unit is newton metre (N m).
力矩是力产生的转动效应。它等于力 F 与从支点到力作用线的垂直距离 d 的乘积，单位为牛顿米（N m）。
moments = sum of anticlockwise moments. This principle designs beams, levers, and bridges.
对于处于静力平衡的物体：顺时针力矩之和 = 逆时针力矩之和。该原理用于设计梁、杠杆和桥梁。
4. Linear Kinematics Equations | 直线运动学公式
relations are used (u = initial velocity, v = final velocity, t = time, s = displacement).
对于匀加速度 a，使用以下 SUVAT 关系（u = 初速度，v = 末速度，t = 时间，s = 位移）。
v = u + a × t
The final velocity equals the initial velocity plus the product of acceleration and time. This is the definition of constant acceleration.
末速度等于初速度加上加速度与时间的乘积，这是匀加速运动的定义式。
s = u × t + ½ a × t²
Displacement is given by the initial velocity multiplied by time plus half the acceleration multiplied by the square of time.
位移等于初速度乘以时间，加上二分之一的加速度乘以时间的平方。
v² = u² + 2 × a × s
This equation relates final velocity squared to initial velocity squared, acceleration, and displacement, eliminating time.
该公式将末速度的平方与初速度的平方、加速度及位移联系起来，消去了时间。
5. Work Done, Energy and Power | 做功、能与功率
W = F × d × cos θ
the force. When force and motion are parallel, θ = 0, so W = F × d. The unit is joule (J).
做功等于力与沿力方向通过的距离的乘积。当力与运动方向平行时，θ = 0，故 W = F × d。单位为焦耳 (J)。
Gravitational potential energy: Eₚ = m × g × h
Stored energy due to height h in a gravitational field of strength g (9.8 m/s² on Earth). m is mass.
物体因高度 h 而在重力场强 g（地球为 9.8 m/s²）中储存的势能。m 为质量。
Kinetic energy: Eₖ = ½ m × v²
Energy possessed by a moving body. Doubling velocity quadruples the kinetic energy.
运动物体具有的能量。速度加倍会使动能变为原来的四倍。
Power: P = W / t = F × v
Power (watt, W) is the rate of doing work, also equal to force times constant speed when force and motion are in the same direction.
功率（瓦特, W）是做功的快慢，当力与运动方向一致时也等于力乘以恒定速度。
6. Mechanical Advantage and Velocity Ratio | 机械效益与速度比
Mechanical Advantage (MA) = Load / Effort
MA indicates how much a machine multiplies the input force. An ideal machine with no friction has MA > 1 for force multipliers.
MA 表示机器放大了多少输入力。理想无摩擦的增力机器具有 MA > 1。
Velocity Ratio (VR) = distance moved by effort / distance moved by load
VR is a purely geometric property determined by the design of the mechanism, such as gear teeth numbers or lever arm lengths.
VR 是纯粹的几何属性，由机构设计决定，如齿轮齿数或杠杆臂长。
For a simple lever: MA = load arm / effort arm (neglecting friction).
对于简单杠杆：MA = 负载臂 / 施力臂（忽略摩擦）。
7. Stress, Strain and Young's Modulus | 应力、应变与杨氏模量
Tensile stress: σ = F / A
Stress is the internal force per unit cross‑sectional area. It is measured in pascals (Pa) or N/m². Tensile stress pulls the material apart.
应力是单位横截面积上的内力，单位为帕斯卡 (Pa) 或 N/m²。拉应力使材料拉伸分离。
Tensile strain: ε = ΔL / L₀
Strain is the fractional change in length; it is dimensionless but often expressed as a percentage. ΔL is the extension, L₀ the original length.
应变是长度的相对变化量，为无量纲量，常以百分数表示。ΔL 为伸长量，L₀ 为原始长度。
Young's modulus: E = σ / ε
Young's modulus measures a material's stiffness in the elastic region. A high E means the material deforms little under load (e.g. steel: ~200 GPa).
杨氏模量衡量材料在弹性区的劲度。E 值高表示材料受载时变形小（例如钢约 200 GPa）。
8. Pressure in Fluids and Hydraulics | 流体压强与液压
Pressure: P = F / A
Pressure (pascal, Pa) is force normal to a surface divided by the area. This applies equally to solids and fluids at rest.
