📚 Year 8 Edexcel Engineering: Formula & Theorem Quick Reference Handbook | Edexcel 八年级工程：公式定理速查手册
This quick reference handbook brings together the essential formulas and principles you need for Year 8 Edexcel Engineering. From mechanical advantage and moments to electrical circuits and material properties, each section presents clear equations, worked definitions and practical relationships. Use it to check facts while designing, testing and evaluating your engineered solutions.
本速查手册汇集了八年级 Edexcel 工程课程所需的关键公式与基本原理。从机械效益和力矩到电路和材料属性，每个部分都提供了清晰的方程、明确的定义和实际应用关系。在设计、测试和评估工程方案时，可随时查阅，巩固核心知识。
1. Mechanical Advantage (MA) | 机械效益 (MA)
Mechanical advantage tells you how many times a mechanism multiplies the effort you put in. A higher MA means you can lift a heavier load with less input force.
机械效益表示机械装置将你的输入力放大了多少倍。MA 值越高，就能用更小的输入力举起更重的负载。
The formula uses only the forces involved, with load being the output force and effort being the input force.
该公式只涉及力，负载为输出力，作用力为输入力。
MA = Load / Effort
Because MA is a ratio of two forces, it has no units. For example, if a pulley system needs 100 N of effort to raise a 400 N load, its MA is 4.
由于 MA 是两个力的比值，因此没有单位。例如，一个滑轮系统需要用 100 N 的力举起 400 N 的负载，其机械效益就是 4。
In real machines, friction reduces the actual MA, making it smaller than the ideal, or theoretical, mechanical advantage.
在真实机械中，摩擦会降低实际 MA，使其小于理想（理论）机械效益。
2. Velocity Ratio (VR) | 速度比 (VR)
Velocity ratio compares the distance moved by the effort to the distance moved by the load in the same time. It tells you how much faster or slower the effort point travels.
速度比比较了在相同时间内作用力移动的距离与负载移动的距离。它反映了作用力点运动得快多少或慢多少。
VR = Distance moved by effort / Distance moved by load
Like MA, velocity ratio is a dimensionless ratio. It depends purely on the geometry of the machine – for instance, the number of rope sections in a pulley block or the arm lengths of a lever.
与 MA 类似，速度比是无量纲的比值。它完全取决于机械的几何结构，例如滑轮组中绳索的股数或杠杆的臂长。
For a perfect machine with no friction, MA equals VR. In practice, VR is always greater than MA because of energy losses.
对于无摩擦的理想机械，MA 等于 VR。实际上，由于能量损失，VR 总是大于 MA。
3. Efficiency of Machines | 机械效率
Efficiency measures how well a machine converts input work into useful output work. It is always less than 100% because some energy is lost as heat or sound.
效率衡量机器将输入功转化为有用输出功的程度。由于部分能量会以热或声音的形式散失，效率始终低于 100%。
Efficiency = (Useful work output / Total work input) × 100%
Work is force multiplied by distance, so efficiency can also be expressed through MA and VR.
功等于力乘以距离，因此效率也可以通过 MA 和 VR 来表达。
Efficiency = (MA / VR) × 100%
A pulley system with an MA of 3 and a VR of 4 has an efficiency of 75%. The remaining 25% is spent overcoming friction and moving the machine parts themselves.
一个 MA 为 3、VR 为 4 的滑轮系统，效率为 75%。其余 25% 用于克服摩擦和移动机械部件本身。
4. The Principle of Moments | 力矩原理
A moment is the turning effect of a force about a pivot. For a lever to be in equilibrium, the total clockwise moments must equal the total anticlockwise moments.
力矩是力对支点产生的转动效果。杠杆平衡时，总顺时针力矩必须等于总逆时针力矩。
Moment = Force × Perpendicular distance from pivot
The unit of moment is the newton-metre (N m). In calculations, the distance must be measured at right angles to the line of action of the force.
力矩的单位是牛顿·米 (N m)。计算时，距离必须是支点到力作用线的垂直距离。
When using the principle to find an unknown force, sum moments about any pivot point and set clockwise sum equal to anticlockwise sum.
利用该原理求未知力时，可以绕任一转动点计算力矩，并令顺时针力矩之和等于逆时针力矩之和。
5. Gear and Pulley Ratios | 齿轮与滑轮比
Gear ratio describes the relationship between a driving gear and a driven gear. It determines whether speed increases or torque increases.
齿轮比描述主动齿轮与从动齿轮之间的关系，决定了是转速增加还是扭矩增加。
Gear Ratio (GR) = Number of teeth on driven gear / Number of teeth on driver gear
If the driven gear has twice as many teeth as the driver, the GR is 2. This halves the output speed but doubles the torque, giving a mechanical advantage of 2.
若从动齿轮齿数是主动齿轮的两倍，齿轮比为 2。这将使输出转速减半，但扭矩加倍，机械效益为 2。
For pulley systems, the velocity ratio equals the number of rope sections supporting the moving pulley block. The same concept links pulley ratio to mechanical advantage.
在滑轮系统中，速度比等于支撑动滑轮块的绳索段数。相同的概念将滑轮比与机械效益联系起来。
6. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object. Energy is the capacity to do work, and power is the rate at which work is done or energy is transferred.
