📚 KS3 AQA Physics: Formula & Theorem Quick Reference Handbook | KS3 AQA 物理：公式定理速查手册
This is your go-to quick reference for the essential formulas and theorems covered in the KS3 AQA Physics syllabus. Each section presents a key relationship, explains its meaning, and shows you how to apply it. Keep this handbook close when revising, completing homework, or preparing for tests. Mastering these building blocks will give you a solid foundation for GCSE Physics and beyond.
这是你在 KS3 AQA 物理课程中所需关键公式和定理的速查手册。每一部分都会展示一个重要的关系式，解释其含义，并说明如何应用。复习、完成作业或准备测验时，这本手册将随时为你提供帮助。掌握这些基础内容，将为你未来的 GCSE 物理学习及更高阶段的知识打下坚实的基础。
1. Speed | 速度
Speed measures how quickly an object moves. The average speed of an object can be calculated by dividing the total distance travelled by the time taken. The formula is often written as:
速度用来衡量一个物体运动得快慢。物体运动的平均速度可以通过总路程除以所用时间来计算。公式通常写作：
average speed = distance / time v = d / t
Where v is speed (in metres per second, m/s), d is distance (in metres, m) and t is time (in seconds, s). You can rearrange this to find distance or time: d = v × t and t = d / v. In everyday situations, speed is often measured in miles per hour or kilometres per hour, but in science we use m/s.
其中 v 表示速度（单位为米每秒，m/s），d 表示路程（单位为米，m），t 表示时间（单位为秒，s）。你可以通过变形公式来求路程或时间：d = v × t 以及 t = d / v。日常生活中，速度常用英里每小时或公里每小时表示，但在科学计算中我们使用 m/s。
2. Acceleration | 加速度
Acceleration tells us how quickly an object’s velocity is changing. It can be a change in speed or a change in direction. For straight-line motion, acceleration is calculated using the change in velocity over the time taken.
加速度表示物体速度变化的快慢。它可以是速度大小的改变，也可以是方向的改变。在直线运动中，加速度可以通过速度的变化量除以所用时间来计算。
acceleration = change in velocity / time a = (v – u) / t
Here a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is time (s). A positive result means an increase in speed (acceleration), while a negative result means a decrease in speed (deceleration). If the acceleration is zero, the object moves at constant velocity.
这里 a 是加速度（m/s²），v 是末速度（m/s），u 是初速度（m/s），t 是时间（s）。结果为正值表示速度增加（加速），结果为负值表示速度减小（减速）。如果加速度为零，物体将保持匀速运动。
3. Newton’s Second Law | 牛顿第二定律
Newton’s Second Law explains the relationship between force, mass, and acceleration. The resultant force on an object is equal to its mass multiplied by its acceleration.
牛顿第二定律解释了力、质量和加速度之间的关系。作用在物体上的合力等于物体的质量乘以加速度。
resultant force = mass × acceleration F = m a
F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in m/s². This law shows that for a given force, a larger mass will accelerate less. It also tells us that if the resultant force is zero, the acceleration is zero – the object stays at rest or continues at constant velocity.
F 表示力，单位是牛顿（N）；m 表示质量，单位是千克（kg）；a 表示加速度，单位是 m/s²。这条定律表明，在相同的力作用下，质量越大，加速度越小。它还告诉我们，如果合力为零，加速度就为零——物体将保持静止或匀速直线运动状态。
4. Weight and Gravity | 重力与重量
Weight is the force of gravity acting on an object. It should not be confused with mass, which is the amount of matter. Weight depends on both the mass of the object and the gravitational field strength of the planet.
重量是地球（或其他天体）对物体的引力作用，要与表示物质多少的质量区分开。重量取决于物体的质量和所在天体引力场强度的大小。
weight = mass × gravitational field strength W = m g
W is weight in newtons (N), m is mass in kg, and g is gravitational field strength in N/kg. On Earth, g is approximately 9.8 N/kg, but for KS3 calculations we often use 10 N/kg. Your mass stays the same wherever you go, but your weight changes if you go to the Moon because g is smaller there.
