📚 Engineering Formulas and Theorems Quick Reference Handbook | 工程公式定理速查手册
This handy reference guide brings together the core formulas and principles that Year 7 CAIE Engineering students will encounter. Keep it nearby when solving problems on motion, forces, energy, electricity and simple machines. Each section presents the key equation in a clear format, followed by an explanation of its meaning and units.
这本便捷的速查手册汇集了 Year 7 CAIE 工程课程中会遇到的核心公式与定理。在解决有关运动、力、能量、电学以及简单机械的问题时，你可随时查阅。每个小节都给出了关键的方程式，并附有含义和单位的解释。
1. Speed, Distance and Time | 速度、距离和时间
Speed tells us how quickly an object moves from one place to another. It does not consider direction, so it is a scalar quantity. To find the average speed of any journey, we divide the total distance covered by the total time taken.
速度告诉我们物体从一处移动到另一处的快慢程度。它不考虑方向，因此是一个标量。要计算任何行程的平均速度，我们用总距离除以总时间。
v = d ÷ t
Here, v represents speed, d stands for distance, and t is time. In SI units, speed is measured in metres per second (m/s). There is also a common practical unit: kilometres per hour (km/h). You can convert between them by remembering that 1 m/s equals 3.6 km/h, or to go from km/h to m/s, divide by 3.6.
这里 v 代表速度，d 代表距离，t 代表时间。在国际单位制中，速度的单位是米每秒（m/s）。此外还有一种常用单位：千米每小时（km/h）。两者转换可记住：1 m/s = 3.6 km/h，或者说从 km/h 换算到 m/s 需除以 3.6。
For example, if a cyclist travels 450 metres in 30 seconds, the average speed is v = 450 ÷ 30 = 15 m/s. Engineers use this relationship when designing timing systems for traffic lights or estimating journey times.
例如，一名自行车手在 30 秒内行驶了 450 米，其平均速度为 v = 450 ÷ 30 = 15 m/s。工程师在设计交通灯计时系统或估算通行时间时就会用到这个关系。
2. Acceleration | 加速度
Acceleration measures how quickly the velocity of an object changes. Because velocity has both magnitude and direction, acceleration can involve speeding up, slowing down, or changing direction. For a straight line motion, we often calculate uniform acceleration using the change in speed over time.
加速度衡量物体速度变化的快慢。由于速度既有大小又有方向，加速度可以表现为加速、减速或改变方向。对于直线运动，我们通常用速度的变化量除以时间来计算匀加速度。
a = (v − u) ÷ t
In this formula, a is acceleration, v is the final velocity, u is the initial velocity, and t is the time taken. The unit of acceleration is metres per second squared (m/s²). If the final speed is lower than the initial speed, the acceleration value is negative, which indicates deceleration.
在这个公式中，a 是加速度，v 是末速度，u 是初速度，t 是所用时间。加速度的单位是米每二次方秒（m/s²）。如果末速度小于初速度，加速度的值就是负的，这表示减速。
Suppose a model car increases its velocity from 2 m/s to 8 m/s in 3 seconds. The acceleration would be a = (8 − 2) ÷ 3 = 2 m/s². Understanding acceleration helps engineers to design safer braking systems and smoother elevators.
假设一辆模型车的速度在 3 秒内从 2 m/s 增加到 8 m/s，那么它的加速度为 a = (8 − 2) ÷ 3 = 2 m/s²。理解加速度有助于工程师设计更安全的制动系统和更平稳的电梯。
3. Newton’s Second Law of Motion | 牛顿第二运动定律
Newton’s Second Law describes the link between the force applied to an object, its mass, and the resulting acceleration. The greater the mass of an object, the more force is needed to produce the same acceleration. This is one of the most fundamental principles in engineering mechanics.
牛顿第二定律描述了施加在物体上的力、物体的质量以及产生的加速度之间的关系。物体质量越大，要产生同样的加速度就需要越大的力。这是工程力学中最基本的原理之一。
F = m × a
Here F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in m/s². One newton is the force required to accelerate a 1 kg mass by 1 metre per second squared.
这里 F 是合力，单位是牛顿（N）；m 是质量，单位是千克（kg）；a 是加速度，单位是 m/s²。1 牛顿就是使 1 千克物体产生 1 m/s² 加速度所需的力。
If a 10 kg box is pushed with a resultant force of 50 N, its acceleration is a = F ÷ m = 50 ÷ 10 = 5 m/s². This law is used in everything from designing rocket engines to calculating the force needed to push a heavy trolley.