力使物体移动时，即做了功。能量是做功的本领，功率则是做功或传递能量的速率。
Work = Force × Distance moved in direction of force (W = F × d)
Work is measured in joules (J), where 1 J = 1 N m. If a 10 N force pushes a box 5 m, the work done is 50 J.
功的单位是焦耳 (J)，1 J = 1 N·m。如果 10 N 的力将箱子推动 5 m，则做功 50 J。
Power = Work done / Time taken (P = W / t)
Power is measured in watts (W); 1 W = 1 J/s. When an object moves at constant speed, power can also be found using P = Force × velocity.
功率的单位是瓦特 (W)；1 W = 1 J/s。当物体匀速运动时，也可用 P = 力 × 速度 计算功率。
7. Ohm’s Law | 欧姆定律
Ohm’s Law describes the relationship between voltage, current and resistance in an electrical circuit. It is the foundation for all simple circuit calculations in engineering.
欧姆定律描述了电路中电压、电流和电阻之间的关系，是工程中所有简单电路计算的基础。
Voltage = Current × Resistance (V = I × R)
Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω). If a resistor of 100 Ω carries a current of 0.05 A, the voltage across it is 5 V.
电压单位为伏特 (V)，电流单位为安培 (A)，电阻单位为欧姆 (Ω)。若一个 100 Ω 的电阻流过 0.05 A 电流，其两端电压为 5 V。
Rearranging the formula gives I = V / R or R = V / I. Always ensure units are in volts, amps and ohms before substituting.
通过变形可得 I = V / R 或 R = V / I。代入前务必确保单位分别为伏、安和欧。
8. Resistance and Resistor Colour Codes | 电阻与电阻色环编码
Fixed resistors use coloured bands to indicate their resistance value and tolerance. The four‑band code is standard in Year 8 engineering projects.
固定电阻器用色环表示电阻值和误差。四色环编码是八年级工程项目中的标准内容。
| Colour | Digit 1/2 | Multiplier | Tolerance | 中文 |
|---|---|---|---|---|
| Black | 0 | ×10⁰ | – | 黑 |
| Brown | 1 | ×10¹ | ±1% | 棕 |
| Red | 2 | ×10² | ±2% | 红 |
| Orange | 3 | ×10³ | – | 橙 |
| Yellow | 4 | ×10⁴ | – | 黄 |
| Green | 5 | ×10⁵ | ±0.5% | 绿 |
| Blue | 6 | ×10⁶ | ±0.25% | 蓝 |
| Violet | 7 | ×10⁷ | ±0.1% | 紫 |
| Grey | 8 | ×10⁸ | – | 灰 |
| White | 9 | ×10⁹ | – | 白 |
| Gold | – | ×10⁻¹ | ±5% | 金 |
| Silver | – | ×10⁻² | ±10% | 银 |
For a four‑band resistor with colours brown‑black‑red‑gold, the resistance is 1 0 ×10² = 1000 Ω (1 kΩ), tolerance ±5%.
对于色环顺序为棕‑黑‑红‑金的四色环电阻，其阻值为 1 0 ×10² = 1000 Ω (1 kΩ)，误差为 ±5%。
9. Material Properties: Density, Stress and Strain | 材料属性：密度、应力与应变
Choosing the right material for an engineering design means knowing its basic physical properties. Density quantifies mass per unit volume.
为工程设计选择合适的材料需要了解其基本物理属性。密度量化了单位体积的质量。
Density = Mass / Volume (ρ = m / V)
Density is measured in kg/m³ or g/cm³. Aluminium has a density around 2700 kg/m³, while steel is about 7850 kg/m³.
密度的单位是 kg/m³ 或 g/cm³。铝的密度约为 2700 kg/m³，钢的密度约为 7850 kg/m³。
Stress measures the internal force carried per unit area when a material is loaded. Strain measures how much the material stretches or compresses relative to its original length.
应力衡量材料受载时单位面积上承受的内力。应变衡量材料相对于原始长度的伸长或缩短量。
Stress = Force / Cross‑sectional area (σ = F / A)
Strain = Change in length / Original length (ε = ΔL / L₀)
Stress has units of pascals (Pa) or N/m². Strain is a ratio, so it has no units. These two concepts help engineers avoid permanent deformation of components.
应力的单位是帕斯卡 (Pa) 或 N/m²。应变是比值，因此无单位。这两个概念帮助工程师避免构件发生永久变形。
10. Safety Factor | 安全系数
A safety factor ensures structures and mechanical parts can withstand loads greater than the expected maximum. It adds a margin of safety against uncertainties in materials and loading.
安全系数确保结构和机械零件能够承受比预期最大负载更大的力。它为材料和载荷的不确定性预留了安全余量。
Safety Factor = Ultimate strength / Allowable working stress
Ultimate strength is the maximum stress a material can bear before failure. The allowable working stress is the stress the part is designed to carry in normal use.
极限强度是材料失效前能承受的最大应力。许用工作应力是零件在正常使用中设计允许的应力。
A safety factor of 2 means the part is twice as strong as it needs to be for the expected load. Critical components in bridges or lifts use higher safety factors, often between 5 and 10.
安全系数为 2 表示该零件的强度是预期载荷所需的两倍。桥梁或电梯中的关键部件采用更高的安全系数，通常在 5 至 10 之间。
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