W 表示重量，单位是牛顿（N）；m 表示质量，单位是 kg；g 表示引力场强度，单位是 N/kg。在地球表面，g 约为 9.8 N/kg，但 KS3 阶段的计算中常近似取为 10 N/kg。无论去到哪里，你的质量保持不变，但如果登上月球，由于那里的 g 较小，你的重量也会变小。
5. Work Done | 做功
When a force moves an object, work is done. Work done measures the energy transferred by a force. The amount of work depends on the size of the force and the distance the object moves in the direction of the force.
力使物体移动时，我们就说做了功。做功量度了力所转移的能量。做功的多少由力的大小以及物体在力的方向上移动的距离决定。
work done = force × distance W = F d
W is work done in joules (J), F is force in newtons (N), and d is distance moved in the direction of the force in metres (m). One joule of work is done when a force of one newton moves an object one metre. If the force is perpendicular to the movement, no work is done on the object.
W 表示做功，单位是焦耳（J）；F 表示力，单位是牛顿（N）；d 表示物体在力的方向上移动的距离，单位是米（m）。当 1 N 的力使物体移动 1 m 时，所做的功就是 1 J。如果力与运动方向垂直，则该力不对物体做功。
6. Power | 功率
Power is the rate at which work is done or energy is transferred. A powerful machine does work quickly, whereas a less powerful one takes longer to transfer the same amount of energy.
功率是做功或能量转移的速率。功率大的机器做功快，功率小的机器转移相同多的能量则需要更长的时间。
power = work done / time P = W / t
P is power in watts (W), W is work done in joules (J) and t is time in seconds (s). One watt is equal to one joule per second. You may also see power written as P = E / t, where E is energy transferred. Knowing the power of an appliance helps you understand how much energy it uses over time.
P 表示功率，单位是瓦特（W）；W 表示做功，单位是焦耳（J）；t 表示时间，单位是秒（s）。1 瓦特等于 1 焦耳每秒。你也会看到公式写作 P = E / t，其中 E 代表转移的能量。了解电器的功率有助于你估算它在一段时间内消耗的能量。
7. Ohm’s Law and Resistance | 欧姆定律与电阻
Ohm’s Law relates voltage, current, and resistance in an electrical circuit. It states that the current through a conductor is directly proportional to the voltage across it, provided the temperature remains constant.
欧姆定律描述了电路中电压、电流和电阻之间的关系。它指出，在温度保持不变的条件下，通过导体的电流与导体两端的电压成正比。
voltage = current × resistance V = I R
V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). From this, resistance can be found using R = V / I. Components that obey Ohm’s Law give a straight-line graph when voltage is plotted against current. Filament bulbs do not obey Ohm’s Law because their resistance increases as they heat up.
V 表示电压，单位是伏特（V）；I 表示电流，单位是安培（A）；R 表示电阻，单位是欧姆（Ω）。由此可以导出 R = V / I 来计算电阻。遵循欧姆定律的元件，其电压-电流图是一条过原点的直线。灯丝灯泡不满足欧姆定律，因为灯丝温度升高时电阻会变大。
8. Electrical Power | 电功率
Electrical power tells us how quickly an electrical component converts energy. It can be calculated from voltage and current, or from current and resistance. These formulas are especially useful when comparing appliances.
电功率表示电器将电能转换为其他形式能量的快慢。可以用电压和电流，或者电流和电阻来计算。比较不同电器的能耗时，这些公式非常实用。
electrical power = voltage × current P = I V
electrical power = current² × resistance P = I² R
P is power in watts (W), I is current in amperes (A), V is voltage in volts (V), and R is resistance in ohms (Ω). The first relationship is used when both voltage and current are known. The second is derived by substituting V = I R into the first. Both give the same result and help us design circuits safely.