压强（帕斯卡, Pa）等于垂直于表面的力除以面积。该式同样适用于固体和静止流体。
Hydraulic press principle: P₁ = P₂ ⇒ F₁/A₁ = F₂/A₂
In a closed hydraulic system, pressure is transmitted undiminished. A small force on a small piston can lift a larger load on a bigger piston.
在封闭液压系统中，压强大小不变地传递。小活塞上的小力可举升大活塞上的大载荷。
Pressure due to liquid column: P = ρ × g × h
At a depth h in a fluid of density ρ, the pressure is ρ g h plus atmospheric pressure if the container is open.
在密度为 ρ 的流体中，深度 h 处的压强为 ρ g h，若容器敞口则需加算大气压强。
9. Ohm's Law and Electrical Power | 欧姆定律与电功率
Ohm's Law: V = I × R
For a metallic conductor at constant temperature, the potential difference V across it is proportional to the current I flowing through it. R is electrical resistance in ohms (Ω).
对于恒温金属导体，其两端的电势差 V 与流经的电流 I 成正比。R 为电阻，单位为欧姆 (Ω)。
Resistors in series: Rtotal = R₁ + R₂ + …
Resistances in series share the same current; total resistance is the sum.
串联电阻流经相同电流；总电阻为各电阻之和。
Resistors in parallel: 1/Rtotal = 1/R₁ + 1/R₂ + …
In parallel circuits the reciprocal total resistance equals the sum of reciprocals. Total resistance is always less than the smallest individual resistor.
并联电路中总电阻的倒数等于各电阻倒数之和。总电阻总小于最小的单个电阻。
Electrical power: P = V × I = I² × R = V²/R
Power dissipated in a resistor can be calculated using any two of V, I, R. The unit is watt (W).
电阻消耗的功率可通过 V、I、R 中任意两者计算，单位为瓦特 (W)。
10. Gear Ratios and Simple Machines | 齿轮比与简单机械
Gear ratio = number of teeth on driven gear / number of teeth on driver gear
A gear ratio greater than 1 reduces speed but increases torque. A ratio less than 1 increases speed and reduces torque. The velocity ratio of a gear pair equals the gear ratio.
齿轮比大于 1 时降低转速但增大扭矩；比小于 1 时增速减扭。齿轮副的速度比等于齿轮比。
Output speed (rpm) = Input speed / Gear ratio
If a driver gear with 20 teeth drives a 60‑tooth gear, the gear ratio is 3; the output speed is one third of the input speed.
若 20 齿的主动齿轮驱动 60 齿的从动轮，齿轮比为 3，输出转速为输入转速的三分之一。
supporting the load (ideal). For a wheel and axle: VR = radius of wheel / radius of axle.
对于滑轮系统：VR = 承托负载的绳段数（理想情况）。对于轮轴：VR = 轮半径 / 轴半径。
11. Density and Material Properties | 密度与材料性质
Density: ρ = m / V
Density (kg/m³) is mass per unit volume. It helps identify materials and determine whether an object will float or sink. Water has a density of ~1000 kg/m³.
密度 (kg/m³) 是单位体积的质量，用于辨别材料并判断物体沉浮。水的密度约 1000 kg/m³。
Stiffness (k) from Hooke's Law: k = F / x
Stiffness is the slope of the force‑extension graph in the elastic region. High stiffness means less deformation for a given load.
劲度是弹性区内力-伸长图的斜率。劲度高表示在给定载荷下变形更小。
Other key material properties: toughness (energy absorbed before fracture), hardness (resistance to indentation), and ductility (ability to be drawn into a wire).
其他关键材料属性：韧性（断裂前吸收的能量）、硬度（抵抗压痕的能力）和延展性（可拉制成丝的能力）。
12. Efficiency and Energy Losses | 效率与能量损失
Efficiency = (Useful energy output / Total energy input) × 100%
tem converts input energy into desired output. It can also be expressed using power: η = Pout / Pin.
效率衡量系统将输入能量转化为期望输出的能力，也可用功率表示：η = Pout / Pin。
For machines: Efficiency = (MA / VR) × 100%
Since friction causes MA to be less than VR, real machines have efficiency below 100%. Lubrication and good design reduce losses.
由于摩擦使 MA 小于 VR，实际机器的效率低于 100%。润滑和良好设计可降低损耗。
Energy cannot be destroyed; lost energy usually appears as heat, sound, or vibration. In bearings, friction torque creates wasted thermal energy.
能量不可被消灭；损失的能量通常表现为热、声音或振动。在轴承中，摩擦力矩会产生浪费的热能。
Published by TutorHao | Engineering Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图