📚 Year 7 AQA Engineering Formula & Theorem Quick Reference Guide | 七年级 AQA 工程公式定理速查手册
This quick reference guide provides a concise overview of essential formulas and principles covered in the Year 7 AQA Engineering curriculum. It serves as a handy revision tool for understanding core concepts in mechanics, electronics, materials and energy. Each entry presents the formula, defines the symbols, and briefly explains its application in engineering contexts.
本速查手册简要概述了七年级 AQA 工程课程中的基本公式和原理。它是复习力学、电子学、材料学和能源等核心概念的便捷工具。每个条目给出公式、定义符号并简要说明其在工程中的应用。
1. Force, Mass and Acceleration | 力、质量与加速度
Newton's Second Law states that the net force acting on an object equals its mass multiplied by its acceleration: F = m × a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²).
牛顿第二定律表明，作用在物体上的净力等于其质量乘以加速度：F = m × a。力的单位是牛顿 (N)，质量的单位是千克 (kg)，加速度的单位是米每二次方秒 (m/s²)。
When an object is dropped near the Earth's surface, the force due to gravity (its weight) is given by W = m × g, where g ≈ 9.8 m/s². This weight always acts downwards towards the centre of the Earth.
物体在地球表面附近下落时，重力（即重量）由 W = m × g 给出，其中 g ≈ 9.8 m/s²。重量始终竖直向下指向地心。
Average speed can be calculated using the distance travelled divided by time taken: v = d ÷ t. In engineering, this helps designers estimate travel times and select suitable motors.
平均速度可以用通过的路程除以时间来计算：v = d ÷ t。在工程中，这有助于设计师估算运动时间并选择合适的电机。
2. Work, Energy and Power | 功、能和功率
Work done by a constant force is the product of the force and the distance moved in the direction of the force: W = F × d. Work is measured in joules (J), where 1 J = 1 N × 1 m.
恒定力所做的功等于力与沿力方向移动距离的乘积：W = F × d。功的单位是焦耳 (J)，1 J = 1 N × 1 m。
Gravitational potential energy gained by an object lifted through a height h is Eₚ = m × g × h. This energy can be converted into kinetic energy as the object falls.
物体被举高高度 h 所获得的重力势能为 Eₚ = m × g × h。物体下落时，这部分能量可转化为动能。
The kinetic energy of a moving object depends on its mass and its speed squared: Eₖ = ½ × m × v². Doubling the speed quadruples the kinetic energy.
运动物体的动能取决于其质量和速度的平方：Eₖ = ½ × m × v²。速度翻倍，动能变为原来的四倍。
Power is the rate at which work is done or energy is transferred: P = W ÷ t (or P = E ÷ t). Power is measured in watts (W), where 1 W = 1 J/s.
功率是做功或能量转移的速率：P = W ÷ t（或 P = E ÷ t）。功率的单位是瓦特 (W)，1 W = 1 J/s。
3. Moments and Equilibrium | 力矩与平衡
The moment of a force about a pivot is the force multiplied by the perpendicular distance from the pivot to the line of action: M = F × d. Moments are measured in newton metres (Nm).
力对支点的力矩等于力乘以支点到力作用线的垂直距离：M = F × d。力矩的单位是牛顿米 (Nm)。
For an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same pivot. This principle is vital when designing bridges, levers and cranes to prevent tipping.
当物体处于转动平衡时，关于同一支点的顺时针力矩之和等于逆时针力矩之和。在设计桥、杠杆和起重机时，这一原理对于防止倾覆至关重要。
In a seesaw, if a heavier child sits closer to the pivot, the moments can be balanced. Engineers use F₁ × d₁ = F₂ × d₂ to calculate unknown forces or distances.
在跷跷板上，如果较重的孩子坐得离支点更近，力矩就能平衡。工程师用 F₁ × d₁ = F₂ × d₂ 来计算未知的力或距离。
4. Mechanical Advantage and Simple Machines | 机械效益与简单机械
Mechanical advantage (MA) tells us how much a machine multiplies the input force: MA = Load force ÷ Effort force. A machine with MA greater than 1 makes a task easier by reducing the effort needed.
