📚 Year 8 SQA Engineering: Quick Reference Guide to Formulas and Theorems | Year 8 SQA 工程：公式定理速查手册
This quick reference guide covers the essential formulas and theorems required for Year 8 SQA Engineering studies. Each key formula is presented clearly, with a brief explanation of its meaning and practical context. Use it as a revision aid to reinforce your understanding of forces, energy, electricity, and mechanical systems.
本速查手册涵盖了 Year 8 SQA 工程学习所需的核心公式和定理。每个关键公式都清晰呈现，并附有简要说明，解释其含义和实际应用场景。请将其作为复习助手，巩固你对力、能量、电学和机械系统的理解。
1. Force and Motion (Newton’s Second Law) | 力和运动（牛顿第二定律）
The net force acting on an object is equal to its mass multiplied by its acceleration. This is expressed as F = m × a.
作用在物体上的合力等于其质量乘以加速度，表达式为 F = m × a。
Force (F) is measured in newtons (N), mass (m) in kilograms (kg), and acceleration (a) in metres per second squared (m/s²).
力（F）的单位是牛顿（N），质量（m）的单位是千克（kg），加速度（a）的单位是米每二次方秒（m/s²）。
This formula tells us that a heavier object needs a greater force to achieve the same acceleration. In engineering, it is used to calculate the push or pull required in moving parts.
该公式说明，较重的物体需要更大的力才能达到相同的加速度。在工程中，它用于计算移动部件所需的推力或拉力。
2. Moments (Turning Effect of a Force) | 力矩（力的转动效应）
The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action of the force.
力对支点的力矩等于力的大小乘以支点到力作用线的垂直距离。
Moment = Force × Distance, or M = F × d. The unit is newton metres (N m).
力矩 = 力 × 距离，即 M = F × d。单位是牛顿米（N m）。
To achieve balance in a lever, the total clockwise moment must equal the total anticlockwise moment: F₁ × d₁ = F₂ × d₂.
要使杠杆平衡，总顺时针力矩必须等于总逆时针力矩：F₁ × d₁ = F₂ × d₂。
This principle is essential when designing bridges, cranes, and simple hand tools like spanners.
该原理在设计桥梁、起重机以及扳手等简单手动工具时至关重要。
3. Speed, Distance, and Time | 速度、距离和时间
The average speed of an object is calculated by dividing the total distance travelled by the time taken.
物体的平均速度等于行驶的总距离除以所用时间。
Average speed = Distance ÷ Time, or v = d / t. Speed is measured in metres per second (m/s), distance in metres (m), and time in seconds (s).
平均速度 = 距离 ÷ 时间，即 v = d / t。速度的单位是米每秒（m/s），距离的单位是米（m），时间的单位是秒（s）。
This relationship allows engineers to estimate travel times and design moving systems such as conveyor belts or vehicles.
这一关系使工程师能够估算行程时间，并设计传送带或车辆等运动系统。
4. Weight and Mass on Earth | 地球上的重量和质量
Weight is the force of gravity acting on an object’s mass. On Earth, the gravitational field strength is approximately 9.8 N/kg.
重量是作用在物体质量上的重力。在地球上，重力场强度约为 9.8 N/kg。
Weight (W) = Mass (m) × Gravitational field strength (g), so W = m × g. Weight is measured in newtons (N).
重量（W） = 质量（m） × 重力场强度（g），即 W = m × g。重量单位是牛顿（N）。
In classroom calculations, g is often taken as 10 N/kg for simplicity. This formula explains why astronauts experience lower weight on the Moon—g is smaller.
在课堂计算中，为简单起见常取 g 为 10 N/kg。该公式解释了为什么宇航员在月球上体验到的重量较小——因为 g 更小。
5. Work Done by a Force | 力做的功
Work is done when a force moves an object through a distance. The amount of work is the product of the force and the distance moved in the direction of the force.
当一个力使物体移动一段距离时，就做了功。功的大小等于力与物体在力的方向上移动距离的乘积。
Work (W) = Force (F) × Distance (d), or W = F × d. Work is measured in joules (J), where 1 J = 1 N × 1 m.
功（W） = 力（F） × 距离（d），即 W = F × d。功的单位是焦耳（J），1 J = 1 N × 1 m。
Understanding work is fundamental to measuring energy transfer in lifting, pushing, or pulling tasks.
理解功是衡量提升、推动或拉拽任务中能量转移的基础。
6. Kinetic Energy | 动能
Any moving object possesses kinetic energy (KE). The kinetic energy depends on the mass and the square of the speed.
