📚 Year 9 Cambridge Physics Formula and Theorem Quick Reference | 九年级剑桥物理公式定理速查手册
This handbook collects the essential formulas, principles and units that appear throughout the Year 9 Cambridge Physics curriculum. It serves as a rapid revision tool, reminding you of the mathematical relationships behind density, motion, forces, energy, electricity and waves. Use it alongside your class notes and past questions to build confidence and accuracy.
本手册汇集了九年级剑桥物理课程中出现的核心公式、原理和单位。它是一份快速复习工具，可帮助你回忆密度、运动、力、能量、电学和波动背后的数学关系。配合课堂笔记和历年试题使用，能有效提升信心与解题准确性。
1. Density | 密度
Density (ρ) is the mass per unit volume of a substance. It describes how tightly matter is packed.
密度（ρ）是物质单位体积的质量，表示物质排列的紧密程度。
ρ = m / V
The standard unit of density is kilogram per cubic metre (kg/m³). For convenience, gram per cubic centimetre (g/cm³) is also used.
密度的标准单位是千克每立方米（kg/m³），为方便也常用克每立方厘米（g/cm³）。
1 g/cm³ = 1000 kg/m³. For example, the density of pure water is 1.0 g/cm³ or 1000 kg/m³.
1 g/cm³ = 1000 kg/m³。例如，纯水的密度为 1.0 g/cm³ 或 1000 kg/m³。
2. Speed and Acceleration | 速度与加速度
Speed is the distance travelled per unit time. It is a scalar quantity.
速度是单位时间内移动的距离，是标量。
v = d / t
The SI unit of speed is metre per second (m/s). Average speed is total distance divided by total time.
速度的国际单位是米每秒（m/s）。平均速度等于总距离除以总时间。
Acceleration is the rate of change of velocity. It is a vector quantity; an object accelerates if its speed or direction changes.
加速度是速度变化的快慢，是矢量；物体速度大小或方向改变即产生加速度。
a = (v - u) / t
Here u is initial velocity, v is final velocity, and t is the time taken. The unit is m/s².
其中 u 为初速度，v 为末速度，t 为所用时间。单位为 m/s²。
3. Force, Mass and Weight | 力、质量与重量
Newton's second law states that the net force (resultant force) acting on an object is equal to its mass multiplied by its acceleration.
牛顿第二定律指出，作用在物体上的合外力等于质量乘以加速度。
F = m × a
Force is measured in newtons (N). One newton accelerates a mass of 1 kg by 1 m/s².
力的单位是牛顿（N）。1 N 可使 1 kg 物体产生 1 m/s² 的加速度。
Weight is the gravitational force acting on a mass. It depends on the local gravitational field strength (g).
重量是作用在质量上的引力，与当地重力场强度（g）有关。
W = m × g
On Earth, g is approximately 9.8 N/kg (often rounded to 10 N/kg). Weight is a force, so its unit is also the newton.
地球表面 g 约为 9.8 N/kg（常取 10 N/kg）。重量是力，单位也是牛顿。
4. Pressure | 压强
Pressure measures how concentrated a force is over an area. A large force on a small area produces high pressure.
压强表示力作用在面积上的集中程度。大力作用在小面积上会产生高压强。
P = F / A
pascal (Pa), where 1 Pa = 1 N/m². Pressure increases if force increases or area decreases.
压强的国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。增大作用力或减小受力面积都会增大压强。
5. Moments | 力矩
A moment is the turning effect of a force about a pivot. It depends on the size of the force and the perpendicular distance from the pivot.
力矩是力绕支点的转动效果，取决于力的大小和从支点到力作用线的垂直距离。
M = F × d
The unit of moment is newton metre (N m). For an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
力矩单位是牛·米（N m）。物体处于转动平衡时，顺时针力矩之和等于逆时针力矩之和。
6. Hooke's Law | 胡克定律
For an elastic material, the extension is directly proportional to the applied force, provided the elastic limit is not exceeded.
对弹性材料，只要不超过弹性限度，伸长量与所施加的力成正比。
F = k × x
Where k is the spring constant (stiffness) in N/m, and x is the extension in metres. A stiffer spring has a larger k.
其中 k 是弹簧常数（刚度），单位为 N/m，x 是伸长量，单位为米。弹簧越硬，k 值越大。
7. Work Done | 做功
Work is done when a force causes a displacement in the direction of the force. Energy is transferred.
力使物体沿力的方向发生位移时即做功，能量发生转移。
W = F × d
Work is measured in joules (J). 1 joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.
功的单位是焦耳（J）。1 J 是指 1 N 的力使物体沿力方向移动 1 m 所做的功。
8. Power | 功率
Power is the rate at which work is done or energy is transferred.
功率是做功或能量转移的速率。
P = W / t = E / t
the watt (W), where 1 W = 1 J/s. A more powerful machine does the same work in less time.
功率的单位是瓦特（W），1 W = 1 J/s。功率越大的机器在越短时间内做等量的功。
9. Efficiency | 效率
Efficiency describes how much of the total input energy is converted into useful output energy. No device is 100% efficient because some energy is always dissipated.
效率表示输入总能量有多少转化为有用输出能量。由于总有能量散失，没有设备能达到 100% 效率。
η = (useful output / total input) × 100%
Efficiency can be expressed as a fraction or as a percentage. Reducing friction and heat losses improves efficiency.
效率可用分数或百分数表示。减少摩擦和热量损失可提高效率。
10. Ohm's Law and Resistance | 欧姆定律与电阻
For a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference (voltage) across it.
对温度恒定的金属导体，通过它的电流与两端电势差（电压）成正比。
V = I × R
V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). Resistance opposes the flow of charge.
V 为电压（伏特 V），I 为电流（安培 A），R 为电阻（欧姆 Ω）。电阻阻碍电荷流动。
Resistors connected in series share the same current. The total resistance is the sum of the individual resistances.
串联电阻电流相同，总电阻等于各电阻之和。
Rtotal = R₁ + R₂ + R₃ + ...
Resistors connected in parallel share the same voltage. The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
并联电阻电压相同，总电阻的倒数等于各电阻倒数之和。
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
11. Wave Equation | 波动方程
All waves transfer energy without transferring matter. The speed of a wave is related to its frequency and wavelength.
所有波动传递能量而不传递物质。波速与频率和波长有关。
v = f × λ
v is the wave speed in m/s, f is the frequency in hertz (Hz), and λ (lambda) is the wavelength in metres.
v 为波速（m/s），f 为频率（Hz），λ（拉姆达）为波长（m）。
Sound waves travel at about 340 m/s in air at room temperature. The frequency determines the pitch; the amplitude determines the loudness.
室温下声波在空气中传播速度约为 340 m/s。频率决定音调高低，振幅决定响度。
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