📚 Year 9 OCR Engineering Formula & Theorem Quick Reference Handbook | Year 9 OCR 工程：公式定理速查手册
Welcome to the Year 9 OCR Engineering quick reference handbook. Whether you are revising for end‑of‑topic tests or building your core engineering knowledge, this guide covers the essential formulas, theorems, and principles you need. Each section pairs an English explanation with a Chinese one, so you can learn key concepts bilingually. Dive in, practise the calculations, and keep this handbook close during your studies.
欢迎使用 Year 9 OCR 工程公式定理速查手册。不论你是在准备阶段测验，还是在构建核心工程知识，这份指南涵盖了你必须掌握的关键公式、定理和原理。每个小节都配有中英文解释，让你可以双语学习重要概念。深入学习、勤加练习，并把这份手册放在手边随时查阅。
1. Ohm’s Law | 欧姆定律
escribes the relationship between voltage (V), current (I), and resistance (R) in a direct‑ re remains constant. The formula is V = I × R, where V is measured in volts (V), I in amperes (A), and R in ohms (Ω).
欧姆定律描述了直流电路中电压 (V)、电流 (I) 和电阻 (R) 之间的关系。它表明，在温度恒定的条件下，通过导体的电流与导体两端的电压成正比。公式为 V = I × R，其中 V 的单位是伏特 (V)，I 的单位是安培 (A)，R 的单位是欧姆 (Ω)。
series circuit, total resistance is the sum of individual resistances: Rₜₒₜₐₗ = R₁ + R₂ + …
求电流或电阻时，可变形为：I = V ÷ R，R = V ÷ I。在串联电路中，总电阻等于各个电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + …
2. Electrical Power | 电功率
ated using P = V × I, where V is voltage and I is current. Power is measured in watts (W).
电功率是电路传输电能的速率。功率 (P) 可用 P = V × I 计算，其中 V 是电压，I 是电流。功率的单位是瓦特 (W)。
las help when only two quantities are known. In engineering systems, understanding power helps specify components such as motors and resistors.
结合欧姆定律，功率也可表示为 P = I²R 或 P = V² ÷ R。当只知道其中两个量时，这些公式非常有用。在工程系统中，理解功率有助于选定电机、电阻等组件。
3. Mechanical Work | 机械功
rk in joules (J), F is the force in newtons (N), and d is the distance moved in metres (m).
当一个力使物体沿力的方向移动时，就做了功。公式为 W = F × d，其中 W 是功，单位为焦耳 (J)；F 是力，单位为牛顿 (N)；d 是移动的距离，单位为米 (m)。
If the force is at an angle to the motion, only the component of force parallel to movement does work. In Year 9, we typically consider forces parallel to displacement. No work is done if the object does not move, even if a force is applied.
如果力与运动方向有夹角，只有与运动方向平行的分力才做功。在 Year 9 阶段，我们通常只考虑力与位移平行的情况。即使施加了力，只要物体没有移动，就没有做功。
4. Mechanical Power | 机械功率
ere P is power in watts (W), W is work done in joules, and t is time taken in seconds (s).
机械功率是做功的速率，公式为 P = W ÷ t，其中 P 是功率，单位为瓦特 (W)；W 是做的功，单位为焦耳；t 是所用时间，单位为秒 (s)。
. This is useful when analysing moving parts in machines, such as conveyor belts or lifting systems.
由于功 = 力 × 距离，功率也可写作 P = (F × d) ÷ t；当速度 (v) 恒定时，P = F × v。在分析机器运动部件（如传送带或升降系统）时，这一公式非常实用。
5. Force and Pressure | 力与压强
n pascals (Pa), F is force in newtons, and A is area in square metres (m²). 1 Pa = 1 N/m².
压强定义为作用在单位面积上的力。公式为 p = F ÷ A，其中 p 是压强，单位为帕斯卡 (Pa)；F 是力，单位为牛顿；A 是面积，单位为平方米 (m²)。1 Pa = 1 N/m²。
A larger area reduces pressure for the same force — this is why heavy vehicles use wide tyres or tracks. Conversely, a small area produces high pressure (e.g. a sharp knife). Understanding pressure is vital in hydraulic and pneumatic systems.
在相同力的情况下，面积越大，压强越小——这就是重型车辆使用宽轮胎或履带的原因。相反，面积小会产生高压强（如锋利的刀）。理解压强对液压和气动系统至关重要。
6. Moments (Turning Effect of Forces) | 力矩（力的转动效应）
f a force about a pivot. It is calculated using M = F × d, where M is the moment in newton‑ ce, and d is the perpendicular distance from the pivot to the line of action of the force.
力矩是力对支点的转动效应，计算公式为 M = F × d，其中 M 是力矩，单位为牛顿·米 (Nm)；F 是力；d 是从支点到力作用线的垂直距离。
The principle of moments states that for an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. This is used in lever systems, seesaws, and structural analysis to ensure balance.