任何运动的物体都具有动能（KE）。动能取决于质量和速度的平方。
KE = ½ × m × v², where m is mass (kg) and v is speed (m/s). KE is in joules (J).
KE = ½ × m × v²，其中 m 为质量（kg），v 为速度（m/s）。KE 的单位是焦耳（J）。
Doubling the speed results in four times the kinetic energy, which has important safety implications in vehicle design.
速度翻倍会导致动能变为原来的四倍，这在车辆设计中具有重要的安全意义。
7. Gravitational Potential Energy | 重力势能
An object raised above the ground stores gravitational potential energy (GPE). This energy is equal to the work done to lift it.
升高到地面以上的物体会储存重力势能（GPE）。该能量等于将其提升所做的功。
GPE = m × g × h, where m is mass (kg), g is gravitational field strength (N/kg), and h is height (m). GPE is in joules (J).
GPE = m × g × h，其中 m 为质量（kg），g 为重力场强度（N/kg），h 为高度（m）。GPE 的单位是焦耳（J）。
When an object falls, GPE is converted into kinetic energy (assuming no air resistance), illustrating energy conservation.
当物体下落时，重力势能转化为动能（假设没有空气阻力），体现了能量守恒。
8. Power: Rate of Doing Work | 功率：做功的快慢
Power measures how quickly work is done or energy is transferred. It is calculated as work done divided by time.
功率衡量做功或能量转移的快慢。它等于做的功除以所用时间。
Power (P) = Work (W) ÷ Time (t), or P = W / t. Power is measured in watts (W), where 1 W = 1 J/s.
功率（P） = 功（W） ÷ 时间（t），即 P = W / t。功率的单位是瓦特（W），1 W = 1 J/s。
In mechanical systems, power can also be expressed as P = F × v (force multiplied by velocity). This is useful when analysing engines.
在机械系统中，功率也可表示为 P = F × v（力乘以速度）。这在分析发动机时非常有用。
9. Ohm’s Law (Electricity) | 欧姆定律（电学）
Ohm’s Law connects voltage, current, and resistance in an electrical circuit: Voltage = Current × Resistance.
欧姆定律连接了电路中的电压、电流和电阻：电压 = 电流 × 电阻。
V = I × R, where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).
V = I × R，其中 V 为电压，单位为伏特（V）；I 为电流，单位为安培（A）；R 为电阻，单位为欧姆（Ω）。
This relationship allows engineers to design circuits with the correct resistors to limit current and protect components.
这一关系使工程师能够设计具有正确电阻的电路，以限制电流并保护元件。
10. Resistors in Series and Parallel | 串联和并联电阻
Total resistance for resistors in series is simply the sum: Rtotal = R₁ + R₂ + R₃ + …
串联电阻的总电阻就是相加：R总 = R₁ + R₂ + R₃ + …
For resistors in parallel, the formula is more complex: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
并联电阻的公式较复杂：1/R总 = 1/R₁ + 1/R₂ + 1/R₃ + …
These rules are vital for combining components and ensuring circuits operate safely and predictably.
这些规则对于组合元件、确保电路安全且可预测地运行至关重要。
11. Pressure | 压强
Pressure is defined as the force acting per unit area. It is calculated by dividing force by area.
压强定义为单位面积上作用的力，用压力除以面积计算。
Pressure (P) = Force (F) ÷ Area (A), or P = F / A. Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m².
压强（P） = 力（F） ÷ 面积（A），即 P = F / A。压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。
High-heeled shoes exert more pressure than flat shoes because the same force is applied over a smaller area. In engineering, this formula helps design foundations and pneumatic systems.
高跟鞋比平底鞋产生的压强大，因为相同的力作用在更小的面积上。在工程中，该公式有助于设计地基和气动系统。
12. Efficiency of a System | 系统的效率
Efficiency compares the useful output energy (or power) to the total input energy. No real machine is 100% efficient.
效率将有用的输出能量（或功率）与总输入能量进行比较。现实中没有任何机器能达到 100% 的效率。
Efficiency (%) = (Useful output energy ÷ Total input energy) × 100. It can also be calculated using power: Efficiency = (Useful power out ÷ Total power in) × 100.
效率（%） = （有用的输出能量 ÷ 总输入能量）× 100。也可用功率计算：效率 = （有用的输出功率 ÷ 总输入功率）× 100。
Understanding efficiency helps engineers reduce waste—often due to friction and heat—and improve performance.
理解效率有助于工程师减少浪费——通常由摩擦和热量引起——并提高性能。
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