📚 Year 7 OCR Engineering: Formula & Theorem Quick Reference Handbook | 7年级OCR工程：公式定理速查手册
This handbook gathers the most important formulas and relationships you will encounter in Year 7 OCR Engineering. Each entry explains the meaning of the symbols, the correct SI units, and gives a worked example. Mastering these fundamentals will help you analyse forces, motion, energy, electricity and material properties in design and practical projects.
本手册汇集了7年级OCR工程中你将会遇到的最重要的公式和关系。每个条目都解释了符号的含义、正确的国际单位制，并给出了一个计算示例。掌握这些基础知识将帮助你在设计与实践项目中分析力、运动、能量、电学和材料性能。
1. Force, Mass and Gravity | 力、质量与重力
Weight is a force caused by gravity acting on an object's mass. The larger the mass, the greater the weight. The relationship is linear and is described by the equation below, where g trength. On Earth, g ≈ 9.8 N/kg, but for simple calculations we often round it to 10 N/kg.
W = m × g
W 表示重量（单位：牛顿，N），m 是质量（单位：千克，kg），g 是重力场强度，地球表面约为 9.8 N/kg，课堂计算中常取 10 N/kg。这一定理说明重量与质量严格正比，是结构承重和材料选择的基础。
= 8 × 10 = 80 N. This means the floor must provide an upward force of 80 N to support it.
示例：一个工具箱质量为 8 kg，它在地球上的重量为 W = 8 × 10 = 80 N。这意味着地板必须提供 80 N 的向上支撑力。
2. Pressure | 压强
Pressure measures how concentrated a force is over an area. A sharp knife cuts easily because the force is applied over a tiny area, giving high pressure. Pressure is calculated by dividing the force by the area over which it acts. The unit of pressure is the pascal (Pa), equivalent to one newton per square metre (N/m²).
P = F ÷ A
P 表示压强（单位帕斯卡，Pa），F 是垂直于表面的力（N），A 是受力面积（m²）。工程师利用这个公式确保地基、轮胎和液压系统不会因压强过大而失效。
.0002 m². The pressure is P = 500 ÷ 0.0002 = 2 500 000 Pa, enough to damage wooden floors.
示例：一个细高跟施加 500 N 的力，鞋跟面积为 0.0002 m²。压强 P = 500 ÷ 0.0002 = 2 500 000 Pa，足以损坏木地板。
3. Work Done and Energy | 做功与能量
In engineering, 'doing work' means transferring energy by applying a force and making something move. When a force moves an object through a distance in the direction of the force, work is done. Work is measured in joules (J), where one joule is one newton of force moving something one metre.
W = F × d
W 表示做功（单位焦耳，J），F 是作用力（N），d 是物体沿力方向移动的距离（m）。这个公式将力与能量直接联系起来，用于计算机械、升降机等装置的能量需求。
he work done is W = 2000 × 6 = 12 000 J (12 kJ). This energy must be supplied by the crane's motor.
示例：一台起重机将 2000 N 的重物垂直提升 6 m。做功 W = 2000 × 6 = 12 000 J (12 kJ)。这些能量必须由起重机的电动机提供。
4. Power | 功率
Power tells us how quickly work is done or energy is transferred. A more powerful engine performs the same amount of work in less time. Power is measured in watts (W), where one watt equals one joule per second (J/s).
P = W ÷ t
P 表示功率（单位瓦特，W），W 是已经做的功或转移的能量（J），t 是所用的时间（s）。高功率意味着可以在短时间内完成大量工作，这对赛车引擎和工厂机器至关重要。
lectric hoist does 2400 J of work in 30 seconds. Its power output is P = 2400 ÷ 30 = 80 W.
示例：一台电动葫芦在 30 秒内做了 2400 J 的功。其输出功率 P = 2400 ÷ 30 = 80 W。
5. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force around a pivot. It increases with a larger force or a greater distance from the pivot. This principle explains how levers, spanners and seesaws work. The moment is calculated by multiplying the force by the perpendicular distance from the pivot to the line of action of the force.
M = F × d
M 表示力矩（单位牛米，Nm），F 是作用力（N），d 是支点到力作用线的垂直距离（m）。在平衡状态下，顺时针力矩之和等于逆时针力矩之和，这是设计桥梁和手动工具的基础。
of a spanner 0.25 m from the nut. The moment applied to the nut is M = 10 × 0.25 = 2.5 Nm.
