📚 Year 8 OCR Physics: Formula & Theorem Quick Reference Guide | Year 8 OCR 物理：公式定理速查手册
This quick reference guide collects the essential formulas and theorems you need for Year 8 OCR Physics. Each section presents the equation, explains every variable, states the correct units, and adds the key points that examiners look for in calculations and written answers. Keep it beside you during revision, homework and practical write-ups.
本速查手册汇总了 Year 8 OCR 物理所需的核心公式与定理。每个小节都给出方程、解释每一个变量、标明正确单位，并补充考官在计算题和文字题中最看重的关键要点。复习、写作业和完成实验报告时，都可以把它放在手边随时查阅。
1. The Speed Equation | 速度公式
Speed describes how fast an object moves, regardless of direction. It is calculated by dividing the distance travelled by the time taken. Because speed records only a magnitude and no direction, it is a scalar quantity, unlike velocity which is a vector.
速度描述物体运动的快慢，不考虑方向。它由移动的距离除以所花的时间得出。由于速度只记录大小、不记录方向，所以它是标量；而速度矢量（velocity）则同时包含方向信息。
v = d / t
Where:
其中：
- v = speed (m/s) | 速度（米/秒）
- d = distance (m) | 距离（米）
- t = time (s) | 时间（秒）
rs - 1 km = 1000 m and 1 h = 3600 s. A car travelling 150 m in 10 s has a speed of 15 m/s.
该公式可以变形为：d = v × t 和 t = d / v。代入数字之前必须先统一单位——1 千米 = 1000 米，1 小时 = 3600 秒。一辆汽车 10 秒行驶 150 米，其速度为 15 米/秒。
2. Distance-Time Graphs | 距离-时间图像
A distance-time graph plots distance travelled on the vertical axis against time on the horizontal axis. The gradient (slope) of the line gives the speed, so a steeper line means a faster object. A flat horizontal line means the object is stationary, and a curve means the speed is changing.
距离-时间图像以距离为纵轴、时间为横轴。直线的斜率即表示速度，因此线越陡表示物体越快。水平的平直线表示物体静止，而曲线表示速度正在变化。
speed = gradient = Δd / Δt
Where:
其中：
- Δd = change in distance (m) | 距离的变化量（米）
- Δt = change in time (s) | 时间的变化量（秒）
| Graph shape | 图像形状 | Meaning | 含义 |
| Steep straight line | 陡直的斜线 | High constant speed | 高速匀速运动 |
| Shallow straight line | 平缓的斜线 | Low constant speed | 低速匀速运动 |
| Horizontal line | 水平线 | Stationary | 静止 |
| Curve getting steeper | 越来越陡的曲线 | Accelerating | 加速 |
When you read a gradient, choose two points that are far apart on the line to reduce error, and remember to include the unit m/s in your answer.
读取斜率时，要选择直线上相距较远的两点以减小误差，并且记得在答案中写上单位米/秒。
3. Acceleration and Speed-Time Graphs | 加速度与速度-时间图像
Acceleration is the rate at which velocity changes. A positive value means the object is speeding up, while a negative value (often called deceleration) means it is slowing down. On a speed-time graph, the gradient gives acceleration and the area under the line gives the distance travelled.
加速度是速度变化的快慢。正值表示物体在加速，负值（常称为减速度）表示物体在减速。在速度-时间图像中，斜率表示加速度，直线下方的面积表示移动的距离。
a = (v − u) / t
Where:
其中：
- a = acceleration (m/s²) | 加速度（米/秒²）
- u = initial speed (m/s) | 初速度（米/秒）
- v = final speed (m/s) | 末速度（米/秒）
- t = time taken (s) | 所用时间（秒）
sides) × height. A bus slowing from 20 m/s to 0 m/s in 5 s has an acceleration of −4 m/s².
对于三角形图像，面积 = ½ × 底 × 高。对于梯形，面积 = ½ ×（两条平行边之和）× 高。一辆公交车 5 秒内从 20 米/秒减速到 0，其加速度为 −4 米/秒²。
4. Density | 密度
Density is a measure of how much mass is packed into a given volume. It helps identify materials and predict whether objects float or sink. Density is a property of the material itself, so a small piece of iron has the same density as a large block of iron.
密度衡量单位体积内含有多少质量。它有助于识别材料，并预测物体是浮还是沉。密度是材料本身的性质，所以一小块铁和大铁块的密度完全相同。
ρ = m / V
Where:
其中：
- ρ (rho) = density (kg/m³) | 密度（千克/立方米）
- m = mass (kg) | 质量（千克）
- V = volume (m³) | 体积（立方米）
consistent units - mixing grams with cm³ gives g/cm³, not kg/m³, and 1 g/cm³ = 1000 kg/m³.