如果一个质量为 10 kg 的箱子受到 50 N 的合力推动，其加速度为 a = F ÷ m = 50 ÷ 10 = 5 m/s²。这一定律被广泛应用于从设计火箭发动机到计算推动重载推车所需作用力的各个领域。
4. Weight and Gravitational Force | 重量与重力
Weight is the name we give to the gravitational pull that a planet exerts on an object. Unlike mass, which is the same everywhere, weight depends on the strength of gravity. Near the Earth’s surface, the gravitational field strength is approximately 9.8 N/kg, meaning each kilogram of mass experiences a downward force of about 9.8 N.
重量是指行星对物体施加的引力。与到处都是相同的质量不同，重量取决于重力场的强弱。在地球表面附近，引力场强度约为 9.8 N/kg，这意味着每千克质量会受到大约 9.8 N 的向下作用力。
W = m × g
W is the weight in newtons (N), m is the mass in kilograms (kg), and g is the gravitational field strength in N/kg. For most calculations at this level, you may use g = 9.8 N/kg or the approximation 10 N/kg.
W 表示重量，单位牛顿（N）；m 表示质量，单位千克（kg）；g 表示引力场强度，单位 N/kg。在本阶段的大多数计算中，可使用 g = 9.8 N/kg 或近似值 10 N/kg。
A person with a mass of 50 kg has a weight W = 50 × 9.8 = 490 N on Earth. On the Moon, where g = 1.6 N/kg, the same person would weigh only 80 N. Structural engineers must consider the weight of materials when designing buildings and bridges.
一名质量为 50 kg 的人在地球上的重量为 W = 50 × 9.8 = 490 N。在月球上，g = 1.6 N/kg，同一个人仅重 80 N。结构工程师在设计建筑和桥梁时必须考虑材料的重量。
5. Work Done | 做功
In engineering, work is done whenever a force moves an object through a distance. If the force is applied but the object does not move, no work is done in the scientific sense. The amount of work depends on both the size of the force and the distance the object moves in the direction of the force.
在工程中，只要力使物体沿力的方向移动一段距离，就做了功。若施加了力而物体并未移动，从科学意义上讲就没有做功。功的大小取决于力的大小以及物体沿力的方向移动的距离。
W = F × d
Here W is the work done in joules (J), F is the force in newtons (N), and d is the distance moved in metres (m). One joule is the work done when a force of one newton moves an object one metre.
这里 W 表示做功，单位焦耳（J）；F 表示力，单位牛顿（N）；d 表示移动的距离，单位米（m）。1 焦耳就是 1 牛顿的力使物体移动 1 米所做的功。
Lifting a 20 N box onto a shelf 1.5 m high requires work W = 20 × 1.5 = 30 J. Understanding work helps engineers to calculate the energy needed by machines and motors.
将一个 20 N 的箱子提到 1.5 m 高的架子上，需要做功 W = 20 × 1.5 = 30 J。理解功有助于工程师计算机器和马达所需的能量。
6. Power | 功率
Power measures how quickly work is done or how fast energy is transferred. A powerful engine can do the same amount of work in a shorter time. Power is a crucial concept when comparing machines and motors.
功率衡量做功的快慢或能量传递的速率。一台大功率的发动机能在更短的时间内完成同样的功。在比较不同机器和马达时，功率是一个至关重要的概念。
P = W ÷ t
P stands for power in watts (W), W is the work done in joules (J), and t is the time taken in seconds (s). One watt equals one joule per second. Often power is also given in kilowatts (1 kW = 1000 W).
P 表示功率，单位瓦特（W）；W 表示做功，单位焦耳（J）；t 表示时间，单位秒（s）。1 瓦特等于每秒 1 焦耳。功率也常用千瓦表示（1 kW = 1000 W）。
If a crane lifts a block and does 6000 J of work in 30 seconds, its useful power output is P = 6000 ÷ 30 = 200 W. Engineers specify motor power ratings to ensure they can lift, push, or pull loads efficiently.
如果一台起重机吊起一块重物并在 30 秒内做了 6000 J 的功，那么它的有用输出功率为 P = 6000 ÷ 30 = 200 W。工程师会明确规定马达的额定功率，以确保能够高效地提升、推动或牵引载荷。
7. Levers and Moments | 杠杆与力矩
A moment is the turning effect produced by a force acting around a pivot. The size of the moment depends on both the magnitude of the force and the perpendicular distance from the pivot to the line of action of the force. Levers use this principle to make it easier to lift heavy loads.