示例：一个 10 N 的力作用在扳手手柄上，距离螺母 0.25 m。施加在螺母上的力矩 M = 10 × 0.25 = 2.5 Nm。
6. Speed, Distance and Time | 速度、距离与时间
Speed describes how fast an object is moving, without worrying about direction. Average speed is found by dividing the total distance travelled by the total time taken. The standard unit of speed is metres per second (m/s), but kilometres per hour (km/h) is also common in transport engineering.
v = s ÷ t
v 表示平均速度（m/s），s 是移动的总距离（m），t 是总时间（s）。这个公式用于计算传送带、车辆和机器装置中零件的运动速率。
conveyor belt moves a package 12 m in 4 seconds. Its average speed is v = 12 ÷ 4 = 3 m/s.
示例：一条传送带在 4 秒内移动包裹 12 m。其平均速度 v = 12 ÷ 4 = 3 m/s。
7. Density | 密度
Density is a measure of how much mass is packed into a given volume. Materials with high density, like steel, feel heavy for their size. Low-density materials, like foam, are light. Density is essential when choosing materials for structures, buoyancy and packaging. It is usually given in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³).
ρ = m ÷ V
ρ （希腊字母 rho）表示密度（kg/m³），m 是质量（kg），V 是体积（m³）。如果已知材料的密度和物体的体积，就可以算出它的质量。
a volume of 0.002 m³. Its density is ρ = 5.4 ÷ 0.002 = 2700 kg/m³ (typical for aluminium).
示例：一块铝的质量为 5.4 kg，体积为 0.002 m³。其密度 ρ = 5.4 ÷ 0.002 = 2700 kg/m³ （铝的典型密度）。
8. Current, Voltage and Resistance (Ohm's Law) | 电流、电压与电阻（欧姆定律）
In electrical circuits, Ohm's Law links the three fundamental quantities. Voltage (the push of electricity) equals the product of current (the flow of charge) and resistance (the opposition to flow). This law helps engineers design circuits so components get the correct current without overheating. Voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω).
V = I × R
V 表示电压（V），I 是电流（A），R 是电阻（Ω）。当电压保持不变时，电阻越大，电流越小；这在选择限流电阻时非常重要。
Ω and a current of 2 A flows through it. The voltage across the lamp is V = 2 × 6 = 12 V.
示例：一盏灯丝的电阻为 6 Ω，通过的电流为 2 A。灯两端的电压 V = 2 × 6 = 12 V。
9. Total Resistance in Series Circuits | 串联电路中的总电阻
When resistors are connected end-to-end in a series circuit, the same current flows through each of them. The overall resistance of the circuit is simply the sum of the individual resistances. Adding more series resistors always increases the total resistance, reducing the current from the battery.
Rₜₒₜₐₗ = R₁ + R₂ + R₃ + ...
Rₜₒₜₐₗ 是串联电路的总电阻（Ω），R₁, R₂, R₃ ... 分别代表各个电阻的值。这个规则在分压电路和传感器电路中经常使用。
Ω, 7 Ω and 9 Ω are connected in series. The total resistance is Rₜₒₜₐₗ = 4 + 7 + 9 = 20 Ω.
示例：三个电阻分别为 4 Ω、7 Ω 和 9 Ω 串联。总电阻 Rₜₒₜₐₗ = 4 + 7 + 9 = 20 Ω。
10. Mechanical Efficiency | 机械效率
No machine is perfect – some input energy is always lost to friction, heat or sound. Mechanical efficiency tells us how much of the input work is usefully transformed into output work. It is expressed as a percentage: a higher percentage means a more effective machine. Efficiency is a key consideration in engine design and sustainable engineering.
Efficiency (%) = (Useful output work ÷ Total input work) × 100
效率（%） = （有用输出功 ÷ 总输入功）× 100。例如，如果一台电动机消耗 1000 J 的电能，但只输出了 750 J 的有用机械功，其效率就是 75%。剩佘的 25% 变成了热量和噪音。
only 400 J is transferred to the load as useful work. Efficiency = (400 ÷ 500) × 100 = 80%.
示例：一套滑轮组需要输入 500 J 的功来提升重物，但只有 400 J 有效作用在重物上。效率 = (400 ÷ 500) × 100 = 80%。
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