📚 Year 7 CIE Engineering: Formula & Theorem Quick Reference Guide | Year 7 CIE 工程：公式定理速查手册
Welcome to the Year 7 CIE Engineering formula and theorem quick reference guide. This handbook collects the essential equations you will encounter in the early stages of engineering study, covering mechanics, electricity, materials and simple machines. Use it to revise key principles, check calculations and strengthen your understanding of how forces, energy and power are quantified. Keep this guide handy as you work through practical projects and theory lessons.
欢迎使用 Year 7 CIE 工程公式定理速查手册。本手册汇集了工程学习初期你将遇到的基本方程，涵盖力学、电学、材料与简单机械。用它来复习核心原理、检查计算，并加深你对力、能量和功率如何量化的理解。在动手实践和理论学习时，请随时查阅。
1. Newton's Second Law of Motion | 牛顿第二运动定律
The net force acting on an object equals the product of its mass and acceleration. This law explains how motion changes when forces are unbalanced. The relationship is given by the formula F = m × a, where F is force in newtons (N), m is mass in kilograms (kg) and a is acceleration in metres per second squared (m/s²).
作用于物体上的合外力等于其质量与加速度的乘积。该定律解释了当力不平衡时运动如何改变。关系由公式 F = m × a 给出，其中 F 是以牛顿 (N) 为单位的力，m 是以千克 (kg) 为单位的质量，a 是以米每二次方秒 (m/s²) 为单位的加速度。
If several forces act together, find the resultant force first before applying the formula.
如果有多个力共同作用，先求出合力再应用公式。
2. Weight and Mass | 重量和质量
Weight is the gravitational force on a mass. Near the Earth's surface the gravitational field strength g is approximately 10 N/kg (or 9.8 N/kg). Weight is calculated by W = m × g. Mass is measured in kilograms (kg) and weight in newtons (N).
重量是作用在质量上的重力。接近地表处重力场强度 g 约为 10 N/kg（或 9.8 N/kg）。重量由 W = m × g 计算。质量以千克 (kg) 为单位，重量以牛顿 (N) 为单位。
Note that mass is a scalar quantity and does not change with location, whereas weight is a vector and depends on the gravitational field. On the Moon, g is about 1.6 N/kg, so your weight would be much less.
注意，质量是标量，不随位置改变，而重量是矢量，取决于重力场。在月球上，g 约为 1.6 N/kg，因此你的重量会小得多。
3. Speed, Distance and Time | 速度、距离和时间
Average speed is defined as the total distance travelled divided by the time taken. The formula is v = s / t, where v is speed in metres per second (m/s), s is distance in metres (m) and t is time in seconds (s). This is a scalar quantity. When direction is included it becomes velocity.
平均速度定义为行驶的总距离除以所用时间。公式为 v = s / t，其中 v 是以米每秒 (m/s) 为单位的速度，s 是以米 (m) 为单位的距离，t 是以秒 (s) 为单位的时间。这是一个标量。当包含方向时，它就成为速度 (velocity)。
You can rearrange to find distance (s = v × t) or time (t = s / v) when the other two values are known.
当已知其他两个量时，你可以变换公式求出距离 (s = v × t) 或时间 (t = s / v)。
4. Work Done | 做功
n the direction of the force. Work = force × distance moved in the direction of the force: W = F × d. Work is measured in joules (J), where 1 J = 1 N·m.
当力使物体沿力的方向移动时，力就做了功。功 = 力 × 沿力方向移动的距离：W = F × d。功以焦耳 (J) 为单位，1 J = 1 N·m。
No work is done if there is no movement, or if the force is perpendicular to the displacement. Lifting a box vertically does work, but carrying it horizontally at constant height does not.
如果没有移动，或者力与位移垂直，则没有做功。垂直提起箱子做功，但水平搬运箱子且高度不变则不做功。
5. Power | 功率
Power is the rate at which work is done or energy is transferred. The formula is P = W / t W), W is work in joules (J) and t is time in seconds (s). One watt equals one joule per second.
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 是以瓦特 (W) 为单位的功率，W 是以焦耳 (J) 为单位的功，t 是以秒 (s) 为单位的时间。一瓦特等于一焦耳每秒。
In mechanical systems, power can also be expressed as P = F × v for a constant force moving at constant speed v. This is useful for engines and motors.
在机械系统中，对于以恒定速度 v 运动且受力恒定的情况，功率也可表示为 P = F × v。这对引擎和电动机很有用。
6. Moments and Levers | 力矩与杠杆
s a measure of its turning effect. Moment = force × perpendicular distance from the pivot: M = F × d. The unit is newton metre (N·m).
力对支点的力矩是衡量其转动效果的物理量。力矩 = 力 × 到支点的垂直距离：M = F × d。单位是牛顿米 (N·m)。
For a lever in equilibrium, the principle of moments states that the sum of clockwise moments equals the sum of anticlockwise moments. This helps calculate unknown forces or distances.
对于处于平衡的杠杆，力矩原理指出顺时针力矩之和等于逆时针力矩之和。这有助于计算未知的力或距离。
7. Mechanical Advantage | 机械利益
Mechanical advantage (MA) tells us how much a machine multiplies the effort force. It is the ratio of the load (output force) to the effort (input force): MA = Load / Effort. It has no units.
机械利益 (MA) 告诉我们机械将输入力放大了多少。它是负载（输出力）与动力（输入力）之比：MA = 负载 / 动力。无单位。
ort / distance moved by load. In real machines, MA is slightly smaller than VR due to friction.
对于无摩擦的理想机械，MA 等于速度比 (VR)。速度比 = 动力移动距离 / 负载移动距离。在实际机械中，由于摩擦，MA 略小于 VR。
8. Pressure | 压强
Pressure is the force acting perpendicularly per unit area. p = F / A ), F is force in newtons (N) and A is area in square metres (m²). 1 Pa = 1 N/m²;.
压强是垂直作用在单位面积上的力。p = F / A，其中 p 是以帕斯卡 (Pa) 为单位的压强，F 是以牛顿为单位的力，A 是以平方米 (m²) 为单位的面积。1 Pa = 1 N/m²;。
A sharp knife exerts high pressure due to a small area, while snowshoes reduce pressure by increasing area. Understanding pressure helps in designing foundations, tyres and cutting tools.
锋利的刀由于面积小而产生高压，而雪鞋通过增大面积来减小压强。理解压强有助于设计地基、轮胎和切割工具。
9. Ohm's Law | 欧姆定律
For a conductor at constant temperature, the current through it is directly proportional to the potential difference (voltage) across it. V = I × R, where V is voltage in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
对于恒温下的导体，通过它的电流与其两端电势差（电压）成正比。V = I × R Published by TutorHao | Year 7 工程 Revision Series | aleveler.com
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