📚 Year 7 AQA Engineering: Formula & Theorem Quick Reference Handbook | Year 7 AQA 工程：公式定理速查手册
This quick reference handbook provides a clear and concise summary of the most important formulas and theorems you will encounter in Year 7 AQA Engineering. It covers key areas such as motion, forces, energy, mechanical systems, electricity, and materials. Each formula is presented with its standard units, a brief explanation, and a worked example to help you apply it with confidence. Use this guide to support your classwork, homework, and revision.
本速查手册清晰简明地总结了 Year 7 AQA 工程课程中最重要的公式与定理，涵盖运动、力、能量、机械系统、电学和材料等关键领域。每个公式都给出了标准单位、简要说明和应用示例，帮助你在课堂、作业和复习中自信运用。
1. Speed and Motion | 速度与运动
Speed is a measure of how quickly an object moves. It is a scalar quantity, meaning it has magnitude but no direction. The average speed of an object can be found if the total distance travelled and the total time taken are known.
速度是衡量物体运动快慢的物理量，为标量，只有大小没有方向。若已知总路程和总时间，即可求出平均速度。
v = s ÷ t
In this equation, v stands for speed in metres per second (m/s), s is the distance in metres (m), and t is the time in seconds (s). The formula can be rearranged to find distance or time: s = v × t and t = s ÷ v.
公式中，v 表示速度（米/秒，m/s），s 表示距离（米，m），t 表示时间（秒，s）。公式可变形为：s = v × t 和 t = s ÷ v。
For example, if a bicycle travels 150 metres in 10 seconds, its speed is 150 ÷ 10 = 15 m/s. If a runner moves at 5 m/s for 20 seconds, the distance covered is 5 × 20 = 100 m.
例如，自行车10秒行驶150米，速度为150 ÷ 10 = 15 m/s。若跑步者以5 m/s运动20秒，经过的距离为5 × 20 = 100 m。
2. Force, Mass and Acceleration | 力、质量与加速度
Newton’s Second Law of Motion explains how an object’s motion changes when a net force acts upon it. The acceleration produced is directly proportional to the net force and inversely proportional to the object’s mass.
牛顿第二定律解释了物体在净力作用下的运动变化。产生的加速度与净力成正比，与物体质量成反比。
F = m × a
Here F is the force measured in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²). One newton is the force needed to accelerate 1 kg by 1 m/s².
其中 F 为力（牛顿，N），m 为质量（千克，kg），a 为加速度（米/秒²，m/s²）。1牛顿即为使1千克物体产生1 m/s²加速度所需的力。
If a trolley of mass 4 kg is pushed and accelerates at 2.5 m/s², the force applied is 4 × 2.5 = 10 N. Conversely, if 20 N acts on an 8 kg object, its acceleration is 20 ÷ 8 = 2.5 m/s².
若质量为4 kg的手推车以2.5 m/s²加速，施加的力为4 × 2.5 = 10 N。反之，若20 N的力作用在8 kg的物体上，其加速度为20 ÷ 8 = 2.5 m/s²。
3. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object in the direction of the force. Energy is the capacity to do work, and power measures how quickly work is done or energy is transferred.
力使物体沿力的方向移动时便做了功。能量是做功的本领，功率则衡量做功或能量转移的快慢。
W = F × d
Work W is measured in joules (J), force F in newtons (N), and displacement d in metres (m). One joule is 1 N of force moving an object through 1 m.
功 W 的单位是焦耳（J），力 F 为牛顿（N），位移 d 为米（m）。1焦耳等于1牛顿的力使物体移动1米所做的功。
P = W ÷ t
Power P is in watts (W), work W in joules (J), and time t in seconds (s). One watt is 1 J of energy transferred per second. The formula can also be written as P = E ÷ t when using transferred energy.
功率 P 的单位是瓦特（W），功 W 为焦耳（J），时间 t 为秒（s）。1瓦特即每秒转移1焦耳能量。当使用转移的能量时，也可写作 P = E ÷ t。
Lifting a 50 N box through 2 m requires 100 J of work. If this work is done in 4 seconds, the power output is 100 ÷ 4 = 25 W.
将50 N的箱子提升2米需做功100 J。若这些功在4秒内完成，功率为100 ÷ 4 = 25 W。
4. Mechanical Advantage | 机械效益
Mechanical advantage (MA) tells us how many times a machine multiplies the input force. It is the ratio of the load (output force) to the effort (input force). A machine with a high MA makes it easier to move a heavy load, but usually requires moving the effort over a greater distance.
机械效益（MA）表示机器将输入力放大的倍数，是负载（输出力）与作用力（输入力）之比。机械效益高的机器能省力，但通常需要将作用力移动更大的距离。
MA = Load ÷ Effort
The load and effort are both measured in newtons (N). MA has no units because it is a ratio. If MA > 1, the machine is a force multiplier; if MA < 1, the machine increases speed or distance.
负载和作用力均以牛顿（N）为单位。MA 是比值，因此无单位。若 MA > 1，机器为力的放大器；若 MA < 1，机器则放大速度或距离。
For a pulley system lifting a 600 N load with an effort of 150 N, the MA = 600 ÷ 150 = 4. This means the effort is multiplied by four.
