📚 Year 7 SQA Engineering: Formulae & Theorems Quick Reference Guide | Year 7 SQA 工程：公式定理速查手册
Engineering is built on a foundation of key formulae and scientific principles. This quick reference guide brings together all the essential equations and theorems you will encounter in Year 7 SQA Engineering, from calculating speed and force to understanding electrical circuits and simple machines. Use this handbook to support your classwork, homework and revision, and make sure you know not just what the formulae are, but also what each symbol represents and when to apply them.
工程学建立在核心公式和科学原理之上。这份速查手册汇集了你在七年级 SQA 工程课程中将遇到的所有基本方程和定理，从计算速度和力到理解电路和简单机械。利用本手册辅助你的课堂学习、作业和复习，不仅要记住公式本身，还要清楚每个符号代表什么以及在什么情况下应用它们。
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most fundamental in engineering and physics. If you know any two of these quantities, you can find the third. The standard formula is written as:
速度、距离和时间之间的关系是工程和物理中最基本的关系之一。如果你知道其中任意两个量，就可以求出第三个。标准公式写作：
v = s ÷ t
where v stands for speed, s stands for distance and t stands for time. Speed is often measured in metres per second (m/s) or kilometres per hour (km/h). When using this formula, always make sure that the units are consistent – for example, if distance is in metres and time is in seconds, then speed will be in m/s. You can rearrange the triangle to find distance (s = v × t) or time (t = s ÷ v).
其中 v 代表速度，s 代表距离，t 代表时间。速度通常以米每秒（m/s）或千米每小时（km/h）为单位。使用这个公式时，务必确保单位一致——例如，若距离以米为单位，时间以秒为单位，那么速度的单位就是 m/s。你可以变换三角形求出距离（s = v × t）或时间（t = s ÷ v）。
2. Force, Mass and Acceleration | 力、质量与加速度
Newton’s Second Law of Motion explains how an object will accelerate when a resultant force acts on it. The formula links force, mass and acceleration, and it is crucial for analysing structures, vehicles and moving parts.
牛顿第二运动定律解释了当有合力作用在物体上时物体会如何加速。该公式联系了力、质量和加速度，对于分析结构、车辆和运动部件至关重要。
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). If more than one force acts on an object, you must first calculate the resultant force. Remember that acceleration happens in the direction of the resultant force.
这里 F 是力，单位为牛顿（N）；m 是质量，单位为千克（kg）；a 是加速度，单位为米每二次方秒（m/s²）。如果有多个力作用在物体上，必须先计算合力。请记住，加速度的方向与合力的方向一致。
3. Pressure | 压强
Pressure is a measure of how concentrated a force is over a certain area. This concept explains why a sharp knife cuts easily while a blunt one does not, and it is essential when designing foundations, hydraulic systems and pneumatic tools.
压强衡量的是力在某个面积上的集中程度。这个概念解释了为什么锋利的刀很容易切割而钝刀却不能，它在设计地基、液压系统和气动工具时至关重要。
P = F ÷ A
P represents pressure in pascals (Pa), F is the force in newtons (N) applied perpendicular to the surface, and A is the area in square metres (m²) over which the force is spread. One pascal equals one newton per square metre. A larger area produces a smaller pressure for the same force.
P 代表压强，单位为帕斯卡（Pa）；F 是垂直作用于表面的力，单位为牛顿（N）；A 是力所分布的面积，单位为平方米（m²）。一帕斯卡等于每平方米一牛顿。在力相同的情况下，面积越大，产生的压强越小。
4. Work, Energy and Power | 功、能量与功率
In engineering, understanding work, energy and power helps us describe how machines perform tasks. Work is done when a force moves an object. Energy is the capacity to do work, and power tells us how quickly that work is done.
在工程领域，理解功、能量和功率有助于我们描述机器如何执行任务。当力使物体移动时就做了功。能量是做功的能力，而功率则告诉我们做功的快慢。
W = F × d
Work (W) is measured in joules (J). It equals the force (F) in newtons multiplied by the distance (d) in metres moved in the direction of the force. If the force is not parallel to the movement, only the component in the direction of motion counts.