密度小于水（1000 千克/立方米）的物体会浮起；密度更大的物体会下沉。务必使用一致的单位——把克与立方厘米混用会得到克/立方厘米，而不是千克/立方米，且 1 克/立方厘米 = 1000 千克/立方米。
5. Weight and Mass | 重量与质量
Mass is the amount of matter in an object and is constant anywhere in the universe. Weight is the gravitational force acting on that mass, so it and depends on the gravitational field strength of the place where the object is. Mass is measured in kilograms with a balance; weight is measured in newtons with a newton meter.
质量是物体所含物质的多少，在宇宙中任何地方都保持不变。重量是作用在该质量上的引力，因此它取决于物体所在位置的引力场强度。质量用天平以千克测量；重量用牛顿计以牛顿测量。
W = m × g
Where:
其中：
- W = weight (N) | 重量（牛顿）
- m = mass (kg) | 质量（千克）
- g = gravitational field strength (N/kg) | 引力场强度（牛/千克）
udent weighs about 588 N on Earth but only about 96 N on the Moon - the mass is still 60 kg in both places.
在地球上 g ≈ 9.8 牛/千克，快速计算时通常取 10 牛/千克。在月球上 g ≈ 1.6 牛/千克，所以一名 60 千克的学生在地球上重约 588 牛，在月球上只重约 96 牛——但两种情况下质量仍然是 60 千克。
6. Forces and Resultant Force | 力与合力
A force is a push or a pull measured in newtons (N). Forces can change an object's speed, direction or shape. When several forces act on one object, the single force that has the same effect is called the resultant force. If the resultant force is zero, the forces are balanced and the object stays still or moves at constant speed.
力是推或拉，单位为牛顿（N）。力可以改变物体的速度、方向或形状。当多个力作用在同一物体上时，与它们效果相同的那个力叫作合力。如果合力为零，这些力就是平衡的，物体保持静止或做匀速运动。
resultant force = Fforward − Fbackward
Where:
其中：
- Forces in the same direction are added | 同方向的力相加
- Forces in opposite directions are subtracted | 反方向的力相减
- Balanced forces give a resultant of 0 N | 平衡力的合力为 0 牛
to motion and transfers energy to the surroundings as heat. A stretched spring obeys Hooke' to extension: F = k × e, with k the spring constant in N/m and e the extension in metres.
摩擦力总是与运动方向相反，并把能量以热量形式转移到周围环境。在弹性限度内被拉伸的弹簧遵循胡克定律，力与伸长量成正比：F = k × e，其中 k 为弹簧常数（牛/米），e 为伸长量（米）。
7. Pressure | 压强
Pressure is the force acting perpendicular to a surface divided by the area of that surface. The same force produces a larger pressure when it is concentrated on a small area, which is why a sharp knife cuts easily and a wide snowshoe stops you sinking.
压强是垂直作用在表面上的力除以该表面的面积。同样的力作用在较小的面积上会产生更大的压强，这就是锋利的刀容易切开物体、宽大的雪地鞋能防止下陷的原因。
p = F / A
Where:
其中：
- p = pressure (Pa) | 压强（帕斯卡）
- F = force (N) | 力（牛顿）
- A = area (m²) | 面积（平方米）
s liquid density and g is gravitational field strength. Atmospheric pressure at sea level is about 100 000 Pa.
1 帕 = 1 牛/平方米。在液体中，压强随深度和密度增大：p = h × ρ × g，其中 h 是深度（米），ρ 是液体密度，g 是引力场强度。海平面处的大气压约为 100 000 帕。
8. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot. It increases when the force is larger or when it acts further from the pivot. A lever is balanced when the total clockwise moment equals the total anticlockwise moment - this is the principle of moments.
力矩是力绕支点产生的转动效果。力越大，或力作用点离支点越远，力矩就越大。当顺时针力矩总和等于逆时针力矩总和时，杠杆处于平衡状态——这就是力矩原理。
M = F × d
Where:
其中：
- M = moment (N m) | 力矩（牛·米）
- F = force (N) | 力（牛顿）
- d = perpendicular distance from pivot (m) | 到支点的垂直距离（米）
Principle of moments:
力矩原理：
F₁ × d₁ = F₂ × d₂
Spanners, wheelbarrows and see-saws all use moments. Note that the unit is N m (not J), because a moment is not energy - the distance is perpendicular to the force.
扳手、独轮车和跷跷板都用到力矩。注意单位是牛·米（不是焦耳），因为力矩不是能量——这里的距离与力方向垂直。
9. Work, Energy and Power | 功、能量与功率
Work is done whenever a force moves an object through a distance. Energy is the ability to do work and is measured in joules (J). Power is the rate at which energy is transferred or work is done, so a more powerful machine does the same job in less time.
