📚 Year 7 CCEA Engineering: Formula & Theorem Quick Reference Handbook | 七年级CCEA工程：公式定理速查手册
This quick reference handbook covers the most essential formulas and theorems you’ll encounter in Year 7 CCEA Engineering. Understanding these principles will help you solve problems logically and build a strong foundation for future studies.
这本速查手册涵盖了七年级CCEA工程中最重要的公式和定理。理解这些原理将帮助你逻辑性地解决实际问题，为未来的学习打下坚实基础。
1. SI Units and Prefixes | 国际单位制与词头
In engineering, we use a standard system of measurement called the International System of Units (SI). The base units include metre (m) for length, kilogram (kg) for mass, second (s) for time, and ampere (A) for electric current. Prefixes like kilo- (k, ×1000), centi- (c, ×0.01), and milli- (m, ×0.001) allow us to express very large or very small measurements conveniently.
在工程中，我们使用国际单位制（SI）。基本单位包括：米（m）表示长度，千克（kg）表示质量，秒（s）表示时间，安培（A）表示电流。词头如千（k，×1000）、厘（c，×0.01）和毫（m，×0.001）可以方便地表达极大或极小的量。
- Length: metre (m) – 长度：米 (m)
- Mass: kilogram (kg) – 质量：千克 (kg)
- Time: second (s) – 时间：秒 (s)
- Electric current: ampere (A) – 电流：安培 (A)
- Temperature: kelvin (K) – 温度：开尔文 (K)
- Prefixes: kilo (k) = ×10³, centi (c) = ×10⁻², milli (m) = ×10⁻³ – 词头：千 (k)=×10³，厘 (c)=×10⁻²，毫 (m)=×10⁻³
2. Force = Mass × Acceleration (Newton’s Second Law) | 力 = 质量 × 加速度（牛顿第二定律）
Force is a push or pull that can change an object’s motion. Newton’s Second Law states that the force applied to an object equals its mass multiplied by its acceleration.
力是能够改变物体运动状态的推或拉。牛顿第二定律指出：作用在物体上的力等于其质量乘以加速度。
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). If the same force is applied to a lighter object, it accelerates more. If you push a toy car with a certain force and a real car with the same force, the toy car moves much faster because it has less mass.
其中 F 是力（牛顿，N），m 是质量（千克，kg），a 是加速度（米每二次方秒，m/s²）。如果对较轻的物体施加相同的力，其加速度会更大。用同样的力推玩具车和真车，玩具车因为质量小会加速得更快。
3. Pressure = Force ÷ Area | 压强 = 力 ÷ 面积
Pressure measures how concentrated a force is over a surface. A force spread over a large area produces low pressure, while the same force on a small area creates high pressure.
压强衡量力在表面上的集中程度。同样的力分布在较大面积上产生低压强，而集中在较小面积上则产生高压强。
P = F ÷ A
where P is pressure in pascals (Pa, which is N/m²), F is force in newtons (N), and A is area in square metres (m²). This explains why a sharp knife cuts easily—the small area of the blade edge gives high pressure. A snowshoe prevents sinking by increasing the area and reducing pressure.
其中 P 是压强（帕斯卡，Pa，即 N/m²），F 是力（牛顿，N），A 是面积（平方米，m²）。这解释了为什么锋利的刀容易切割——刀刃接触面积小，压强高。雪鞋通过增大受力面积降低压强，防止陷入雪中。
4. Work Done = Force × Distance | 做功 = 力 × 距离
In engineering, ‘work’ is done when a force moves an object over a distance. If there is no movement, no work is done no matter how much force is applied.
在工程中，“做功”是指力使物体移动一段距离。如果没有移动，无论施加多大的力，都没有做功。
W = F × d
where W is work done in joules (J), F is force in newtons (N), and d is distance moved in the direction of the force in metres (m). Lifting a book from the floor to a shelf does work against gravity; holding the book stationary does not, because distance is zero.
其中 W 是做功（焦耳，J），F 是力（牛顿，N），d 是沿力的方向移动的距离（米，m）。把书从地板抬起放到书架上是对抗重力做功；而只是拿着书本不动则没有做功，因为距离为零。
5. Power = Work Done ÷ Time | 功率 = 做功 ÷ 时间
Power tells us how quickly work is done or energy is transferred. A more powerful engine can do the same amount of work in less time.
功率表示做功或能量转化的快慢。更强大的发动机能在更短时间内完成同样的功。
P = W ÷ t
where P is power in watts (W, which is J/s), W is work done in joules (J), and t is time in seconds (s). If a crane lifts a load doing 2000 J of work in 5 seconds, its power output is 400 W. The same crane taking 10 seconds would only have 200 W.