对于提升600 N负载仅需150 N作用力的滑轮系统，MA = 600 ÷ 150 = 4，即作用力被放大了四倍。
5. Pressure and Density | 压强与密度
Pressure describes how concentrated a force is over an area. Density measures how much mass is packed into a given volume. Both concepts are essential when designing structures and choosing materials.
压强描述力在面积上的集中程度。密度衡量单位体积内所含质量的多少。这两个概念在结构设计和选材中至关重要。
P = F ÷ A
Pressure P is in pascals (Pa), force F is in newtons (N), and area A is in square metres (m²). 1 Pa = 1 N/m².
压强 P 的单位为帕斯卡（Pa），力 F 为牛顿（N），面积 A 为平方米（m²）。1 Pa = 1 N/m²。
ρ = m ÷ V
Density ρ (rho) is in kilograms per cubic metre (kg/m³), mass m in kg, and volume V in cubic metres (m³). Water has a density of roughly 1000 kg/m³.
密度 ρ 的单位为千克/立方米（kg/m³），质量 m 为 kg，体积 V 为 m³。水的密度约为1000 kg/m³。
A block weighing 50 N resting on an area of 0.2 m² exerts a pressure of 50 ÷ 0.2 = 250 Pa. If a metal cube of mass 2.7 kg occupies a volume of 0.001 m³, its density is 2.7 ÷ 0.001 = 2700 kg/m³, typical for aluminium.
一块重50 N的物体压在0.2 m²面积上，产生的压强为50 ÷ 0.2 = 250 Pa。若一金属立方体质量2.7 kg，体积0.001 m³，其密度为2.7 ÷ 0.001 = 2700 kg/m³，这是铝的典型密度。
6. Ohm’s Law and Electrical Circuits | 欧姆定律与电路
Ohm’s Law is a fundamental principle for electric circuits, linking voltage, current, and resistance. It states that the current through a conductor is directly proportional to the voltage across it, provided the temperature remains constant.
欧姆定律是电路的基本原理，连接了电压、电流和电阻。它指出，在温度不变的情况下，通过导体的电流与其两端的电压成正比。
V = I × R
Voltage V is in volts (V), current I is in amperes (A), and resistance R is in ohms (Ω). The formula can be rearranged as I = V ÷ R and R = V ÷ I.
电压 V 的单位为伏特（V），电流 I 为安培（A），电阻 R 为欧姆（Ω）。公式可变形为 I = V ÷ R 和 R = V ÷ I。
For a lamp with a resistance of 10 Ω connected to a 5 V supply, the current is 5 ÷ 10 = 0.5 A. If a resistor in a circuit has 6 V across it and a current of 2 A, its resistance is 6 ÷ 2 = 3 Ω.
若一个电阻为10 Ω 的灯泡接在5 V电源上，电流为5 ÷ 10 = 0.5 A。若电路中某电阻两端电压为6 V，电流为2 A，则电阻为6 ÷ 2 = 3 Ω。
7. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot. It depends on the size of the force and the perpendicular distance from the pivot to the line of action of the force. Levers use moments to make work easier.
力矩是力使物体绕支点转动的效应，取决于力的大小以及支点到力作用线的垂直距离。杠杆利用力矩来省力。
M = F × d
Moment M is measured in newton metres (Nm), force F in newtons (N), and perpendicular distance d in metres (m). For a lever to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments.
力矩 M 的单位为牛顿米（Nm），力 F 为牛顿（N），垂直距离 d 为米（m）。杠杆平衡时，顺时针力矩之和必等于逆时针力矩之和。
If a spanner is used with a 15 N force applied 0.2 m from the bolt, the turning moment is 15 × 0.2 = 3 Nm. On a seesaw, a child of weight 300 N sitting 2 m from the pivot can be balanced by a 600 N adult sitting 1 m from the pivot, since 300 × 2 = 600 × 1 = 600 Nm.
若用扳手在距螺栓0.2 m处施加15 N的力，力矩为15 × 0.2 = 3 Nm。在跷跷板上，重300 N的小孩坐在距支点2 m处，可由重600 N的大人坐在距支点1 m处平衡，因为 300 × 2 = 600 × 1 = 600 Nm。
8. Efficiency | 效率
Efficiency measures how well a system converts input energy or power into useful output. No real machine is 100 % efficient because some energy is always lost, usually as heat due to friction or resistance.
效率衡量系统将输入能量或功率转化为有用输出的程度。现实中没有机器能达到100 %的效率，因为总会有一部分能量损失，通常因摩擦或电阻而转化为热量。
η = (Useful output work ÷ Total input work) × 100 %
Efficiency η (eta) is expressed as a percentage. You can also use power instead of work: η = (Useful output power ÷ Total input power) × 100 %. The result is always between 0 % and 100 %.
效率 η 以百分数表示。也可以用功率代替功：η = (有用输出功率 ÷ 总输入功率) × 100 %。计算结果总是在0 %到100 %之间。
An electric motor lifts a weight when supplied with 500 J of electrical energy and does 400 J of useful work against gravity. Its efficiency is (400 ÷ 500) × 100 % = 80 %. The remaining 20 % is lost as heat and sound.
一台电动机获得500 J电能后提升重物，做了400 J 有用功。其效率为 (400 ÷ 500) × 100 % = 80 %，剩余20 %以热量和声音形式损失。
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