📚 Year 8 Edexcel Engineering Formulas & Theorems Quick Reference | Year 8 Edexcel 工程：公式定理速查手册
Engineering at Year 8 introduces you to the core ideas that shape the world around us — from simple mechanisms to electrical circuits and material choices. This guide pulls together the essential formulas and theorems you need to master for the Edexcel curriculum, explained step by step. Each section pairs a key concept with practical examples so you can apply your knowledge confidently in the classroom, in projects, and during assessments.
Year 8 工程课程带你了解塑造世界的核心思想——从简单机械到电路和材料选择。本手册汇集了 Edexcel 课程中必须掌握的基本公式和定理，并逐步讲解。每个部分将关键概念与实例配对，让你能在课堂、项目和评估中自信运用所学知识。
1. Speed and Velocity | 速度与速率
The most basic relationship in mechanics links distance, time, and speed. In engineering, understanding how fast something moves is essential for designing vehicles, conveyor belts, and timing systems.
力学中最基本的关系将路程、时间和速度联系在一起。在工程中，了解物体移动的快慢对于设计车辆、传送带和定时系统至关重要。
Average speed is calculated by dividing the total distance travelled by the time taken. If you walk 100 metres in 40 seconds, your average speed is 2.5 metres per second.
平均速度等于总路程除以所用时间。如果你在 40 秒内走了 100 米，那么你的平均速度是 2.5 米每秒。
speed (m/s) = distance (m) ÷ time (s)
速度 (m/s) = 路程 (m) ÷ 时间 (s)
When direction matters, we talk about velocity rather than speed. Velocity can be positive or negative depending on which way the object is moving along a straight line.
当方向很重要时，我们称它为速度而非速率。根据物体沿直线的运动方向，速度可以是正或负。
2. Acceleration | 加速度
Acceleration tells us how quickly an object changes its velocity. A roller coaster accelerating down a slope experiences an increase in speed; if it slows down, that is deceleration (negative acceleration).
加速度表示物体速度变化的快慢。过山车沿斜坡加速俯冲时速度增加；如果减慢，那就是减速（负加速度）。
Acceleration is the change in velocity divided by the time taken for that change. If a bicycle goes from 2 m/s to 8 m/s in 3 seconds, its acceleration is (8 − 2) ÷ 3 = 2 m/s².
加速度等于速度的变化量除以发生变化所用的时间。如果一辆自行车在 3 秒内从 2 m/s 加速到 8 m/s，其加速度为 (8 − 2) ÷ 3 = 2 m/s²。
acceleration (m/s²) = (final velocity − initial velocity) (m/s) ÷ time (s)
加速度 (m/s²) = (末速度 − 初速度) (m/s) ÷ 时间 (s)
In engineering, acceleration is crucial for analysing the forces on structures, vehicles, and moving parts in machines. Too much acceleration can damage components or make a ride uncomfortable.
在工程中，加速度对分析结构、车辆和机器运动部件的受力至关重要。加速度过大会损坏零件或使乘坐不舒适。
3. Newton’s Second Law of Motion | 牛顿第二运动定律
The link between force, mass, and acceleration is the cornerstone of dynamics. Whenever an unbalanced force acts on an object, the object accelerates in the direction of the force.
力、质量和加速度之间的关系是动力学的基石。只要物体受到非平衡力的作用，它就会沿力的方向加速。
The formula is beautifully simple: force equals mass multiplied by acceleration. A car of mass 1200 kg accelerating at 3 m/s² requires an engine force of 3600 newtons.
公式极其简单：力等于质量乘以加速度。一辆质量为 1200 kg 的汽车以 3 m/s² 加速，需要 3600 牛顿的发动机力。
F = m × a
Force (N) = mass (kg) × acceleration (m/s²)
力 (N) = 质量 (kg) × 加速度 (m/s²)
This law also explains why lighter vehicles accelerate faster with the same engine force, and why heavy loads need stronger motors in lifting equipment.
这一定律也解释了为什么较轻的车辆用同样的发动机力加速更快，以及为什么吊装重物需要更强的电动机。
4. Moment of a Force (Torque) | 力矩（扭矩）
A moment is the turning effect of a force around a pivot. Spanners, seesaws, and door handles all rely on moments to work efficiently.
力矩是力绕支点产生的转动效应。扳手、跷跷板和门把手都依赖力矩来高效工作。
The moment is calculated by multiplying the force applied by the perpendicular distance from the pivot to the line of action of the force. A spanner pushed with 20 N at a distance of 0.2 m from the centre of a bolt exerts a moment of 4 N m.
力矩等于作用力乘以从支点到力作用线的垂直距离。一把扳手在距螺栓中心 0.2 m 处施以 20 N 的力，产生的力矩为 4 N·m。
moment (N m) = force (N) × perpendicular distance from pivot (m)
力矩 (N·m) = 力 (N) × 支点到力的垂直距离 (m)
For an object to be in equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments about any point. This principle is used to design balanced structures and lever mechanisms.
