📚 Year 8 AQA Physics Formula & Theorem Quick Reference Handbook | Year 8 AQA 物理：公式定理速查手册
This quick reference handbook covers the essential formulas and theorems you need for Year 8 AQA Physics. Each entry explains the formula, defines every symbol, states the correct unit, and works through a practical example. Use it to revise the big ideas of motion, forces, energy, electricity and waves, and keep it beside you when you attempt past-paper style questions or end-of-topic tests.
本速查手册囊括了 Year 8 AQA 物理必备的公式与定理。每一条都会解释公式本身、说明每个符号的含义、给出正确的单位，并配一道实例演算。你可以用它复习运动、力、能量、电学和波这几大核心概念，在做模拟题或单元测验时把它放在手边随时查阅。
The handbook is written for KS3 learners working towards AQA Combined Science and Separate Science pathways. Where a formula is an extension idea beyond the Year 8 programme of study, it is clearly labelled so that you know what is core and what is stretch.
本手册面向正在为 AQA 综合科学（Combined Science）与分科科学（Separate Science）打基础的 KS3 学生。凡是超出 Year 8 课程范围、属于拓展内容的公式，文中都会明确标注，方便你区分哪些是必考核心、哪些是拔高内容。
1. Speed and the Distance-Time Relationship | 速度与路程—时间关系
Speed measures how quickly an object moves. It is the total distance travelled divided by the time taken, and the standard unit is metres per second (m/s). Because speed has no direction, it is a scalar quantity; velocity is the same calculation but with a stated direction.
速度衡量物体运动的快慢。它等于通过的总路程除以所用的时间，标准单位是米每秒 (m/s)。速度没有方向，因此是标量；而速度（velocity，矢量）做的是同样的计算，但必须标明方向。
v = d ÷ t
Where v = speed (m/s), d = distance travelled (m), and t 5 = 20 m/s. To convert m/s into km/h, multiply by 3.6; to go the other way, divide by 3.6.
其中 v 代表速度（m/s），d 代表通过的路程（m），t 代表所用时间（s）。若一辆汽车 5 秒行驶 100 米，其速度为 100 ÷ 5 = 20 m/s。若要把 m/s 换算成 km/h，乘以 3.6；反向换算则除以 3.6。
On a distance-time graph, the gradient of the line equals the speed. A horizontal line means the object is stationary, a straight sloping line means constant speed, and a line that curves upwards means the object is accelerating. Average speed is calculated over the whole journey, while instantaneous speed is the speed at one particular moment.
在路程—时间图像上，直线的斜率就等于速度。水平线表示物体静止，倾斜的直线表示匀速运动，向上弯曲的曲线表示物体在加速。平均速度是对整段行程计算的结果，而瞬时速度是某一具体时刻的速度。
- Flat line → stationary | 水平线 → 静止
- Steeper line → greater speed | 斜率越大 → 速度越大
- Curve getting steeper → acceleration | 曲线越来越陡 → 加速
2. Weight and Gravity | 重力与引力
Weight is the force of gravity pulling an object towards the centre of a planet. It depends on the object's mass and on the gravitational field strength (g) at that location. Weight is measured in newtons (N), while mass is measured in kilograms (kg) and never changes with location.
重力（weight）是引力把物体拉向星球中心的作用力。它取决于物体的质量和当地的重力场强度 (g)。重力的单位是牛顿 (N)，而质量的单位是千克 (kg)，质量不会随地点改变。
W = m × g
W = weight (N), m = mass (kg), g = gravitational field strength (N/kg). On Earth, g of 5 × 10 = 50 N. On the Moon, g ≈ 1.6 N/kg, so the same 5 kg object would weigh only 8 N.
W 代表重力（N），m 代表质量（kg），g 代表重力场强度（N/kg）。在地球上 g ≈ 10 N/kg，所以一个 5 kg 的物体所受重力为 5 × 10 = 50 N。在月球上 g ≈ 1.6 N/kg，同一个 5 kg 物体的重力只有 8 N。
Note that g is often quoted as 9.8 N/kg in more advanced work, but Year 8 AQA questions normally use 10 N/kg to keep the arithmetic simple. Always write the unit N/kg rather than m/s² at this level, and remember that gravitational field strength is also the acceleration due to free fall.
注意：在更深入的题目中 g 常写作 9.8 N/kg，但 Year 8 AQA 的题目通常取 10 N/kg 以便计算。这个阶段请把单位写成 N/kg 而不是 m/s²，同时要记住重力场强度在数值上也等于自由落体的加速度。
3. Work Done | 做功
distance moved in the direction of that force. The unit is the joule (J), and 1 J = 1 N m.
力使物体移动一段距离时，就做了功。做功等于力乘以物体在力的方向上移动的距离。单位是焦耳 (J)，且 1 J = 1 N m。
W = F × d
W = work done (J), F = force applied (N), d m). Applying a force of 30 N to push a box 2 m along the floor does 30 × 2 = 60 J of work.