P 表示功率，单位是瓦特（W）；I 表示电流，单位是安培（A）；V 表示电压，单位是伏特（V）；R 表示电阻，单位是欧姆（Ω）。已知电压和电流时，使用第一个公式更方便。第二个公式由 V = I R 代入第一个公式得到。两者给出的结果相同，这有助于我们设计安全的电路。
9. Wave Speed | 波速
All waves, whether water waves, sound waves or light waves, obey the same general relationship between speed, frequency and wavelength. This formula is fundamental to understanding how waves behave.
所有的波，无论是水波、声波还是光波，都遵循波速、频率和波长之间相同的基本关系。这个公式是理解波动行为的基础。
wave speed = frequency × wavelength v = f λ
v is wave speed in metres per second (m/s), f is frequency in hertz (Hz), and λ (lambda) is wavelength in metres (m). Frequency is the number of complete waves passing a point each second. If you double the frequency while keeping the wavelength constant, the wave speed doubles. This equation works for both transverse and longitudinal waves.
v 表示波速，单位是米每秒（m/s）；f 表示频率，单位是赫兹（Hz）；λ 表示波长，单位是米（m）。频率是每秒通过某一完整波的个数。在波长不变的情况下，频率加倍，波速也会加倍。这个公式既适用于横波，也适用于纵波。
10. Density | 密度
Density describes how much mass is packed into a given volume. Materials with high density feel heavy for their size, while those with low density feel light. Density is a property that can help identify substances.
密度描述了一定体积内所含质量的多寡。密度大的材料感觉更“沉”，密度小的则更“轻”。密度是可用于鉴别物质的重要属性之一。
density = mass / volume ρ = m / V
ρ (rho) is density in kilograms per metre cubed (kg/m³), m is mass in kg and V is volume in m³. Sometimes density is also given in g/cm³. For example, water has a density of about 1000 kg/m³ (or 1 g/cm³). Objects with density less than water will float; those with greater density will sink.
ρ 表示密度，单位是千克每立方米（kg/m³）；m 表示质量，单位是 kg；V 表示体积，单位是 m³。有时密度也用 g/cm³ 表示。例如，水的密度约为 1000 kg/m³（即 1 g/cm³）。密度比水小的物体会漂浮，密度比水大的会下沉。
11. Pressure | 压强
Pressure is a measure of how concentrated a force is over an area. When the same force is applied over a smaller area, the pressure is larger. This explains why sharp knives cut more easily and why nails have pointed ends.
压强表示力在面积上分布的集中程度。相同大小的力作用在更小的面积上时，产生的压强更大。这就解释了为什么锋利的刀具切东西更省力、钉子要做成尖头。
pressure = force / area p = F / A
p is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m²). One pascal equals one newton per square metre. Pressure in liquids increases with depth and can be calculated using p = ρ g h, where h is the depth of the liquid. However, at KS3 we focus mainly on the force-area relationship.
p 表示压强，单位是帕斯卡（Pa）；F 表示力，单位是牛顿（N）；A 表示受力面积，单位是平方米（m²）。1 Pa 等于 1 N/m²。液体压强随深度增加而增大，可以用 p = ρ g h 计算，其中 h 为液体深度。不过在 KS3 阶段，我们主要掌握力与面积的关系即可。
12. Moments | 力矩
A moment is the turning effect of a force. It explains how levers, see-saws and spanners work. For an object to be balanced, the sum of clockwise moments must equal the sum of anticlockwise moments about the pivot.
力矩是力产生的转动效应，它解释杠杆、跷跷板和扳手的工作原理。要使物体保持平衡，绕支点的顺时针力矩总和必须等于逆时针力矩总和。
moment of a force = force × perpendicular distance from pivot M = F d
M is the moment in newton metres (N m), F is force in newtons (N), and d is the perpendicular distance from the pivot to the line of action of the force in metres (m). When you increase the distance from the pivot, a smaller force can produce the same turning effect. This is why a long spanner is easier to use than a short one.
M 表示力矩，单位是牛顿·米（N m）；F 表示力，单位是牛顿（N）；d 表示从支点到力作用线的垂直距离，单位是米（m）。增大作用力到支点的距离，用较小的力就能产生同样的转动效果。这就是长扳手比短扳手更省力的原因。
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