KS3 Cambridge Engineering: Quick Reference Formula & Theorem Handbook | KS3 剑桥工程：公式定理速查手册

📚 KS3 Cambridge Engineering: Quick Reference Formula & Theorem Handbook | KS3 剑桥工程：公式定理速查手册

Engineering at the Key Stage 3 level introduces you to the fundamental principles that govern the designed world. This handbook brings together the essential formulas, theorems and constant values you will need, from forces and energy to electricity and structures. Used as a quick revision aid, it helps you solve problems with confidence and build a solid foundation for IGCSE and beyond.

KS3 阶段的工程学为你打开了理解人造世界基本原理的大门。这份速查手册汇集了从力与能量、电学到结构力学所必需的核心公式、定理和常数。它可以作为快速复习工具，帮助你自信地解决问题，并为 IGCSE 及更高阶段的学习打下坚实基础。

1. Force and Motion | 力与运动

The relationship between an object’s mass, its acceleration and the net force acting on it is given by Newton’s Second Law. It is the most important equation in dynamics.

物体的质量、加速度与作用在其上的净力之间的关系由牛顿第二定律给出，这是动力学中最重要的方程。

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).

其中 F 表示力，单位牛顿 (N)；m 表示质量，单位千克 (kg)；a 表示加速度，单位米每二次方秒 (m/s²)。

Weight is a specific type of force caused by gravity. On Earth, it can be calculated directly from mass.

重量是由重力引起的一种特定的力。在地球上，可以直接通过质量来计算。

W = m × g

The gravitational field strength g on Earth is approximately 9.8 N/kg (often rounded to 10 N/kg in KS3 problems).

地球上的引力场强度 g 约为 9.8 N/kg（KS3 习题中常取 10 N/kg 的近似值）。

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2. Speed, Distance and Time | 速度、距离与时间

For objects moving at a constant speed, the relationship between distance travelled, time taken and speed is linear and straightforward.

对于匀速运动的物体，行进的距离、所用的时间与速度之间呈简单的线性关系。

v = d / t

Here v is speed (m/s), d is distance (m), and t is time (s). This can be rearranged to d = v × t or t = d / v.

式中 v 为速度 (m/s)，d 为距离 (m)，t 为时间 (s)。公式可变形为 d = v × t 或 t = d / v。

Average speed is used when movement is not constant. The total distance divided by the total time gives the average speed.

当运动不均匀时使用平均速度。总距离除以总时间即可得出平均速度。

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3. Energy and Power | 能量与功率

Energy is the capacity to do work. In mechanical systems, work done is equal to the force applied multiplied by the distance moved in the direction of the force.

能量是做功的本领。在机械系统中，做的功等于施加的力乘以物体在力的方向上移动的距离。

W = F × d

Work W is measured in joules (J), force F in newtons (N), and distance d in metres (m).

功 W 的单位是焦耳 (J)，力 F 的单位是牛顿 (N)，距离 d 的单位是米 (m)。

Power is the rate at which work is done or energy is transferred. It tells you how quickly energy is being used.

功率是做功或能量转移的速率，它告诉你能量被使用的快慢。

P = W / t

or equivalently P = E / t, where P is power in watts (W), W (or E) is work or energy in joules (J), and t is time in seconds (s).

或等效为 P = E / t，其中 P 为功率，单位瓦特 (W)；W（或 E）为功或能量，单位焦耳 (J)；t 为时间，单位秒 (s)。

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4. Kinetic and Potential Energy | 动能与势能

A moving object possesses kinetic energy. The amount depends on its mass and the square of its speed.

运动的物体具有动能。动能的大小取决于物体的质量和速度的平方。

KE = ½ × m × v²

KE is kinetic energy in joules (J), m is mass in kilograms (kg), and v is speed in metres per second (m/s).

KE 为动能，单位焦耳 (J)；m 为质量，单位千克 (kg)；v 为速度，单位米每秒 (m/s)。

An object raised against gravity stores gravitational potential energy. This energy can be released as the object falls.

被举高反抗重力的物体储存着重力势能。当物体下落时，这部分能量可以被释放出来。

GPE = m × g × h

h is the height in metres (m) above a reference level. The gravitational field strength g is 9.8 N/kg (or 10 N/kg).

h 为相对某一参考平面的高度，单位米 (m)；引力场强度 g 取 9.8 N/kg（或 10 N/kg）。

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5. Ohm’s Law and Electrical Quantities | 欧姆定律与电学量

In many conductors, the current flowing through a component is directly proportional to the potential difference (voltage) across it, provided the temperature remains constant.

在许多导体中，只要温度保持恒定，流过元件的电流与其两端的电势差（电压）成正比。

V = I × R

V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).

V 为电压，单位伏特 (V)；I 为电流，单位安培 (A)；R 为电阻，单位欧姆 (Ω)。

An alternative way to calculate electrical power uses voltage and current. This is particularly useful for choosing correct fuses and cables.

另一种计算电功率的方法使用电压和电流，这在选择正确的保险丝和电缆时特别有用。

P = V × I

Combined with Ohm’s law, this gives two further forms: P = I² × R and P = V² / R.

结合欧姆定律，还可推导出另外两种形式：P = I² × R 和 P = V² / R。

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6. Density and Material Properties | 密度与材料特性

Density is a measure of how much mass is packed into a given volume. It helps engineers decide which material to use for a specific application.

