📚 Year 8 WJEC Engineering: Quick Reference to Formulas and Theorems | 八年级 WJEC 工程：公式定理速查手册
Welcome to your go-to revision sheet for Year 8 WJEC Engineering. This article packs all the essential formulas and principles you need to know, from forces and motion to electricity and materials. Use it to revise for tests, support your project work, and strengthen your engineering understanding. Each formula is presented with clear notation, and every section explains both the science and the engineering application, so you can confidently connect theory to practice.
欢迎使用这本八年级 WJEC 工程课程的速查手册。本文汇集了力与运动、电学、材料等所有核心公式和定理。你可以用它来备考、辅助项目设计，并加深对工程原理的理解。每个公式都有清晰的符号说明，每个小节既解释科学原理也说明工程应用，帮助你自信地将理论与实际联系起来。
1. Force, Mass and Acceleration (Newton’s Second Law) | 力、质量与加速度（牛顿第二定律）
Newton’s Second Law states that the force acting on an object is equal to its mass multiplied by its acceleration. In equation form, F = m × a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²). This relationship is the foundation of mechanical design, from calculating the force needed to start a vehicle moving to determining the load on a component in a structure.
牛顿第二定律指出，作用在物体上的力等于物体的质量乘以加速度。公式为 F = m × a。力的单位是牛顿 (N)，质量的单位是千克 (kg)，加速度的单位是米每二次方秒 (m/s²)。这一关系是机械设计的基础，从计算启动车辆所需的力到确定结构中部件承受的载荷都离不开它。
- F = m × a (Resultant force = mass × acceleration)
- 1 N = 1 kg × 1 m/s²
2. Weight and Gravitational Force | 重力与引力
Weight is the force of gravity acting on a mass. It is given by W = m × g, where g is the gravitational field strength. On Earth, g is approximately 9.8 m/s², but for Year 8 engineering problems, we often use 10 m/s² for simplicity. Weight is a force, so it is measured in newtons. Understanding weight is crucial when designing supports, bridges and lifting systems.
重力是地球对物体施加的引力。公式为 W = m × g，其中 g 是重力场强度。地球表面的 g 约为 9.8 m/s²，但在八年级工程问题中，我们通常简化为 10 m/s²。重量是一种力，因此单位也是牛顿。在设计支撑结构、桥梁和提升系统时，理解重力至关重要。
W = m × g (Weight = mass × gravitational field strength)
3. Pressure in Solids and Fluids | 固体与流体的压强
Pressure is the amount of force applied per unit area. The formula is P = F ÷ A, where P is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m²). A small force over a small area can create a huge pressure, which is why sharp tools cut easily. In fluids, pressure increases with depth and can be calculated using P = h × ρ × g, where h is depth, ρ is density and g is gravity. Engineers use these formulas when designing hydraulic systems, foundations and cutting instruments.
压强是单位面积上承受的力的大小。公式为 P = F ÷ A，其中 P 表示压强，单位是帕斯卡 (Pa)；F 是力，单位是牛顿 (N)；A 是面积，单位是平方米 (m²)。很小的力作用在很小的面积上也能产生巨大压强，这就是为什么锋利的工具更容易切割。在流体中，压强随深度增加，可用 P = h × ρ × g 计算，其中 h 是深度，ρ 是密度，g 是重力加速度。工程师在设计液压系统、地基和切割工具时都会用到这些公式。
P = F / A and P = h × ρ × g
4. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force. It depends on two things: the size of the force and the perpendicular distance from the pivot to the line of action of the force. The formula is M = F × d, where M is the moment in newton-metres (Nm), F is force in newtons (N) and d is distance in metres (m). For an object to be balanced, the total clockwise moment must equal the total anticlockwise moment. This principle, often called the principle of moments, is used to design levers, seesaws and even crane counterweights.