功（W）以焦耳（J）为单位。它等于作用力（F，牛顿）乘以在力的方向上移动的距离（d，米）。如果力不平行于运动方向，则只有沿运动方向的分量计入。
P = W ÷ t
Power (P) is the rate of doing work, measured in watts (W). One watt is one joule per second. You may also see power calculated using P = F × v, where v is the constant speed. This is useful for moving vehicles and machinery.
功率（P）是做功的速率，单位为瓦特（W）。一瓦特等于每秒一焦耳。你也许还会见到用 P = F × v 计算功率，其中 v 是恒定速度。这对于移动的车辆和机械非常有用。
5. Ohm’s Law | 欧姆定律
Ohm’s Law is the foundation of electrical engineering. It describes the relationship between voltage, current and resistance in a circuit. Knowing any two of these values lets you predict the third, which is essential for designing safe and effective circuits.
欧姆定律是电气工程的基础。它描述了电路中电压、电流和电阻之间的关系。知道其中任意两个值就能推算出第三个，这对设计安全有效的电路至关重要。
V = I × R
Here V is voltage measured in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω). The formula can be rearranged to I = V ÷ R and R = V ÷ I. Ohm’s Law applies only to ohmic conductors where temperature remains constant.
这里 V 是电压，单位为伏特（V）；I 是电流，单位为安培（A）；R 是电阻，单位为欧姆（Ω）。该公式可变形为 I = V ÷ R 和 R = V ÷ I。欧姆定律仅适用于温度保持恒定的欧姆导体。
6. Mechanical Advantage | 机械利益
Simple machines such as levers, pulleys and ramps help us move heavy loads by giving a mechanical advantage. This quantity tells us how many times a machine multiplies the input force.
杠杆、滑轮和斜面等简单机械通过提供机械利益来帮助我们移动重物。这个量告诉我们机器将输入力放大了多少倍。
MA = Load ÷ Effort
Mechanical advantage (MA) has no units – it is a ratio. The load is the force you want to overcome (often the weight of an object), and the effort is the force you apply. If MA is greater than 1, the machine multiplies your force; if it is less than 1, it increases speed or distance instead.
机械利益（MA）没有单位——它是一个比值。负载是你想要克服的力（通常是物体的重量），动力是你施加的力。如果 MA 大于 1，机器就放大了你的力；如果小于 1，它则增大了速度或距离。
7. Levers and Moments | 杠杆与力矩
A moment is the turning effect of a force around a pivot. Understanding moments is vital for designing bridges, tools and any structure that must stay balanced. The principle of moments states that for a lever to be in equilibrium, the total clockwise moment must equal the total anticlockwise moment.
力矩是力绕支点的转动效应。理解力矩对于设计桥梁、工具以及任何必须保持平衡的结构都至关重要。力矩原理指出，要使杠杆平衡，总顺时针力矩必须等于总逆时针力矩。
M = F × d
Here M is the moment measured in newton metres (Nm), F is the force in newtons and d is the perpendicular distance from the pivot to the line of action of the force, in metres. Always measure the distance at right angles to the force.
这里 M 是力矩，单位为牛米（Nm）；F 是力，单位为牛顿；d 是从支点到力作用线的垂直距离，单位为米。务必始终以与力成直角的方向测量距离。
8. Area and Volume of Common Shapes | 常用形状的面积与体积
Engineers regularly calculate areas and volumes when planning projects, estimating materials and working out costs. The following formulae are the building blocks you will use again and again.
工程师在规划项目、估算材料和计算成本时经常需要计算面积和体积。以下公式是你会反复用到的基础模块。
Rectangle area: A = l × w (length times width)
矩形面积： A = l × w（长乘以宽）
Triangle area: A = ½ × b × h (half base times vertical height)
三角形面积： A = ½ × b × h（底乘以垂直高度的一半）
Circle area: A = π × r² (pi times radius squared, π ≈ 3.14)
圆的面积： A = π × r²（π 乘以半径的平方，π ≈ 3.14）
Cuboid volume: V = l × w × h
长方体体积： V = l × w × h
Cylinder volume: V = π × r² × h
圆柱体体积： V = π × r² × h
Remember that area is measured in square units (e.g. cm², m²) and volume in cubic units (e.g. cm³, m³). For composite shapes, break them down into simpler parts, calculate each area or volume separately, then add or subtract as needed.
