📚 Year 7 OCR Engineering: Quick-Reference Handbook of Formulas & Theorems | Year 7 OCR 工程：公式定理速查手册
This quick-reference handbook brings together the essential formulas, theorems and numerical relationships that form the core of Year 7 OCR Engineering. Whether you are designing a simple lever, calculating electrical power or checking unit conversions, the formulae collected here will help you work accurately and confidently. Keep this guide handy for homework, practicals and revision.
本速查手册汇集了 Year 7 OCR 工程课程的核心公式、定理与数量关系。无论你是在设计简单的杠杆、计算电功率还是校验单位换算，这里整理的公式都能帮助你准确而自信地解决问题。请将本手册保留在手边，用于作业、实验和考前复习。
1. Measurement, Units and Conversions | 测量、单位与换算
All engineering quantities are built on the International System of Units (SI). The three base units you will use most often are the metre (m) for length, the kilogram (kg) for mass and the second (s) for time. Derived units, such as the newton (N) for force and the pascal (Pa) for pressure, are combinations of these base quantities.
所有的工程量都建立在国际单位制 (SI) 之上。你最常使用的三个基本单位是长度单位米 (m)、质量单位千克 (kg) 和时间单位秒 (s)。导出单位如力的牛顿 (N) 和压强的帕斯卡 (Pa) 则是由这些基本量组合而成。
Metric prefixes let you express very large or very small measurements compactly. The table below lists the prefixes you must know for OCR Engineering.
公制前缀让你能简洁地表示极大或极小的测量值。下表列出了 OCR 工程课程中必须掌握的前缀。
| Prefix | Symbol | Factor |
|---|---|---|
| kilo | k | 10³ (1000) |
| centi | c | 10⁻² (0.01) |
| milli | m | 10⁻³ (0.001) |
To convert from a larger unit to a smaller unit, multiply by the conversion factor. To convert from a smaller unit to a larger unit, divide. For example, 2.5 m = 2.5 x 100 = 250 cm, and 500 g = 500 / 1000 = 0.5 kg.
从大单位转换为小单位，乘以换算因子；从小单位转换为大单位，除以换算因子。例如，2.5 m = 2.5 × 100 = 250 cm，而 500 g = 500 ÷ 1000 = 0.5 kg。
value in new unit = value in old unit × conversion factor
2. Speed and Acceleration | 速度与加速度
Average speed tells you how fast an object moves over a journey. It is the total distance covered divided by the total time taken. In symbols, v = d / t, where v is speed, d is distance and t is time. The SI unit of speed is metres per second (m/s), but you will also use kilometres per hour (km/h) in design contexts.
平均速度描述物体在一段行程中的快慢程度。它等于总距离除以总时间。用符号表示为 v = d / t，其中 v 是速度，d 是距离，t 是时间。速度的国际单位是米每秒 (m/s)，但在设计场景中你也会用到千米每小时 (km/h)。
average speed = total distance ÷ total time v = d / t
Acceleration is the rate at which an object’s speed changes. If an object speeds up from an initial velocity u to a final velocity v over time t, the acceleration a is given by the change in velocity divided by time:
加速度是物体速度变化的快慢程度。如果一个物体在时间 t 内从初速度 u 加速到末速度 v，则加速度 a 等于速度变化量除以时间：
acceleration = (final velocity – initial velocity) / time a = (v – u) / t
If the acceleration is negative (v < u), the object is decelerating. Always include direction when describing velocity in engineering challenges.
若加速度为负值 (v < u)，则物体在减速。在工程问题中描述速度时，务必包含方向信息。
3. Force, Mass and Weight | 力、质量与重量
Newton’s Second Law of Motion states that the net force acting on an object is equal to the object’s mass multiplied by its acceleration. This relationship is the foundation of most mechanical calculations:
牛顿第二运动定律指出，作用在物体上的合力等于物体的质量乘以加速度。这一关系是大多数力学计算的基础：
F = m × a
Force is measured in newtons (N). A force of 1 N gives a mass of 1 kg an acceleration of 1 m/s². Mass describes how much matter an object contains and is constant everywhere, while weight is the gravitational force acting on that mass.
力的单位是牛顿 (N)。1 N 的力能使 1 kg 的质量产生 1 m/s² 的加速度。质量描述物体所含物质的多少，处处恒定；而重量是作用在该质量上的重力。
weight = mass × gravitational field strength W = m × g
On Earth, g ≈ 9.8 m/s², so an object with a mass of 1 kg has a weight of about 9.8 N. In simple classroom problems, g is often rounded to 10 m/s² for quick estimation.
在地球上，g ≈ 9.8 m/s²，因此 1 kg 质量的物体重量约为 9.8 N。在简单的课堂问题中，g 常取近似值 10 m/s² 以便快速估算。
4. Pressure | 压强
Pressure is the amount of force applied perpendicularly over a given area. It tells you how concentrated a force is. A sharp knife exerts high pressure because the area of its edge is tiny; a snowshoe reduces pressure by spreading the force over a larger area.
压强是垂直作用在单位面积上的力。它表示力的集中程度。锋利的刀刃因接触面积极小而产生高压强；雪鞋则通过将力分散到较大面积来降低压强。
pressure = force / area p = F / A
The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². Because a pascal is a very small pressure, you will often use kilopascals (kPa) in engineering. For example, atmospheric pressure is about 101 kPa.