W 代表做功（J），F 代表施加的力（N），d 代表物体沿力的方向移动的距离（m）。用 30 N 的力把箱子沿地面推动 2 米，做功为 30 × 2 = 60 J。
The direction matters. If you carry a heavy bag horizontally, you are not doing work on the bag against gravity, because the movement is at right angles to the weight. If the force and the motion are in the same direction, use the full value of the force; if they are at an angle, only the component along the direction of motion counts.
方向很关键。如果你水平提着沉重的书包走路，你并没有克服重力对书包做功，因为运动方向与重力方向垂直。若力与运动方向相同，就用力的全部数值；若两者成一定角度，只有沿运动方向的分力才计入做功。
4. Gravitational Potential Energy | 重力势能
Gravitational potential energy (Eₚ) is the energy stored in an object because of its height above a reference level. Lifting an object transfers energy from your muscles into the gravitational store, and this energy can be released when the object falls.
重力势能 (Eₚ) 是物体由于高于某个参考高度而被举高所储存的能量。把物体举高，是把能量从你的肌肉转移到重力势能储存中；物体下落时，这些能量又会被释放出来。
Eₚ = m × g × h
Eₚ = gravitational potential energy (J), m = mass (kg), g = 10 N/kg on Earth, h reference level (m). A 2 kg book placed on a 1.5 m shelf stores Eₚ = 2 × 10 × 1.5 = 30 J.
Eₚ 代表重力势能（J），m 代表质量（kg），g 在地球上取 10 N/kg，h 代表相对参考高度上升的高度（m）。一本 2 kg 的书放在 1.5 m 高的书架上，储存的重力势能为 Eₚ = 2 × 10 × 1.5 = 30 J。
h is the distance moved, so Eₚ is really work done against gravity. Height must always be measured from a clearly stated reference level, usually the ground or the lowest point of the motion.
你会发现，这个公式与 W = F × d 本质相同：重力 m × g 是力，h 是移动的距离，所以重力势能其实就是克服重力所做的功。计算时高度必须从明确指定的参考面量起，通常是地面或运动的最低点。
5. Kinetic Energy | 动能
Kinetic energy (Eₖ) is the energy stored in any moving object. It depends on the mass of the object and on the square of its speed, which means fast-moving objects carry a very large amount of energy.
动能 (Eₖ) 是任何运动物体所储存的能量。它取决于物体的质量和速度的平方，这意味着高速运动的物体会携带很大的能量。
Eₖ = ½ × m × v²
Eₖ = kinetic energy (J), m = mass (kg), v speed (m/s). A 4 kg bowling ball rolling at 3 m/s has Eₖ = ½ × 4 × 3² = ½ × 4 × 9 = 18 J.
Eₖ 代表动能（J），m 代表质量（kg），v 代表速度（m/s）。一个 4 kg 的保龄球以 3 m/s 滚动，其动能为 Eₖ = ½ × 4 × 3² = ½ × 4 × 9 = 18 J。
Because speed is squared, doubling the speed multiplies the kinetic energy by four, and trebling the speed multiplies it by nine. This is why stopping distances rise so sharply with speed and why road-safety campaigns focus on even small reductions in driving speed.
由于速度是平方项，速度加倍会使动能变为原来的四倍，速度变三倍则动能变为九倍。这就是刹车距离随车速急剧增加的原因，也是道路安全宣传强调哪怕稍稍降低车速也很重要的原因。
6. Energy Stores, Transfers and Conservation | 能量储存、转移与守恒
The law of conservation of energy states that energy cannot be created or destroyed, only transferred between stores and pathways. In a closed system, the total energy before an event equals the total energy after it.
能量守恒定律指出：能量既不能被创造，也不能被消灭，只能在各个能量储存之间、通过各种途径转移。在一个封闭系统中，事件发生前的总能量等于事件发生后的总能量。
Total energy in = Total energy out
Common energy stores include kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, magnetic, electrostatic and vibrational. Common transfer pathways are mechanical work (a force moving an object), electrical work (a current flowing), heating (due to a temperature difference) and radiation (light or sound waves).
常见的能量储存包括：动能、重力势能、弹性势能、热（内）能、化学能、核能、磁能、静电势能和振动能。常见的转移途径有：机械做功（力使物体移动）、电功（电流流动）、加热（由于温差）和辐射（光波或声波）。
A pendulum is a classic example. At the highest point of the swing, the energy is almost entirely gravitational potential; at the lowest point it is almost entirely kinetic. In reality, some energy is always transferred to the thermal store of the surroundings by friction and air resistance, so the swing gradually dies away.
单摆是经典例子。摆到最高点时，能量几乎全是重力势能；摆到最低点时，能量几乎全是动能。而在现实中，总有一部分能量通过摩擦和空气阻力转移到周围环境的热（内）能储存中，所以摆幅会逐渐减小直至停止。
| Store | 储存 | Example | 例子 |
| Kinetic | 动能 | A cyclist moving | 骑行中的自行车 |
| Gravitational | 重力势能 | A book on a shelf | 书架上的书 |
| Elastic | 弹性势能 | A stretched spring | 被拉长的弹簧 |
| Thermal | 热（内）能 | A hot cup of tea | 一杯热茶 |
| Chemical | 化学能 | Food or a battery | 食物或电池 |
7. Efficiency and Power | 效率与功率
iency compares the useful energy or power output with the total energy or power input, and is usually written as a percentage.