请记住，面积以平方单位（如 cm²、m²）计量，体积以立方单位（如 cm³、m³）计量。对于组合形状，可将其分解为简单的部分，分别计算每个面积或体积，然后根据需要进行加减。
9. Density | 密度
Density describes how much mass is packed into a given volume. It helps engineers choose the right materials for different jobs – for instance, a lightweight material with low density for aircraft, or a high‑density material for ballast.
密度描述单位体积内所含质量的大小。它帮助工程师为不同的工作选择合适的材料——例如，密度低的轻质材料用于飞机，或高密度材料用于压载。
ρ = m ÷ V
In this formula, ρ (Greek letter rho) is density in kilograms per cubic metre (kg/m³), m is mass in kilograms and V is volume in cubic metres. Water has a density of approximately 1000 kg/m³. Materials with density less than water float; those with greater density sink.
在这个公式中，ρ（希腊字母 rho）表示密度，单位为千克每立方米（kg/m³）；m 是质量，单位为千克；V 是体积，单位为立方米。水的密度约为 1000 kg/m³。密度小于水的材料会浮起，大于水的则会下沉。
10. Efficiency | 效率
No machine is perfect – there are always energy losses, mainly due to friction and heat. Efficiency tells us how good a machine is at converting input energy into useful output energy. It is always less than 100% for real machines.
没有完美的机器——总是存在能量损耗，主要是由于摩擦和发热。效率告诉我们机器将输入能量转化为有用输出能量的能力如何。对于真实的机器，效率总是低于 100%。
Efficiency = (Useful output energy ÷ Total input energy) × 100%
You can also use power instead of energy: Efficiency = (Useful output power ÷ Total input power) × 100%. Efficiency is expressed as a percentage. When comparing machines, a higher efficiency means less wasted energy and lower running costs.
你也可以用功率代替能量：效率 =（有用输出功率 ÷ 总输入功率）× 100%。效率以百分数表示。在比较机器时，效率更高意味着浪费的能量更少，运行成本更低。
11. Hooke’s Law | 胡克定律
Hooke’s Law describes the behaviour of springs and elastic materials when they are stretched or compressed. It applies as long as the material is not deformed beyond its elastic limit.
胡克定律描述了弹簧和弹性材料在被拉伸或压缩时的行为。只要材料没有超过弹性极限而发生永久变形，该定律就适用。
F = k × x
F is the force applied to the spring in newtons, k is the spring constant (or stiffness) in newtons per metre (N/m), and x is the extension or compression in metres. The spring constant tells you how stiff the spring is – a higher k means a stiffer spring that requires more force to stretch.
F 是施加在弹簧上的力，单位为牛顿；k 是弹簧常数（或刚度），单位为牛每米（N/m）；x 是伸长量或压缩量，单位为米。弹簧常数告诉你弹簧的刚度——k 值越大，弹簧越硬，需要更大的力才能拉伸。
12. Gears and Pulley Ratios | 齿轮与滑轮比
Gears and pulleys are used to change the speed, torque and direction of rotation in machines. The ratio between the sizes or numbers of teeth determines the mechanical advantage and the output speed.
齿轮和滑轮用于改变机器中的转速、扭矩和旋转方向。尺寸或齿数之间的比决定了机械利益和输出速度。
Gear ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear
If the driven gear has more teeth, the output speed decreases but the torque increases, giving a mechanical advantage. For pulleys, the velocity ratio is the diameter of the driven pulley divided by the diameter of the driver pulley. A large pulley driving a small one increases speed but reduces turning force.
如果从动齿轮的齿数更多，输出速度会降低，但扭矩会增大，从而获得机械利益。对于滑轮，速度比是从动滑轮的直径除以主动滑轮的直径。大滑轮驱动小滑轮可以增加速度，但会减小转动力。
Published by TutorHao | Engineering Revision Series | aleveler.com
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