力矩是由一个力绕支点产生的转动效应。力矩的大小既取决于力的大小，也取决于从支点到力作用线的垂直距离。杠杆利用这个原理使得举起重物变得更加轻松。
M = F × d
M is the moment measured in newton-metres (Nm), F is the force in newtons (N), and d is the perpendicular distance from the pivot in metres (m). When a lever is balanced, the sum of clockwise moments equals the sum of anticlockwise moments.
M 表示力矩，单位牛顿·米（Nm）；F 表示力，单位牛顿（N）；d 表示从支点起算的垂直距离，单位米（m）。当杠杆平衡时，顺时针力矩之和等于逆时针力矩之和。
For instance, if you push a spanner with a force of 30 N at a distance of 0.2 m from the nut, the turning moment is M = 30 × 0.2 = 6 Nm. This principle explains why a longer spanner makes it easier to undo a tight bolt.
例如，如果用 30 N 的力在距离螺母 0.2 m 处推动扳手，产生的转动力矩为 M = 30 × 0.2 = 6 Nm。这个原理也解释了为什么更长的扳手更容易拧松紧固的螺栓。
8. Pressure | 压强
Pressure describes how concentrated a force is over a given area. A large force applied over a small area produces high pressure, whereas the same force spread over a larger area produces lower pressure. This concept is vital in designing foundations, tyres, and hydraulic systems.
压强描述的是力在给定面积上的集中程度。一个较大的力作用在较小的面积上会产生较高的压强，而同样的力分散在较大的面积上则压强较低。这一概念在设计地基、轮胎和液压系统时至关重要。
P = F ÷ A
P is the pressure in pascals (Pa), where 1 Pa = 1 N/m²; F is the force in newtons (N); and A is the area in square metres (m²). A thin knife cuts easily because the force is concentrated on a very small edge area, producing a very high pressure.
P 表示压强，单位帕斯卡（Pa），1 Pa = 1 N/m²；F 表示力，单位牛顿（N）；A 表示面积，单位平方米（m²）。一把薄刀之所以能轻松切割，是因为力集中在极小的刀刃面积上，产生了很高的压强。
If a person weighing 600 N stands on a board with an area of 0.3 m², the pressure under the board is P = 600 ÷ 0.3 = 2000 Pa. Engineers use this formula to ensure that the ground can support the pressure from a building’s foundations without sinking.
如果一个重 600 N 的人站在一块面积为 0.3 m² 的木板上，板下的压强为 P = 600 ÷ 0.3 = 2000 Pa。工程师利用这一公式确保地基承受的压强不会导致建筑物下陷。
9. Electric Current, Voltage and Resistance | 电流、电压和电阻
Electric current is the flow of electric charge through a conductor. Voltage is the energy provided to each unit of charge, pushing the current around the circuit. Resistance is a measure of how much a component opposes the flow of current. These three quantities are linked in every circuit.
电流是电荷在导体中的流动。电压是提供给每单位电荷的能量，推动电流在电路中流动。电阻则是衡量元件对电流阻碍作用大小的物理量。这三个物理量在任何电路中都是相互关联的。
Current (I) is measured in amperes (A), voltage (V) in volts (V), and resistance (R) in ohms (Ω). A battery provides a voltage; a light bulb or a resistor offers resistance. The current that flows depends on the voltage supplied and the total resistance in the circuit.
电流（I）的单位是安培（A），电压（V）的单位是伏特（V），电阻（R）的单位是欧姆（Ω）。电池提供电压；灯泡或电阻器提供电阻。电路中流动的电流取决于所施加的电压和总电阻的大小。
10. Ohm’s Law | 欧姆定律
Ohm’s Law states that the current flowing through a conductor at constant temperature is directly proportional to the voltage across it and inversely proportional to its resistance. This simple rule allows engineers to predict how an electrical circuit will behave.
欧姆定律指出，在温度不变的条件下，流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。这条简单的规律使工程师能够预测电路的工作状态。
V = I × R
V is the potential difference in volts (V), I is the current in amperes (A), and R is the resistance in ohms (Ω). Rearranging gives I = V ÷ R and R = V ÷ I. This formula is fundamental when choosing resistors to protect LEDs or when calculating wire thickness.
V 表示电压，单位伏特（V）；I 表示电流，单位安培（A）；R 表示电阻，单位欧姆（Ω）。变形后可得到 I = V ÷ R 和 R = V ÷ I。在选用保护 LED 的电阻
Published by TutorHao | Year 7 工程 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导