机械效益 (MA) 表示机器将输入力放大了多少倍：MA = 负载力 ÷ 作用力。机械效益大于 1 的机器能减少所需的作用力，使工作更省力。
Velocity ratio (VR) compares the distance moved by the effort to the distance moved by the load: VR = Distance moved by effort ÷ Distance moved by load. For an ideal machine without friction, MA = VR.
速度比 (VR) 比较作用力移动的距离与负载移动的距离：VR = 作用力移动的距离 ÷ 负载移动的距离。对于无摩擦的理想机器，MA = VR。
For a simple lever, the fulcrum is positioned between the effort and the load. The mechanical advantage can also be expressed as MA = Effort arm length ÷ Load arm length. Pulleys and inclined planes also provide mechanical advantage.
对于简单杠杆，支点位于作用力和负载之间。机械效益也可表示为 MA = 作用力臂长 ÷ 负载臂长。滑轮和斜面同样能够提供机械效益。
5. Gears and Gear Ratios | 齿轮与齿轮比
Gears transmit rotary motion and torque. The gear ratio is determined by the number of teeth on each gear: Gear ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear.
齿轮传递旋转运动和扭矩。齿轮比由每个齿轮的齿数决定：齿轮比 = 从动轮齿数 ÷ 主动轮齿数。
If the driven gear has more teeth than the driver, the output speed decreases but the torque increases. The speed relationship is Output speed = Input speed ÷ Gear ratio.
如果从动轮齿数多于主动轮，输出转速会降低，但扭矩会增大。转速关系为 输出转速 = 输入转速 ÷ 齿轮比。
For a pair of meshing gears, the number of teeth is inversely proportional to rotational speed: N₁ × ω₁ = N₂ × ω₂, where N is number of teeth and ω (omega) is angular speed. This ensures the same number of teeth pass the contact point per minute on both gears.
对于一对啮合齿轮，齿数与转速成反比：N₁ × ω₁ = N₂ × ω₂，其中 N 为齿数，ω（欧米伽）为角速度。这保证了每分钟通过啮合点的齿数相同。
6. Ohm's Law and Electrical Circuits | 欧姆定律与电路
Ohm's Law links voltage, current and resistance in a conductor: V = I × R. Voltage (V) is measured in volts, current (I) in amperes, and resistance (R) in ohms (Ω).
欧姆定律将导体中的电压、电流和电阻联系起来：V = I × R。电压 (V) 的单位是伏特，电流 (I) 的单位是安培，电阻 (R) 的单位是欧姆 (Ω)。
For resistors connected in series, the total resistance is the sum of individual resistances: Rtotal = R₁ + R₂ + …. The current is the same through all components in series.
电阻串联时，总电阻等于各电阻之和：R总 = R₁ + R₂ + …。串联电路中各处电流相等。
For resistors connected in parallel, the total resistance is found using: 1 ÷ Rtotal = 1 ÷ R₁ + 1 ÷ R₂ + …. The voltage across each parallel branch is the same.
电阻并联时，总电阻的倒数等于各电阻倒数之和：1 ÷ R总 = 1 ÷ R₁ + 1 ÷ R₂ + …。并联各支路电压相等。
Electrical power is the product of current and voltage: P = I × V. This can be combined with Ohm's Law to give P = I² × R or P = V² ÷ R. Energy transferred is E = P × t.
电功率是电流与电压的乘积：P = I × V。结合欧姆定律可得 P = I² × R 或 P = V² ÷ R。转移的能量为 E = P × t。
7. Stress, Strain and Young's Modulus | 应力、应变与杨氏模量
Stress measures the internal force per unit area within a material: σ = F ÷ A. Stress (σ, sigma) has units of pascals (Pa) or N/m².
应力衡量材料内部单位面积上的内力：σ = F ÷ A。应力 (σ) 的单位是帕斯卡 (Pa) 或 N/m²。
Strain is the extension per unit original length caused by stress: ε = ΔL ÷ L₀. Strain (ε, epsilon) has no units because it is a ratio of lengths.