密度衡量的是在一定体积内所包含的质量，它帮助工程师为特定用途选择合适的材料。

ρ = m / V

ρ (rho) is density in kilograms per cubic metre (kg/m³), m is mass (kg), and V is volume (m³).

ρ 为密度，单位千克每立方米 (kg/m³)；m 为质量 (kg)；V 为体积 (m³)。

The stiffness of a material is described by the Young’s modulus, but at KS3 level you mainly need to know the relationship between stress and strain qualitatively, along with Hooke’s Law for springs.

材料的刚度由杨氏模量描述，但在 KS3 阶段你主要需要定性地了解应力与应变的关系，以及弹簧的胡克定律。

F = k × e

or F = k × x, where F is force applied (N), k is spring constant (N/m), and e or x is extension (m).

或 F = k × x，其中 F 为施加的力 (N)，k 为弹簧常数 (N/m)，e 或 x 为伸长量 (m)。

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7. Pressure in Solids and Fluids | 固体与流体中的压强

Pressure is defined as the force acting perpendicularly per unit area. It explains why sharp objects cut easily and why wide tyres do not sink into mud.

压强定义为垂直作用在单位面积上的力。它能解释为什么尖锐的物体容易切入，而宽轮胎不会陷入泥地。

p = F / A

p is pressure in pascals (Pa), where 1 Pa = 1 N/m². F is force in newtons (N) and A is area in square metres (m²).

p 为压强，单位帕斯卡 (Pa)，1 Pa = 1 N/m²；F 为力 (N)；A 为面积 (m²)。

For a liquid at rest, pressure increases with depth and depends on the density of the liquid. This is crucial when designing dams and submarines.

对于静止的液体，压强随深度增加，且与液体密度有关。在设计水坝和潜水器时这至关重要。

p = ρ × g × h

Here ρ is the liquid’s density (kg/m³), g is gravitational field strength (N/kg), and h is depth (m).

式中 ρ 为液体密度 (kg/m³)，g 为引力场强度 (N/kg)，h 为深度 (m)。

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8. Levers, Moments and Equilibrium | 杠杆、力矩与平衡

A moment is the turning effect of a force about a pivot. It is the product of the force and the perpendicular distance from the pivot to the line of action of the force.

力矩是力对支点的转动效应，等于力的大小与支点到力作用线的垂直距离的乘积。

M = F × d

M is the moment in newton metres (N m), F is the force (N), and d is the perpendicular distance (m).

M 为力矩，单位牛顿·米 (N·m)；F 为力 (N)；d 为垂直距离 (m)。

For an object to be in equilibrium, two conditions must be met: the sum of all forces must be zero, and the sum of all clockwise moments must equal the sum of all anticlockwise moments about the same pivot.

要使物体处于平衡状态，必须满足两个条件：所有力的合力为零，且对同一支点的顺时针力矩总和等于逆时针力矩总和。

Σ F = 0

Σ M˳ = Σ M˳

The principle of moments is used extensively in designing bridges, cranes and simple tools such as wheelbarrows.

力矩原理被广泛应用于桥梁、起重机以及手推车等简单工具的设计中。

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9. Efficiency | 效率

No machine is perfect; some input energy is always converted into forms that are not useful, mostly heat due to friction. Efficiency tells us how good a machine is at converting input energy into useful output energy.

没有完美的机器，总有一些输入的能量转化为无用的形式，主要是由于摩擦产生的热量。效率告诉我们一台机器将输入能量转化为有用输出能量的能力有多好。

Efficiency = (Useful output energy / Total input energy) × 100%

or equivalently, Efficiency = (Useful power output / Total power input) × 100%.

或等效为 效率 = （有用输出功率 / 总输入功率）× 100%。

Efficiency can never be greater than 100% because of the conservation of energy. At KS3, you will often be asked to calculate efficiency from Sankey diagrams or simple data.

根据能量守恒定律，效率不可能大于 100%。在 KS3 中，你经常会遇到根据桑基图或简单数据计算效率的问题。

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10. Key Constants and Unit Conversions | 关键常数与单位换算

Engineering calculations require consistent units. The following reference table contains the most useful constants and conversion factors you will need for KS3 problems.

工程计算需要一致的单位。下面的参考表包含了 KS3 习题中最常用的常数和换算因子。

Acceleration of free fall, g	9.8 m/s² (or 10 m/s²)
Speed of sound in air	343 m/s (approx)
1 kilometre (km)	1000 metres (m)
1 hour (h)	3600 seconds (s)
1 tonne	1000 kilograms (kg)
1 litre (L)	0.001 m³ (or 1000 cm³)
1 atmosphere (atm)	101325 Pa (approx 100 kPa)

When speed is given in km/h, always convert to m/s (divide by 3.6) before using it in the v = d/t formula alongside other SI units. Similarly, convert grams to kilograms and square centimetres to square metres for pressure calculations.

当速度以 km/h 为单位给出时，在代入 v = d/t 公式前一定要先换算成 m/s（除以 3.6），以便与其他国际单位保持一致。类似地，计算压强时需将克换算为千克、平方厘米换算为平方米。

Published by TutorHao | Engineering Revision Series | aleveler.com

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