当力使物体移动一段距离时，就说做了功。能量是做功的本领，单位是焦耳（J）。功率是能量转移或做功的快慢，因此功率越大的机器完成同样的工作所需时间越短。
W = F × d P = E / t
Where:
其中：
- W = work done (J) | 做功（焦耳）
- F = force (N) | 力（牛顿）
- d = distance moved in the direction of the force (m) | 沿力的方向移动的距离（米）
- P = power (W) | 功率（瓦特）
- E = energy transferred (J) | 转移的能量（焦耳）
- t = time taken (s) | 所用时间（秒）
Other useful forms are gravitational potential energy Ep = m × g × h and kinetic energy Ek Energy is always conserved: it is transferred between stores, never created or destroyed.
其他常用形式有重力势能 Ep = m × g × h 和动能 Ek = ½ × m × v²。能量总是守恒的：它只在各个能量库之间转移，既不会凭空产生，也不会凭空消失。
10. Efficiency | 效率
No device transfers all of its input energy into useful output energy. Some is always wasted, usually as heat or sound. Efficiency compares the useful output with the total input and is usually written as a percentage.
没有任何装置能把输入能量全部转化为有用的输出能量，总有一部分以热量或声音的形式损耗掉。效率比较的是有用输出与总输入，通常用百分数表示。
efficiency = (useful output energy ÷ total input energy) × 100%
Where:
其中：
- Useful output energy (J) | 有用的输出能量（焦耳）
- Total input energy (J) | 总输入能量（焦耳）
- Efficiency has no unit | 效率没有单位
Efficiency can never be greater than 100%, and a value above 100% always means a calculation error. A filament lamp is only about 10% efficient, while a modern LED can reach 80% or more.
效率永远不可能大于 100%，只要算出大于 100% 就一定是计算错误。白炽灯的效率只有约 10%，而现代 LED 可以达到 80% 甚至更高。
11. Electricity: Charge, Current, Voltage and Resistance | 电学：电荷、电流、电压与电阻
Current is the rate of flow of electric charge around a circuit and is measured with an ammeter placed in series. Voltage (potential difference) is the energy transferred per unit charge and is measured with a voltmeter placed in parallel across a component. Resistance opposes the current and is measured in ohms (Ω).
电流是电荷在电路中流动的速率，用串联接入的电流表测量。电压（电势差）是每单位电荷所转移的能量，用并联在元件两端的电压表测量。电阻阻碍电流，单位是欧姆（Ω）。
Q = I × t V = I × R P = V × I
Where:
其中：
- Q = charge (C) | 电荷量（库仑）
- I = current (A) | 电流（安培）
- t = time (s) | 时间（秒）
- V = potential difference (V) | 电势差（伏特）
- R = resistance (Ω) | 电阻（欧姆）
- P = power (W) | 功率（瓦特）
In a series circuit the current is the same everywhere and the voltages add up to the supply voltage. In a parallel circuit the voltage across each branch is the same and the currents add up to the total current.
在串联电路中，各处电流相同，各元件电压之和等于电源电压。在并联电路中，各支路两端的电压相同，各支路电流之和等于总电流。
12. Waves, Sound and Light | 波、声音与光
A wave transfers energy from one place to another without transferring matter. The frequency is the number of complete waves passing a point each second, the wavelength is the distance between two identical points on neighbouring waves, and the amplitude is the maximum displacement from the rest position.
波把能量从一个地方传到另一个地方，但不转移物质。频率是每秒通过某一点的完整波的个数，波长是相邻两个波上相同点之间的距离，振幅是离开平衡位置的最大位移。
v = f × λ T = 1 / f
Where:
其中：
- v = wave speed (m/s) | 波速（米/秒）
- f = frequency (Hz) | 频率（赫兹）
- λ (lambda) = wavelength (m) | 波长（米）
- T = period (s) | 周期（秒）
vel through a vacuum at 3 × 10⁸ m/s, which is why we see lightning before we hear thunder.
声音是需要介质的纵波，在空气中传播速度约为 340 米/秒。光是能够穿过真空的横波（电磁波），速度为 3 × 10⁸ 米/秒，这就是我们先看到闪电、后听到雷声的原因。
Use this guide as a checklist: cover the equations, write each one from memory, then check the units of every variable before you substitute numbers. In OCR-style questions, marks are often given for correct substitution and correct units, not just for the final answer, so always show your working line by line.
把这份手册当作自查清单使用：先遮住公式，凭记忆写出每一个，然后在代入数字前核对每个变量的单位。在 OCR 风格的题目中，分数往往给在正确的代入和正确的单位上，而不仅仅是最终答案，所以一定要一步步写出计算过程。
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