📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook brings together all the key equations and principles you need for Year 8 Cambridge Physics. Each topic is presented with the fundamental relationship, its standard symbols and the practical meaning behind it – so you can revise quickly and confidently before tests and exams.
本手册汇集了 Year 8 剑桥物理所需的所有核心公式与定理。每个主题都给出了基本关系式、常用符号和实际含义，帮助你在测试和考试前快速、自信地复习。
1. Speed | 速度
Speed is the distance travelled per unit time. The average speed of an object is calculated by dividing the total distance by the total time taken.
速度是单位时间内通过的路程。物体的平均速度等于总路程除以所用的总时间。
v = s / t
where v is the speed (m/s), s is the distance travelled (m) and t is the time taken (s). This formula works for uniform motion; for changing speeds, it gives the average speed.
其中 v 表示速度（米/秒），s 是运动距离（米），t 是所用时间（秒）。该公式适用于匀速运动；对于变速运动，它给出平均速度。
2. Acceleration | 加速度
Acceleration tells us how quickly the velocity of an object changes. It is defined as the change in velocity per unit time.
加速度描述物体速度变化的快慢，定义为单位时间内速度的变化量。
a = (v − u) / t
where a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is the time taken for the change (s). A negative value indicates deceleration.
其中 a 是加速度（米/秒²），v 是末速度（米/秒），u 是初速度（米/秒），t 是变化所用的时间（秒）。负值表示减速。
3. Density | 密度
Density measures how much mass is packed into a given volume. It is a characteristic property of a material and does not depend on the size of the sample.
密度衡量单位体积内所含物质的质量，是材料的一种特性，与样品大小无关。
ρ = m / V
where ρ (rho) is density (kg/m³ or g/cm³), m is mass (kg or g) and V is volume (m³ or cm³). Solids are usually denser than liquids, and liquids denser than gases.
其中 ρ（rho）是密度（千克/米³ 或 克/厘米³），m 是质量（千克或克），V 是体积（米³ 或 厘米³）。固体通常比液体密，液体比气体密。
4. Pressure | 压强
Pressure is the force acting perpendicularly on a unit area. It explains why sharp objects cut easily and why wide tyres do not sink into soft ground.
压强是垂直作用在单位面积上的力。它解释了为什么尖锐物体容易切割，以及为什么宽轮胎不会陷入软地面。
P = F / A
where P is pressure (N/m² or Pa), F is the force (N) perpendicular to the surface and A is the area (m²) over which the force is spread. A larger area reduces pressure for the same force.
其中 P 是压强（牛/米² 或帕斯卡），F 是垂直于表面的力（牛），A 是力散布的面积（米²）。相同力下，面积越大压强越小。
5. Moment of a Force | 力矩
A moment is the turning effect of a force about a pivot. It depends on both the size of the force and its distance from the pivot.
力矩是力对支点的转动效应，取决于力的大小和力到支点的垂直距离。
moment = F × d
where F is the applied force (N) and d is the perpendicular distance from the pivot to the line of action of the force (m). The unit is newton metre (N·m). Equilibrium occurs when the total clockwise moment equals the total anticlockwise moment.
其中 F 是作用力（牛），d 是从支点到力作用线的垂直距离（米）。单位是牛·米（N·m）。当顺时针力矩之和等于逆时针力矩之和时，系统达到平衡。
6. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object. The amount of work transfers energy from one store to another.
力使物体移动时就做了功。功的大小等于能量从一个储存库转移到另一个储存库的量。
W = F × s
where W is work done (J), F is the force applied in the direction of motion (N) and s is the distance moved in that direction (m). Power is the rate of doing work:
其中 W 是做功（焦耳），F 是运动方向上的力（牛），s 是沿该方向移动的距离（米）。功率是做功的速率：
P = W / t or P = E / t
where P is power (W), W or E is energy transferred (J) and t is time (s). 1 watt = 1 joule per second.
其中 P 是功率（瓦特），W 或 E 是转化或传递的能量（焦耳），t 是时间（秒）。1 瓦特 = 1 焦耳/秒。
7. Ohm’s Law and Resistance | 欧姆定律与电阻
Ohm’s law relates the current through a conductor to the voltage across it, provided temperature remains constant.
欧姆定律描述了在温度不变的条件下，通过导体的电流与两端电压之间的关系。
V = I × R
where V is potential difference (V), I is current (A) and R is resistance (Ω). Resistance opposes the flow of charge; a higher resistance gives a smaller current for the same voltage.
其中 V 是电压（伏特），I 是电流（安培），R 是电阻（欧姆）。电阻阻碍电荷流动；电压相同时，电阻越大电流越小。
8. Electrical Power | 电功率
Electrical power tells us how much electrical energy is transferred per second in a circuit component.
电功率表示电路元件每秒转化电能的多少。
P = I × V
where P is power (W), I is current (A) and V V). This formula can be combined with Ohm’s law to give P = I²R or P = V²/R for resistors.
其中 P 是功率（瓦特），I 是电流（安培），V 是电压（伏特）。此式结合欧姆定律可得出电阻的功率公式 P = I²R 或 P = V²/R。
9. Wave Speed | 波速
The speed of a wave depends on its frequency and wavelength. This relationship applies to sound, light and water waves.
波速由波的频率和波长决定，适用于声波、光波和水波等。
v = f × λ
where v is wave speed (m/s), f is frequency (Hz) and λ (lambda) is wavelength (m). When waves enter a new medium, frequency stays the same; speed and wavelength change.
其中 v 是波速（米/秒），f 是频率（赫兹），λ（lambda）是波长（米）。波进入新介质时，频率不变，波速和波长改变。
10. Weight and Gravitational Force | 重量与重力
Weight is the force of gravity acting on an object’s mass. It is different from mass, which measures the amount of matter and stays the same everywhere.
重量是地球（或其他天体）引力对物体质量的作用力。它与质量不同，质量是物体所含物质的量，处处相同。
W = m × g
where W is weight (N), m is mass (kg) and g is gravitational field strength (about 9.8 N/kg on Earth, often rounded to 10 N/kg for calculations). Remember: weight is a force; mass is a scalar.
其中 W 是重量（牛），m 是质量（千克），g 是引力场强度（地球上约 9.8 牛/千克，计算时常取 10 牛/千克）。记住：重量是一种力；质量是标量。
11. Hooke’s Law | 胡克定律
Hooke’s law describes the stretch of a spring under a load, as long as the elastic limit is not exceeded.
胡克定律描述了在不超过弹性限度时，弹簧的伸长量与载荷之间的线性关系。
F = k × x
where F is the force applied to the spring (N), k is the spring constant (N/m) measuring stiffness, and x is the extension (m) from its original length. A stiffer spring has a larger k.
其中 F 是施加在弹簧上的力（牛），k 是弹簧常数（牛/米），表示弹簧的劲度，x 是弹簧的伸长量（米）。弹簧越硬，k 值越大。
12. Conservation of Energy | 能量守恒
Energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed. The total energy of a closed system remains constant.
能量可以被有效传递、储存或散失，但不能被创造或消灭。孤立系统的总能量保持不变。
The principle is expressed as: total energy input = useful energy output + wasted energy. Efficiency is calculated by:
其原理可表示为：输入总能量 = 有用输出能量 + 浪费的能量。效率计算如下：
efficiency = (useful output energy / total input energy) × 100%
This concept appears in every energy topic – thermal, kinetic, electrical, light and sound. Sankey diagrams visually represent the energy transfers and highlight useful vs wasted energy.
这一概念贯穿所有能量主题——热、动能、电、光和声。桑基图直观展示能量传递过程并对比有用能量与浪费的能量。
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