📚 Year 10 SQA Engineering: Quick Reference Guide to Formulas & Principles | Year 10 SQA 工程：公式定理速查手册
This handbook provides a concise summary of the essential formulas, laws and principles you will need for Year 10 SQA Engineering. Use it alongside your practical work and problem-solving exercises to reinforce your understanding of mechanics, electricity, materials and energy systems.
本手册简要总结了Year 10 SQA工程课程中必须掌握的核心公式、定律与原理。在动手操作和解题练习时参考本手册，可以巩固你对力学、电学、材料学和能量体系的理解。
1. Newton's Laws of Motion | 牛顿运动定律
Newton's first law: An object remains at rest or moves with constant velocity unless acted upon by a resultant force. This is often called the law of inertia.
牛顿第一定律：除非受到合外力的作用，物体将保持静止或匀速直线运动状态。这也常被称为惯性定律。
Newton's second law: The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
牛顿第二定律：物体的加速度与合外力成正比，与物体的质量成反比。
F = m × a
F is the resultant force in newtons (N), m is mass in kilograms (kg) and a is acceleration in metres per second squared (m/s²).
F 表示合外力，单位为牛顿 (N)；m 表示质量，单位为千克 (kg)；a 表示加速度，单位为米每二次方秒 (m/s²)。
Newton's third law: For every action force there is an equal and opposite reaction force. The two forces act on different objects.
牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力。这两个力作用在不同的物体上。
2. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot point. It depends on both the size of the force and the perpendicular distance from the pivot to the line of action of the force.
力矩是力绕支点产生的转动效应。它取决于力的大小以及从支点到力作用线的垂直距离。
Moment = Force × Perpendicular Distance
M = F × d
M is the moment in newton metres (Nm), F the force in newtons (N) and d the perpendicular distance in metres (m).
M 表示力矩，单位为牛顿米 (Nm)；F 表示力，单位为牛顿 (N)；d 表示垂直距离，单位为米 (m)。
For a lever in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
对于处于平衡状态的杠杆，顺时针力矩之和等于逆时针力矩之和。
Effort × Effort Arm = Load × Load Arm
E × dₑ = L × dₗ
Here E is the effort force, dₑ the effort arm, L the load force and dₗ the load arm.
这里 E 为作用力，dₑ 为力臂，L 为负载，dₗ 为负载臂。
3. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object in the direction of the force. Energy is transferred when work is done.
当一个力使物体沿力的方向移动时，力就对物体做了功。做功的同时也发生了能量的转移。
Work Done = Force × Distance moved in the direction of the force
W = F × d
W is work in joules (J), F in newtons and d in metres. 1 joule is equal to 1 newton metre.
W 表示功，单位为焦耳 (J)；F 单位为牛顿；d 单位为米。1 焦耳等于 1 牛·米。
Gravitational potential energy gained by an object lifted in a gravitational field:
物体在重力场中被抬高时所增加的重力势能：
Eₚ = m × g × h
m is mass (kg), g is gravitational field strength (9.8 N/kg or m/s² on Earth) and h is vertical height (m).
m 表示质量 (kg)，g 表示重力场强度（地球上约为 9.8 N/kg 或 m/s²），h 表示垂直高度 (m)。
Kinetic energy of a moving object:
运动物体的动能：
Eₖ = ½ × m × v²
v is the speed of the object in metres per second (m/s).
v 表示物体的速率，单位为米每秒 (m/s)。
Power is the rate of doing work or transferring energy.
功率是做功或传递能量的速率。
P = W / t or P = E / t
P is power in watts (W), W work in joules, E energy in joules and t time in seconds (s).
P 表示功率，单位为瓦特 (W)；W 功或者 E 能量单位为焦耳；t 时间单位为秒 (s)。
4. Electrical Fundamentals: Ohm's Law and Power | 电学基础：欧姆定律与功率
Ohm's law relates the voltage across a conductor, the current flowing through it and its resistance.
欧姆定律描述了导体两端的电压、流过导体的电流以及导体的电阻之间的关系。
V = I × R
V is voltage in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
V 表示电压，单位为伏特 (V)；I 表示电流，单位为安培 (A)；R 表示电阻，单位为欧姆 (Ω)。
Electrical power is the product of voltage and current. It can also be expressed using resistance.
电功率等于电压与电流的乘积，也可以利用电阻来表示。
P = V × I and P = I² × R and P = V² / R
P is power in watts (W). With a constant resistance, doubling the current increases the power by a factor of four.
P 表示功率，单位为瓦特 (W)。在电阻不变的情况下，电流加倍会使功率变为原来的四倍。
5. Resistors in Series and Parallel | 电阻的串联与并联
When resistors are connected end‑to‑end (in series), the total resistance is the sum of the individual resistances.
当电阻器首尾相连（串联）时，总电阻等于各电阻之和。
Rₜₒₜₐₗ = R₁ + R₂ + R₃ + ...
The same current flows through each resistor, but the total voltage is shared across them.
每个电阻中流过相同的电流，但总电压被分配给各个电阻。
For resistors connected side‑by‑side (in parallel), the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances.
对于并联连接的电阻器，总电阻的倒数等于各电阻倒数之和。
1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃ + ...
The voltage across each branch is the same, while the total current splits between the branches.