力矩原理指出，对于处于转动平衡的物体，顺时针力矩的总和等于逆时针力矩的总和。这被用于杠杆系统、跷跷板和结构分析中，以确保平衡。
7. Speed and Acceleration | 速度与加速度
velocity: a = (v − u) ÷ t, where a is acceleration (m/s²), v is final velocity, u is initial velocity, and t is time.
速度是单位时间内移动的距离：v = s ÷ t，其中 v 是速度 (m/s)，s 是距离 (m)，t 是时间 (s)。加速度是速度变化的速率：a = (v − u) ÷ t，其中 a 是加速度 (m/s²)，v 是末速度，u 是初速度，t 是时间。
so encounter s = ut + ½at² and v² = u² + 2as. These link distance, time, and acceleration.
在工程中，这些方程可用于模拟车辆、机械臂和抛射体的运动。当加速度恒定时，还会用到 s = ut + ½at² 和 v² = u² + 2as，它们将距离、时间和加速度联系起来。
8. Hooke’s Law | 胡克定律
mit is not exceeded. The formula is F = k × x, where F is force (N), k is the spring constant (N/m), and x is extension (m).
胡克定律指出，在弹性限度内，弹性材料（如弹簧）的伸长量与施加的力成正比。公式为 F = k × x，其中 F 是力 (N)，k 是弹簧常数 (N/m)，x 是伸长量 (m)。
The spring constant k represents the stiffness of the spring. A stiffer spring has a larger k. Hooke’s Law is widely used in designing suspension systems, weighing scales, and force sensors.
弹簧常数 k 代表弹簧的刚度。弹簧越硬，k 值越大。胡克定律被广泛应用于悬架系统、称重传感器和力传感器的设计。
9. Kinetic Energy and Gravitational Potential Energy | 动能与重力势能
l energy (GPE) is the energy stored due to an object’s height: GPE = m × g × h, where g is the gravitational field strength (≈9.8 N/kg on Earth) and h is height (m).
动能 (KE) 是物体由于运动而拥有的能量：KE = ½ × m × v²，其中 m 是质量 (kg)，v 是速度 (m/s)。重力势能 (GPE) 是由于物体高度而储存的能量：GPE = m × g × h，其中 g 是重力场强度（地球上约 9.8 N/kg），h 是高度 (m)。
In many engineering systems, energy converts between KE and GPE — for example, on a roller coaster or in a pendulum. Ignoring friction, the total mechanical energy (KE + GPE) stays constant.
在许多工程系统中，能量在动能和重力势能之间转换——例如在过山车或摆锤中。忽略摩擦时，总机械能 (KE + GPE) 保持不变。
10. Efficiency | 效率
erts input energy into useful output energy. It is expressed as a percentage: Efficiency (% formula applies using power: Efficiency = (Useful power output ÷ Total power input) × 100.
效率衡量系统将输入能量转化为有用输出能量的程度，以百分比表示：效率 (%) = (有用输出能量 ÷ 总输入能量) × 100。使用功率时，公式相同：效率 = (有用输出功率 ÷ 总输入功率) × 100。
No real system is 100% efficient because energy is always lost to the surroundings — mostly as heat due to friction, air resistance, or electrical resistance. Improving efficiency is a key goal in engineering design.
现实中没有 100% 效率的系统，因为能量总会散失到周围环境中——主要是由于摩擦、空气阻力或电阻而以热量形式散失。提高效率是工程设计的关键目标。
11. Gear Ratio | 齿轮比
e gear ratio can be calculated as: Gear ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear.
齿轮比描述了两个啮合齿轮齿数之间的关系，它决定了输出速度和扭矩。对于两个齿轮，齿轮比可计算为：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 torque increases (a ‘gear down’). If the driven gear has fewer teeth, speed increases and torque decreases (a ‘gear up’). Simple gear trains multiply these ratios and are fundamental in bicycles, car transmissions, and robotic arms.
如果从动轮的齿数多于主动轮，输出速度降低但扭矩增大（“减速”）；如果从动轮齿数较少，则速度增加、扭矩减小（“增速”）。简单的齿轮系会将这些比值相乘，是自行车、汽车变速箱和机械臂的基础。
12. Conservation of Energy | 能量守恒
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another. In any engineering system, the total energy before an event equals the total energy after it, even if some energy is dissipated as waste heat or sound.
能量守恒原理指出，能量既不能创造也不能消灭，只能从一种形式转化为另一种形式。在任何工程系统中，事件发生前的总能量等于事件发生后的总能量，即使部分能量以废热或声音的形式耗散。
This principle is used when analysing systems with KE, GPE, work done by motors, and energy lost to friction. It allows engineers to predict performance and identify where energy losses occur.
这一原理用于分析包含动能、重力势能、电机做功和摩擦损耗的系统。它帮助工程师预测性能，并确定能量损耗发生的位置。
Published by TutorHao | Engineering Revision Series | aleveler.com
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