其中 P 是功率（瓦特，W，即 J/s），W 是做功（焦耳，J），t 是时间（秒，s）。如果一台起重机在 5 秒内做了 2000 J 的功，其功率为 400 W；若用 10 秒完成同样功，功率仅为 200 W。
6. Ohm’s Law: Voltage = Current × Resistance | 欧姆定律：电压 = 电流 × 电阻
In an electrical circuit, the voltage (potential difference) drives the current, and resistance opposes it. Ohm’s Law relates these three quantities.
在电路中，电压（电势差）驱动电流，电阻阻碍电流。欧姆定律表达了这三者之间的关系。
V = I × R
where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). If the resistance stays constant, doubling the voltage will double the current. If the voltage is fixed, a higher resistance results in a lower current.
其中 V 是电压（伏特，V），I 是电流（安培，A），R 是电阻（欧姆，Ω）。如果电阻保持不变，电压加倍则电流加倍；如果电压固定，电阻越大电流越小。
7. Principle of Moments | 力矩原理
A moment is the turning effect of a force about a pivot. The Principle of Moments states that for a system in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
力矩是力绕支点产生的转动效果。力矩原理指出：处于平衡状态的系统，顺时针力矩之和等于逆时针力矩之和。
Moment = Force × perpendicular distance from pivot
Σ clockwise moments = Σ anticlockwise moments
Moment is measured in newton metres (Nm). A small force far from the pivot can balance a larger force near the pivot. For example, a see-saw balances when the product of weight and distance from the centre is equal on both sides.
力矩的单位是牛顿·米 (Nm)。离支点较远的小力可以平衡离支点较近的大力。例如，跷跷板平衡的条件是两侧的重量乘以到中心距离相等。
8. Density = Mass ÷ Volume | 密度 = 质量 ÷ 体积
Density describes how much mass is packed into a given volume. Materials with high density feel heavy for their size, like iron; low density materials are light, like polystyrene.
密度描述单位体积内所含物质质量的多少。密度高的材料（如铁）同体积下较重；密度低的材料（如聚苯乙烯泡沫）较轻。
ρ = m ÷ V
where ρ (Greek letter rho) is density in kg/m³, m is mass in kg, and V is volume in m³. Water has a density of about 1000 kg/m³. An object floats if its density is less than the fluid it is placed in.
其中 ρ（希腊字母 rho）是密度（千克每立方米，kg/m³），m 是质量（千克，kg），V 是体积（立方米，m³）。水的密度约为 1000 kg/m³。物体的密度小于液体时，它就会漂浮。
9. Efficiency = (Useful Output ÷ Total Input) × 100% | 效率 = （有用输出 ÷ 总输入）× 100%
No machine can convert all input energy into useful work; some is always lost, often as heat. Efficiency tells us how good a system is at converting input into useful output.
没有机器能将输入的能量完全转化为有用功；总会有一部分损失，通常以热量形式散失。效率告诉我们系统将输入转化为有用输出的能力好坏。
η = (Useful energy output ÷ Total energy input) × 100%
where η is efficiency (%). For example, a light bulb that produces 15 J of light from 100 J of electrical energy has an efficiency of 15%. The remaining 85 J becomes heat. High efficiency means less waste.
其中 η 是效率（%）。例如，一个灯泡消耗 100 J 电能产生 15 J 光能，其效率为 15%，其余 85 J 转化为热量。高效率意味着更少的浪费。
10. Simple Machines: Mechanical Advantage & Velocity Ratio | 简单机械：机械利益与速比
Simple machines like levers, pulleys, and gears help us do work by multiplying force or changing its direction. Two key concepts are mechanical advantage (MA) and velocity ratio (VR).
杠杆、滑轮、齿轮等简单机械通过放大力量或改变方向帮助我们做功。两个关键概念是机械利益（MA）和速比（VR）。
MA = Load (output force) ÷ Effort (input force)
VR = Distance moved by effort ÷ Distance moved by load
Mechanical advantage tells us how many times the machine multiplies the input force. Velocity ratio depends on the geometry of the machine and ignores friction. Efficiency can also be calculated as MA ÷ VR × 100%. For example, a lever with MA = 4 lifts a 400 N load with only 100 N of effort.
机械利益表示机器将输入力放大了多少倍。速比取决于机器的几何结构，且忽略摩擦。效率也可以通过 MA ÷ VR × 100% 计算。例如，一个机械利益为 4 的杠杆，仅用 100 N 的力就能抬起 400 N 的载荷。
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