压强的国际单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。由于帕斯卡是一个非常小的压强，工程中经常使用千帕 (kPa)。例如，大气压强约为 101 kPa。
When a force of 10 N acts on an area of 2 m², the pressure is 5 Pa. Understanding pressure helps you design safe structures, hydraulic systems and even packaging.
当 10 N 的力作用在 2 m² 的面积上时，压强为 5 Pa。理解压强有助于设计安全的结构、液压系统乃至包装。
5. Work, Energy and Power | 功、能与功率
When a force moves an object through a distance in the direction of the force, work is done. Work is a form of energy transfer and is calculated as the product of force and distance:
当力使物体沿力的方向移动一段距离时，就做了功。功是能量传递的一种形式，其大小为力与距离的乘积：
work done = force × distance moved in the direction of the force W = F × d
Work and energy are both measured in joules (J). One joule is the work done when a force of 1 N moves an object 1 m.
功和能量的单位都是焦耳 (J)。1 焦耳就是 1 N 的力使物体移动 1 m 所做的功。
Two important forms of mechanical energy are kinetic energy (Ek) and gravitational potential energy (Ep).
两种重要的机械能形式是动能 (Ek) 和重力势能 (Ep)。
kinetic energy = ½ × mass × speed² Ek = ½ m v²
gravitational potential energy = mass × g × height Ep = m g h
Power is the rate at which work is done or energy is transferred. A machine with a higher power rating can do the same work in less time.
功率是做功或能量传递的快慢程度。功率越大的机器，完成同样功所需的时间越短。
power = work done / time = energy transferred / time P = W / t = E / t
The unit of power is the watt (W); 1 W = 1 J/s.
功率的单位是瓦特 (W)；1 W = 1 J/s。
6. Levers and Moments | 杠杆与力矩
A lever is a simple machine that rotates around a fixed point called the pivot or fulcrum. The turning effect of a force is called a moment. The size of a moment depends on both the magnitude of the force and its perpendicular distance from the pivot.
杠杆是一种绕固定点（支点）转动的简单机械。力的转动效应称为力矩。力矩的大小既取决于力的大小，也取决于力到支点的垂直距离。
moment = force × perpendicular distance from pivot M = F × d
Moments are measured in newton-metres (Nm). For a lever to be in equilibrium (balanced), the sum of the clockwise moments must equal the sum of the anticlockwise moments. This is the principle of moments:
力矩的单位是牛顿米 (Nm)。杠杆平衡时，顺时针力矩之和必须等于逆时针力矩之和。这就是力矩原理：
F₁ × d₁ = F₂ × d₂ (clockwise moments = anticlockwise moments)
Using this equation, you can find unknown forces or distances in tools such as crowbars, scissors and wheelbarrows.
利用这个等式，你可以计算撬棍、剪刀、手推车等工具中未知的力或距离。
7. Mechanical Advantage and Efficiency | 机械利益与效率
Mechanical advantage (MA) tells you how many times a machine multiplies the effort (input force). It is the ratio of the load force to the effort force. A mechanical advantage greater than 1 means the machine helps you lift a heavier load with a smaller effort.
机械利益 (MA) 表示机器将输入力放大了多少倍。它是负载力与作用力的比值。机械利益大于 1 意味着机器能让你用较小的作用力举起较重的负载。
mechanical advantage = load (output force) / effort (input force) MA = Fload / Feffort
Velocity ratio (VR) is determined by the geometry of the machine. It compares the distance moved by the effort to the distance moved by the load in the same time.
速度比 (VR) 由机器的几何构造决定，它比较在相同时间内作用力移动的距离与负载移动的距离。
velocity ratio = distance moved by effort / distance moved by load VR = deffort / dload
No machine is perfect; some input energy is always lost to friction. Efficiency measures how much of the input work is converted into useful output work.
没有机器是完美的，总有一部分输入能量因摩擦而损失。效率衡量输入功中有多少被转化为有用输出功。
efficiency = (mechanical advantage / velocity ratio) × 100% η = (MA / VR) × 100%
Efficiency is always less than 100 %. Designing low-friction bearings and using lubricants can raise efficiency.
效率始终小于 100%。设计低摩擦轴承和使用润滑剂可以提高效率。
8. Electrical Circuits: Ohm’s Law | 电路：欧姆定律
An electric circuit needs a complete loop for current to flow. Three key electrical quantities are voltage (V), current (I) and resistance (R). Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω).
电路需要形成完整回路，电流才能流动。三个关键的电学量是电压 (V)、电流 (I) 和电阻 (R)。电压的单位是伏特 (V)，电流的单位是安培 (A)，电阻的单位是欧姆 (Ω)。
Ohm’s Law describes the relationship between these three quantities for a metallic conductor at constant temperature. It states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.
欧姆定律描述了在恒温条件下，金属导体中这三个量之间的关系：通过导体的电流与导体两端的电压成正比，与导体的电阻成反比。
V = I × R or I = V / R or R = V / I
If you know any two of these values, you can always find the third. For example, a 12 V supply connected to a 4 Ω resistor pushes a current of 3
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