物体要处于平衡状态，顺时针力矩之和必须等于逆时针力矩之和。这一原理用于设计平衡结构和杠杆机构。
5. Work Done and Energy Transferred | 做功与能量转换
When a force moves an object through a distance, work is done and energy is transferred from one store to another. This is a fundamental idea behind every machine: the force does work to lift a weight, turn a shaft, or compress a spring.
当一个力使物体移动一段距离时，就做了功，能量从一个储存库转移到另一个。这是每台机器的基本思想：力做功来升起重物、转动轴或压缩弹簧。
Work done equals the force applied multiplied by the distance moved in the direction of the force. Lifting a 50 N toolbox 2 metres vertically requires 100 joules of work.
功等于作用力乘以物体沿力方向移动的距离。将一个重 50 N 的工具箱垂直提升 2 米，需要做 100 焦耳的功。
W = F × d
Work done (J) = force (N) × distance moved in direction of force (m)
功 (J) = 力 (N) × 沿力方向移动的距离 (m)
Work done against friction is often wasted as heat, which is why engineers try to minimise friction in moving systems through lubrication and bearings.
克服摩擦所做的功通常以热能形式散失，因此工程师努力通过润滑和轴承来减少运动系统中的摩擦。
6. Power and Efficiency | 功率与效率
Power measures how quickly work is done or energy is transferred. A powerful engine can do the same amount of work in less time, which is critical for vehicles, drills, and manufacturing machines.
功率衡量做功或能量转换的快慢。强大的发动机能在更短时间内完成同量的功，这对车辆、钻机和制造机器至关重要。
Power is calculated by dividing the work done by the time taken. A motor that does 600 J of work in 5 seconds has a power output of 120 watts.
功率等于功除以所用时间。一台电动机在 5 秒内做 600 J 的功，其功率输出为 120 瓦。
P = W ÷ t
Power (W) = work done (J) ÷ time taken (s)
功率 (W) = 功 (J) ÷ 时间 (s)
Efficiency tells us how well a device converts input energy into useful output. No machine is 100% efficient — some energy is always lost, usually as heat or sound.
效率告诉我们设备将输入能量转换为有用输出的程度。没有任何机器能达到 100% 的效率，总有一些能量损失，通常是热能或声音。
efficiency (%) = (useful output energy ÷ total input energy) × 100
效率 (%) = (有用的输出能量 ÷ 总输入能量) × 100
7. Mechanical Advantage and Velocity Ratio | 机械效益与速比
Simple machines such as levers, pulleys, and gears help us multiply forces. Mechanical advantage (MA) is the factor by which a machine amplifies the effort force. A system with an MA of 5 means you only need to apply one‑fifth of the load force.
杠杆、滑轮和齿轮等简单机械帮助我们放大力的效果。机械效益 (MA) 是机器放大作用力的倍数。MA 为 5 意味着只需施加负载力五分之一的力。
| Mechanical advantage (MA) = load force (N) ÷ effort force (N) |
| 机械效益 (MA) = 负载力 (N) ÷ 作用力 (N) |
Velocity ratio (VR) compares the distance moved by the effort to the distance moved by the load. In an ideal frictionless machine, MA equals VR, but in reality friction reduces MA.
速比 (VR) 比较作用力移动的距离与负载移动的距离。在理想无摩擦机器中，MA 等于 VR，但现实中摩擦会降低 MA。
| Velocity ratio (VR) = distance moved by effort ÷ distance moved by load |
| 速比 (VR) = 作用力移动的距离 ÷ 负载移动的距离 |
8. Gears and Gear Ratios | 齿轮与齿轮比
Gears transmit rotational motion and torque. The gear ratio tells you how the speed and torque change between the driving gear and the driven gear. A large driving gear turning a small driven gear increases speed but reduces torque.
齿轮传递旋转运动和扭矩。齿轮比告诉你主动齿轮与从动齿轮之间的速度和扭矩变化。大主动齿轮带动小从动齿轮会增加速度但降低扭矩。
Gear ratio can be calculated using the number of teeth on each gear. If a driving gear has 30 teeth and the driven gear has 10 teeth, the gear ratio is 30:10 or 3:1. This means the driven gear rotates 3 times for every rotation of the driver — a speed increase.
齿轮比可用每个齿轮的齿数计算。如果主动齿轮有 30 齿，从动齿轮有 10 齿，齿轮比为 30:10 或 3:1。这表示主动齿轮每转一圈，从动齿轮转 3 圈——速度增加。
gear ratio = number of teeth on driven gear ÷ number of teeth on driving gear
齿轮比 = 从动齿轮齿数 ÷ 主动齿轮齿数
When two gears mesh, they always turn in opposite directions. An idler gear can be placed between them to make the driver and driven rotate in the same direction.
两个齿轮啮合时，转动方向总是相反。可以在中间放置一个惰轮，使主动轮和从动轮转向相同。
9. Ohm’s Law and Electrical Power | 欧姆定律与电功率
Electrical circuits are the backbone of modern engineering. Ohm’s Law connects voltage, current, and resistance in a simple equation that helps us design safe and functional circuits.