力矩是力产生的转动效应，它取决于两个因素：力的大小和支点到力作用线的垂直距离。公式为 M = F × d，其中 M 表示力矩，单位是牛顿·米 (Nm)；F 是力 (N)；d 是距离 (m)。要使物体平衡，顺时针力矩的总和必须等于逆时针力矩的总和。这个原理通常称为力矩原理，被用于设计杠杆、跷跷板甚至起重机的配重。
M = F × d (Moment = Force × perpendicular distance)
5. Work Done and Energy Transfer | 做功与能量转移
Work is done whenever a force moves an object. The amount of work is calculated by W = F × d, where W is work in joules (J), F is force in newtons (N) and d is distance moved in the direction of the force in metres (m). One joule is equal to one newton-metre. Work done is a measure of energy transferred. In engineering, you calculate work done to determine how much energy a machine needs to lift a load or move a vehicle.
只要力使物体移动，就做了功。做功的大小用 W = F × d 计算，其中 W 表示功，单位是焦耳 (J)；F 是力 (N)；d 是物体沿力的方向移动的距离 (m)。1 焦耳等于 1 牛顿·米。功是能量转移的量度。在工程中，你可以通过计算做功来确定机器举起重物或移动车辆所需的能量。
W = F × d (Work = Force × distance)
6. Power and Efficiency | 功率与效率
Power is the rate at which work is done or energy is transferred. The formula is P = W ÷ t or P = E ÷ t, where P is power in watts (W), W is work in joules (J), E is energy in joules (J), and t is time in seconds (s). One watt is one joule per second. Efficiency is a measure of how well a device converts input energy into useful output energy. It is calculated as Efficiency = (Useful output energy ÷ Total input energy) × 100%. Engineering systems always aim for high efficiency to reduce energy waste and cost.
功率是做功或能量转移的速率。公式为 P = W ÷ t 或 P = E ÷ t，其中 P 表示功率，单位是瓦特 (W)；W 是功 (J)；E 是能量 (J)；t 是时间 (s)。1 瓦特等于每秒 1 焦耳。效率衡量设备将输入能量转换为有用输出能量的程度，计算公式为 效率 = (有用输出能量 ÷ 总输入能量) × 100%。工程系统总是追求高效率以减少能量浪费和成本。
P = E / t and Efficiency = (Euseful / Einput) × 100%
7. Kinetic and Potential Energy | 动能与势能
Moving objects possess kinetic energy, given by KE = ½ × m × v². Here m is mass in kilograms (kg) and v is velocity in metres per second (m/s). Objects raised above the ground store gravitational potential energy, GPE = m × g × h, where h is height in metres (m) and g is gravitational field strength (N/kg). These energy formulas are vital when analysing vehicles, roller coasters and any system where energy is conserved and converted between forms.
运动的物体具有动能，公式为 KE = ½ × m × v²，其中 m 是质量 (kg)，v 是速度 (m/s)。被举高的物体储存重力势能，GPE = m × g × h，其中 h 是高度 (m)，g 是重力场强度 (N/kg)。这些能量公式在分析车辆、过山车以及任何能量转化和守恒的系统时至关重要。
KE = ½ m v² and GPE = m g h
8. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most used formulas in engineering. Speed = Distance ÷ Time, or v = d ÷ t. Speed is often measured in metres per second (m/s) or kilometres per hour (km/h). By rearranging the formula, you can also calculate distance (d = v × t) or time (t = d ÷ v). These calculations are fundamental for planning journeys, designing conveyor belts, and programming automated guided vehicles.