并联时各支路的电压相同，总电流则在各支路之间分配。
6. Stress and Strain | 应力与应变
Stress is a measure of the internal force acting per unit area within a material when it is subjected to an external load.
应力是材料承受外部载荷时内部单位面积上的作用力。
Stress (σ) = Force / Area
σ = F / A
Stress is measured in pascals (Pa) or newtons per square metre (N/m²). F is the force in newtons and A is the cross‑sectional area in square metres (m²).
应力单位为帕斯卡 (Pa) 或牛顿每平方米 (N/m²)。F 为受力 (N)，A 为横截面积 (m²)。
Strain is the ratio of extension to original length. It describes how much a material deforms.
应变是伸长量与原长之比，它描述了材料的变形程度。
Strain (ε) = Change in Length / Original Length
ε = ΔL / L₀
Strain has no units because it is a ratio of two lengths. ΔL is the extension and L₀ is the original length.
应变没有单位，因为它是一个比值。ΔL 表示伸长量，L₀ 表示原长。
Young's modulus describes the stiffness of a material within its elastic limit.
杨氏模量描述材料在弹性限度内的刚度。
Young's Modulus (E) = Stress / Strain
It is measured in pascals (Pa). A high Young's modulus indicates a stiff material.
杨氏模量单位为帕斯卡 (Pa)。模量越高，材料越刚硬。
7. Energy Efficiency | 能量效率
No real device converts all input energy into useful output energy; some energy is always dissipated, often as heat or sound.
任何真实的设备都无法将全部输入能量转化为有用的输出能量；总有一部分能量被耗散，通常以热或声音的形式散失。
Efficiency = (Useful Energy Output / Total Energy Input) × 100%
Efficiency can also be expressed in terms of power:
效率也可以用电功率表示：
Efficiency = (Useful Power Output / Total Power Input) × 100%
Efficiency is a ratio with no units, or expressed as a percentage. In engineering design, improving efficiency reduces waste and saves energy.
效率是一个无量纲的比值，或用百分数表示。在工程设计中，提高效率可以减少浪费并节约能源。
8. Gear Ratios and Mechanical Drives | 齿轮比与传动
Gears transmit rotational motion and torque. The gear ratio determines how speed and torque are changed between the driving gear and the driven gear.
齿轮用于传递旋转运动和转矩。齿轮比决定了主动轮与从动轮之间转速和转矩的改变。
Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear
If the driven gear has more teeth, the output speed decreases and torque increases. If it has fewer teeth, speed increases and torque decreases.
如果从动轮齿数多于主动轮，输出转速降低而转矩增大；反之则转速升高、转矩减小。
For belt or chain drives, the speed ratio is given by pulley diameters or sprocket teeth.
对于带传动或链传动，速比由带轮直径或链轮齿数决定。
Speed Ratio = Diameter of Driven Pulley / Diameter of Driver Pulley
9. Fluid Pressure and Hydraulics | 流体压力与液压
Pressure in a fluid is the force exerted per unit area. In a hydraulic system, pressure is transmitted equally throughout the fluid.
流体压强是单位面积上承受的力。在液压系统中，压强在整个流体内等大传递。
P = F / A
P is pressure in pascals (Pa), F force in newtons and A area in m². 1 Pa = 1 N/m².
P 表示压强 (Pa)，F 表示力 (N)，A 表示面积 (m²)。1 Pa = 1 N/m²。
Hydraulic systems use the principle that pressure is the same throughout a confined fluid. A small force applied to a small piston creates a large pressure that can produce a much larger force on a larger piston.
液压系统利用了密闭流体中各点压强相等的原理。施加在小活塞上的小力产生较大压强，从而在大活塞上产生大得多的力。
F₁ / A₁ = F₂ / A₂
This relationship allows hydraulic machines to multiply force at the expense of distance moved.
此关系表明液压机械能够以小距离为代价放大作用力。
In a liquid column, pressure increases with depth due to the weight of the liquid above.
在液柱中，由于上方液体的重量，压强随深度增加。
P = ρ × g × h
ρ (rho) is the liquid density in kg/m³, g is gravitational field strength and h is the depth in metres.
ρ 为液体密度 (kg/m³)，g 为重力场强度，h 为深度 (m)。
10. Temperature and Heat | 温度与热量
Heat is a form of energy transferred between objects due to a temperature difference. The specific heat capacity of a material tells us how much energy is needed to raise the temperature of 1 kg of the material by 1 °C.
热是一种因温度差而在物体之间转移的能量形式。比热容表示将 1 千克材料升高 1 °C 所需的能量。
Q = m × c × Δθ
Q is heat energy in joules (J), m is mass (kg), c is specific heat capacity in J/kg°C and Δθ is the change in temperature (°C).
Q 为热量 (J)，m 为质量 (kg)，c 为比热容 (J/kg°C)，Δθ 为温度变化 (°C)。
When a material changes state (e.g. melting or boiling), the temperature stays constant while latent heat is absorbed or released.
当材料发生物态变化（例如熔化或沸腾）时，温度保持不变，同时材料吸收或释放潜热。
Q = m × L
L is the specific latent heat in J/kg. This energy does not change the temperature but breaks or forms intermolecular bonds.
L 为比潜热 (J/kg)。这部分能量不改变温度，而是用于破坏或形成分子间的作用力。
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