电路是现代工程的支柱。欧姆定律用一个简单方程将电压、电流和电阻联系起来，帮助我们设计安全实用的电路。
If the voltage across a resistor is 9 V and the current flowing through it is 0.5 A, the resistance is 9 ÷ 0.5 = 18 Ω. Components must be rated to handle the expected current without overheating.
若一个电阻器两端电压为 9 V，流过电流为 0.5 A，则电阻为 9 ÷ 0.5 = 18 Ω。元器件必须额定到能承受预期的电流而不过热。
V = I × R
Voltage (V) = current (A) × resistance (Ω)
电压 (V) = 电流 (A) × 电阻 (Ω)
Electrical power is the rate at which electrical energy is converted. A lamp with 0.3 A flowing through it at 6 V consumes power of 6 × 0.3 = 1.8 W.
电功率是电能转换的速率。一盏灯在 6 V 电压下流过 0.3 A 电流，消耗的功率为 6 × 0.3 = 1.8 W。
P = V × I
Power (W) = voltage (V) × current (A)
功率 (W) = 电压 (V) × 电流 (A)
10. Density and Material Properties | 密度与材料特性
Understanding materials is crucial for selecting the right ones for a project. Density links the mass of a material to its volume and explains why some objects float while others sink.
了解材料对于为项目选择正确的材料至关重要。密度将材料的质量与体积联系起来，并解释了为什么有些物体浮起来而有些沉下去。
Density is mass per unit volume. A block of aluminium with mass 2.7 g and volume 1 cm³ has a density of 2.7 g/cm³. Steel has a much higher density, so a steel bolt feels heavier than an aluminium one of the same size.
密度是单位体积的质量。一块质量为 2.7 g、体积为 1 cm³ 的铝块，其密度为 2.7 g/cm³。钢的密度高得多，因此相同尺寸的钢螺栓比铝螺栓重。
ρ = m ÷ V
Density (kg/m³ or g/cm³) = mass (kg or g) ÷ volume (m³ or cm³)
密度 (kg/m³ 或 g/cm³) = 质量 (kg 或 g) ÷ 体积 (m³ 或 cm³)
Engineers also consider other properties such as hardness, toughness, electrical conductivity, and thermal conductivity when choosing materials for specific applications.
工程师在为特定应用选择材料时，还会考虑硬度、韧性、导电性和导热性等其他特性。
11. Stress, Strain and Hooke’s Law | 应力、应变与胡克定律
Materials stretch, compress, and bend when forces are applied. Hooke’s Law describes the elastic behaviour of springs and many engineering materials below their limit of proportionality.
材料在受力时会拉伸、压缩和弯曲。胡克定律描述了弹簧和许多工程材料在比例极限内的弹性行为。
The extension of a spring is directly proportional to the force applied, as long as the spring is not overstretched. If a spring stretches 0.05 m under a load of 10 N, its spring constant is 10 ÷ 0.05 = 200 N/m.
只要弹簧不过度拉伸，其伸长量与施加的力成正比。若一个弹簧在 10 N 载荷下伸长 0.05 m，则其弹簧常数为 10 ÷ 0.05 = 200 N/m。
F = k × x
Force (N) = spring constant (N/m) × extension (m)
力 (N) = 弹簧常数 (N/m) × 伸长量 (m)
Engineers perform tensile tests to find the yield strength and ultimate tensile strength of materials, ensuring structures can withstand expected loads without permanent deformation.
工程师通过拉伸试验来找出材料的屈服强度和抗拉强度，确保结构能承受预期的载荷而不会发生永久变形。
12. Pressure in Fluids and Pneumatics | 流体与气动压力
Pressure measures how concentrated a force is over an area. Sharp blades cut easily because they have a tiny surface area, producing high pressure even with a small force.
压力衡量力在某一面积上的集中程度。锋利的刀刃能轻松切割，因为它的表面积很小，即使很小的力也能产生高压力。
Pressure is force divided by area. A force of 500 N acting on an area of 0.1 m² creates a pressure of 5000 Pa (or 5 kPa). Pneumatic and hydraulic systems use this principle to magnify forces — a small force on a small piston can generate a large force on a bigger piston.
压力等于力除以面积。500 N 的力作用在 0.1 m² 的面积上产生 5000 Pa（即 5 kPa）的压力。气动和液压系统利用这一原理来放大力的作用——小活塞上的小力可以在大活塞上产生大力。
P = F ÷ A
Pressure (Pa) = force (N) ÷ area (m²)
压力 (Pa) = 力 (N) ÷ 面积 (m²)
In a hydraulic press, pressure is the same throughout the fluid, so a large output piston provides a high mechanical advantage. The same principle operates in car brakes and heavy lifting equipment.
在液压机中，流体中各处压力相同，因此大输出活塞能提供很高的机械效益。汽车制动器和重型起重设备就应用了同一原理。
Published by TutorHao | Engineering Revision Series | aleveler.com
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