功率是能量转移的速率，也就是做功的快慢。单位是瓦特 (W)，1 W = 1 J/s。效率是比较有用的能量（或功率）输出与总能量（或功率）输入之间的关系，通常用百分数表示。
P = E ÷ t
Efficiency = (useful output ÷ total input) × 100%
P = power (W), E = energy transferred (J), t lectrical energy and transfers only 60 J as useful light, its efficiency is 60 ÷ 100 × 100% = 60%.
P 代表功率（W），E 代表转移的能量（J），t 代表所用时间（s）。一台电动机 6 秒内转移 300 J 能量，其功率为 300 ÷ 6 = 50 W。若一盏灯输入 100 J 电能而只有 60 J 转化为有用的光，其效率为 60 ÷ 100 × 100% = 60%。
Efficiency can never exceed 100%. The wasted energy is not lost, but transferred to less useful stores, most often the thermal store of the surroundings. Machines are made more efficient by reducing friction, using lubricants, and streamlining shapes to cut air resistance.
效率永远不可能超过 100%。被浪费的能量并没有消失，而是转移到了不太有用的储存中，最常见的是周围环境的热（内）能。通过减小摩擦、使用润滑剂、把外形设计成流线型以降低空气阻力，可以提高机械的效率。
8. Forces, Resultant Force and Balance | 力、合力与平衡
A force is a push or a pull, measured in newtons (N). Forces can be contact forces (friction, air resistance, tension, normal contact) or non-contact forces (gravity, magnetism, electrostatic). When several forces act on one object, they can be combined into a single resultant force.
力是推或拉的作用，单位是牛顿 (N)。力可以分为接触力（摩擦力、空气阻力、张力、支持力）和非接触力（重力、磁力、静电力）。当多个力作用在同一物体上时，可以把它们合成为一个合力。
Fresultant = Σ forces (taking direction into account)
ght while friction pushes with 8 N to the left has a resultant of 20 − 8 = 12 N to the right.
若各力方向相同，则将它们相加；若方向相反，则用较大的力减去较小的力。一个箱子被向右的 20 N 推动，同时摩擦力向左 8 N，则合力为 20 − 8 = 12 N，方向向右。
orce is not zero, the object speeds up, slows down or changes direction. As an extension, resultant force, mass and acceleration are linked by F = m × a.
当合力为零时，各力平衡：物体保持静止，或沿直线匀速运动。当合力不为零时，物体会加速、减速或改变方向。作为拓展，合力、质量与加速度之间的关系为 F = m × a。
9. Pressure | 压强
a), and 1 Pa = 1 N/m². For the same force, a smaller area produces a much larger pressure.
压强是垂直作用在单位面积上的力。单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。在力相同的条件下，受力面积越小，压强越大。
p = F ÷ A
p = pressure (Pa), F = force applied at right angles to the surface (N), A (m²). A force of 400 N acting on an area of 0.5 m² gives a pressure of 400 ÷ 0.5 = 800 Pa.
p 代表压强（Pa），F 代表垂直作用在表面上的力（N），A 代表接触面积（m²）。400 N 的力作用在 0.5 m² 的面积上，压强为 400 ÷ 0.5 = 800 Pa。
extension, pressure in a liquid increases with depth and density: p = ρ × g × h, where ρ is the density in kg/m³.
这就解释了为什么锋利的刀容易切开物体（接触面积极小，压强极大），而雪地靴能防止下陷（面积大，压强小）。作为拓展，液体内部的压强随深度和密度增加：p = ρ × g × h，其中 ρ 是密度，单位 kg/m³。
10. Electric Circuits: Current, Charge, Potential Difference and Resistance | 电路：电流、电荷、电压与电阻
Electric current is the rate of flow of charge, measured in amperes (A) with an ammeter connected in series. Potential difference (often called voltage) is the energy transferred per unit charge, measured in volts (V) with a voltmeter connected in parallel across a component.
电流是电荷流动的速率，用安培 (A) 计量，电流表需串联接入电路。电压（电位差）是每单位电荷所转移的能量，用伏特 (V) 计量，电压表需并联在元件两端。
Q = I × t V = I × R
Q = charge (C), I = current (A), t = time (s), V = potential difference (V), R rge. A current of 2 A through a 6 Ω resistor needs a potential difference of 2 × 6 = 12 V.
Q 代表电荷量（C），I 代表电流（A），t 代表时间（s），V 代表电压（V），R 代表电阻（Ω）。3 A 的电流持续 60 秒，转移的电荷量为 3 × 60 = 180 C。2 A 的电流通过 6 Ω 的电阻，所需电压为 2 × 6 = 12 V。
- Series circuit: current is the same everywhere; potential differences add up. | 串联电路：各处电流相同；各元件电压相加。
- Parallel circuit: potential difference is the same across each branch; branch currents add up. | 并联电路：各支路电压相同；各支路电流相加。
- Resistance is increased by making a wire longer, thinner, or hotter. | 导线越长、越细、温度越高，电阻越大。
11. Electrical Power and
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