速度、距离和时间之间的关系是工程中最常用的公式之一。速度 = 距离 ÷ 时间，即 v = d ÷ t。速度的常用单位是米每秒 (m/s) 或千米每小时 (km/h)。通过变形公式，你还可以计算距离 (d = v × t) 或时间 (t = d ÷ v)。这些计算是规划行程、设计传送带以及编程自动引导车辆的基础。
v = d / t d = v × t t = d / v
9. Ohm’s Law and Electrical Circuits | 欧姆定律与电路
Ohm’s Law connects voltage, current and resistance in an electrical circuit. The formula is V = I × R, where V is potential difference (voltage) in volts (V), I is current in amperes (amps, A), and R is resistance in ohms (Ω). This law helps engineers choose the correct resistors, design safe circuits, and ensure components receive the right voltage and current. In series circuits, current is the same everywhere; in parallel circuits, voltage is the same across each branch.
欧姆定律描述了电路中电压、电流和电阻之间的关系。公式为 V = I × R，其中 V 是电势差（电压），单位是伏特 (V)；I 是电流，单位是安培 (A)；R 是电阻，单位是欧姆 (Ω)。这条定律帮助工程师选择合适的电阻、设计安全电路，并确保元件获得正确的电压和电流。串联电路中电流处处相等；并联电路中各支路两端电压相等。
V = I R (Voltage = Current × Resistance)
10. Electrical Power and Energy | 电功率与电能
Electrical power is the rate at which electrical energy is transferred by a circuit. It can be calculated using P = I × V, where P is power in watts (W), I is current in amperes (A), and V is voltage in volts (V). Alternatively, using Ohm’s Law, P = I² R or P = V² / R. Electrical energy consumed is E = P × t, usually measured in watt-hours (Wh) or kilowatt-hours (kWh). These formulas are used when selecting power supplies, batteries, and estimating running costs of devices.
电功率是电路传输电能的速率。可用 P = I × V 计算，其中 P 是功率 (W)，I 是电流 (A)，V 是电压 (V)。结合欧姆定律，还可得到 P = I² R 或 P = V² / R。消耗的电能为 E = P × t，通常用瓦时 (Wh) 或千瓦时 (kWh) 计量。这些公式用于选择电源、电池以及估算设备的运行成本。
P = I V P = I² R E = P t
11. Hooke’s Law and Springs | 胡克定律与弹簧
Hooke’s Law describes the stretch of elastic materials like springs. It states that the extension of a spring is directly proportional to the force applied, as long as the limit of proportionality is not exceeded. The formula is F = k × x, where F is force in newtons (N), k is the spring constant (stiffness) in newtons per metre (N/m), and x is extension in metres (m). Engineers use this law to design suspension systems, measuring instruments and any component that relies on predictable elastic behaviour.
胡克定律描述了弹簧等弹性材料的拉伸规律。它指出，只要不超过比例极限，弹簧的伸长量与所施加的力成正比。公式为 F = k × x，其中 F 是力 (N)，k 是弹簧常量（刚度），单位是 N/m，x 是伸长量 (m)。工程师利用这一定律设计悬挂系统、测量仪器以及任何依赖可预测弹性行为的部件。
F = k x (Force = spring constant × extension)
12. Simple Machines and Mechanical Advantage | 简单机械与机械利益
Simple machines like levers, pulleys and ramps make work easier by reducing the effort force needed. Mechanical advantage (MA) is the ratio of the load force to the effort force. MA = Load ÷ Effort. A mechanical advantage greater than 1 means the machine multiplies the effort. Velocity ratio (VR) compares the distance moved by the effort to the distance moved by the load. Efficiency of a machine is the ratio of these two: Efficiency = (MA ÷ VR) × 100%. These ideas underpin the design of tools, gears and lifting systems.
杠杆、滑轮和斜面等简单机械通过减小所需的动力让工作更轻松。机械利益 (MA) 是负载力与动力的比值。MA = 负载 ÷ 动力。机械利益大于 1 表示机械放大了动力。速比 (VR) 是动力移动的距离与负载移动的距离的比值。机械效率则是这两者的比值：效率 = (MA ÷ VR) × 100%。这些概念是工具、齿轮和提升系统设计的基础。
MA = Load / Effort VR = deffort / dload η = (MA / VR) × 100%
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