应变是应力引起的单位原始长度的伸长量：ε = ΔL ÷ L₀。应变 (ε) 没有单位，因为它是长度的比值。
Young's modulus (E) describes the stiffness of a material and is the ratio of stress to strain in the elastic region: E = σ ÷ ε. A high Young's modulus means the material is stiff and resists deformation.
杨氏模量 (E) 描述材料的刚度，是弹性区域内应力与应变的比值：E = σ ÷ ε。杨氏模量高表示材料刚硬、不易变形。
8. Thermal Expansion and Heat Transfer | 热膨胀与传热
Most materials expand when heated. The change in length due to thermal expansion is given by: ΔL = α × L₀ × ΔT, where α (alpha) is the linear expansion coefficient, L₀ is original length, and ΔT is change in temperature.
大多数材料受热膨胀。热膨胀引起的长度变化为：ΔL = α × L₀ × ΔT，其中 α 为线膨胀系数，L₀ 为原始长度，ΔT 为温度变化。
The amount of heat energy required to raise the temperature of a substance is: Q = m × c × ΔT. Here c is specific heat capacity (J/kg°C), m is mass, and Q is heat energy in joules.
使物体温度升高所需的热量为：Q = m × c × ΔT。其中 c 为比热容 (J/kg°C)，m 为质量，Q 为热量（焦耳）。
Heat transfers by conduction, convection and radiation. Engineers must account for thermal expansion by including expansion joints in bridges and pipes to prevent buckling.
热量通过传导、对流和辐射传递。工程师必须考虑热膨胀，在桥梁和管道中设置伸缩缝，以防弯曲变形。
9. Fluid Pressure and Buoyancy | 流体压强与浮力
Pressure is defined as force per unit area: P = F ÷ A. The unit of pressure is the pascal (Pa), equal to one newton per square metre.
压强定义为力除以面积：P = F ÷ A。压强的单位是帕斯卡 (Pa)，等于每平方米一牛顿。
In a static liquid, pressure increases with depth and depends on the liquid density: P = ρ × g × h, where ρ (rho) is density (kg/m³), g is gravitational field strength, and h is depth below the surface.
在静止液体中，压强随深度增加，并取决于液体密度：P = ρ × g × h，其中 ρ 为密度 (kg/m³)，g 为重力场强度，h 为液面下深度。
Archimedes' principle states that the upthrust (buoyant force) on an object submerged in a fluid equals the weight of the fluid displaced: Fupthrust = ρfluid × g × Vdisplaced. This principle explains why ships float and how submarines dive.
阿基米德原理指出，浸在流体中的物体受到的浮力等于它排开的流体的重量：F浮 = ρ流体 × g × V排开。此原理解释了船为什么能浮在水面以及潜艇如何下潜。
10. Waves and Sound in Engineering | 工程中的波与声音
The wave equation links speed, frequency and wavelength: v = f × λ. Speed (v) is in metres per second, frequency (f) in hertz (Hz), and wavelength (λ, lambda) in metres.
波动方程将波速、频率和波长联系起来：v = f × λ。波速 (v) 单位是米每秒，频率 (f) 单位是赫兹 (Hz)，波长 (λ) 单位是米。
Sound waves are longitudinal mechanical waves. In air at room temperature, the speed of sound is approximately 343 m/s. This value is used in ultrasound testing and sonar to measure distances and detect flaws in materials.
声波是纵波。室温下空气中的声速约为 343 m/s。这一数值用于超声波检测和声纳，以测量距离和探测材料内部缺陷。
The period (T) of a wave is the time for one complete cycle and is the reciprocal of frequency: T = 1 ÷ f. Engineers use wave principles when designing musical instruments, loudspeakers and noise-reducing structures.
波的周期 (T) 是完成一次全振动所需的时间，是频率的倒数：T = 1 ÷ f。工程师在设计乐器、扬声器和降噪结构时都会用到波动原理。
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