📚 Year 9 CAIE Physics: Formula & Theorem Quick Revision Handbook | Year 9 CAIE 物理：公式定理速查手册
This handbook gathers the essential formulas, laws and theorems you need for Year 9 CAIE Physics. Use it for quick checks, last‑minute revision and to build confidence before your assessments.
本手册汇集了 Year 9 CAIE 物理课程所需的关键公式、定律与定理。适合在测验前快速查阅、冲刺复习，帮助你巩固核心概念。
1. Motion and Speed | 运动与速度
The speed of an object tells us how fast it is moving. Average speed is the total distance travelled divided by the total time taken. When an object covers equal distances in equal intervals of time, it moves at constant speed.
速度描述物体运动的快慢。平均速度等于总路程除以总时间。若物体在相等的时间间隔内通过相等的距离，则它做匀速运动。
average speed = total distance / total time or v = d / t
On a distance–time graph, a straight line represents constant speed. The slope (gradient) of the line equals the speed. A horizontal line means the object is stationary.
在距离–时间图像中，直线表示匀速运动，其斜率（梯度）等于速度的大小；水平线表示物体静止。
2. Acceleration and Force | 加速度与力
Acceleration is the rate of change of velocity. When an object speeds up, slows down or changes direction, it accelerates. The formula involves the change in velocity and the time taken.
加速度是速度变化的快慢。物体加速、减速或改变方向时都具有加速度。用速度的变化量除以时间可以计算加速度。
a = (v − u) / t
where v is final velocity, u is initial velocity and t is time. A resultant force causes acceleration. Newton's second law links force, mass and acceleration.
其中 v 是末速度，u 是初速度，t 是时间。合力使物体产生加速度，牛顿第二定律给出了力、质量与加速度的关系。
F = m a
Weight is the gravitational force on a mass. Near the Earth's surface the gravitational field strength g is approximately 10 m/s².
重量是作用在物体质量上的引力。靠近地球表面，引力场强度 g 约为 10 米每二次方秒。
W = m g
Newton's first law states that an object remains at rest or moves with constant velocity unless a resultant force acts on it.
牛顿第一定律指出，若无合力作用，物体将保持静止或匀速直线运动状态。
3. Mass, Weight and Density | 质量、重量与密度
Mass is the amount of matter in an object, measured in kilograms (kg). Weight is a force caused by gravity, measured in newtons (N). Density describes how much mass is packed into a given volume.
质量是物体所含物质的多少，单位为千克 (kg)。重量是引力引起的力，单位为牛顿 (N)。密度表示单位体积内所含的质量。
density = mass / volume or ρ = m / V
An object floats if its density is less than the density of the fluid it is placed in. The standard unit of density is kg/m³, but g/cm³ is also common in the lab.
物体的密度小于所在流体的密度时会上浮。密度的国际单位是千克每立方米 (kg/m³)，实验室也常用克每立方厘米 (g/cm³)。
4. Pressure and Moments | 压强与力矩
Pressure is the force acting per unit area. A sharp edge exerts greater pressure because the force is concentrated on a small area.
压强是单位面积上承受的压力。接触面越小，同样大小的力产生的压强越大。
p = F / A
The unit of pressure is the pascal (Pa), equivalent to 1 N/m². In liquids, pressure increases with depth and acts in all directions.
压强的单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。在液体中，压强随深度增加且向各个方向传递。
The moment of a force (turning effect) depends on the size of the force and the perpendicular distance from the pivot.
力矩（力的转动效应）与力的大小和支点到力作用线的垂直距离有关。
moment = force × perpendicular distance or M = F d
A lever balances when the clockwise moments equal the anticlockwise moments. This is the principle of moments.
当顺时针力矩等于逆时针力矩时，杠杆平衡，这就是力矩原理。
5. Energy, Work and Power | 能量、功与功率
Work is done when a force moves an object in the direction of the force. Energy is the ability to do work; both are measured in joules (J).
力使物体沿力的方向移动时做功。能量是做功的能力，两者单位都是焦耳 (J)。
W = F d
Kinetic energy is the energy of motion. Gravitational potential energy (GPE) is stored when an object is raised above the ground.
动能是物体由于运动而具有的能量。重力势能是物体被举高后储存的能量。
KE = ½ m v² and GPE = m g h
In a closed system with no friction, energy is conserved. Total energy before a change equals total energy after.
在无摩擦的封闭系统中能量守恒，变化前后的总能量相等。
Power is the rate of doing work or transferring energy. A more powerful device transfers energy in a shorter time.
功率是做功或转移能量的快慢。功率越大的装置在相同时间内转移的能量越多。
P = W / t or P = E / t
6. Properties of Waves | 波的基本性质
Waves transfer energy without transferring matter. In transverse waves (e.g. light, water ripples) vibrations are perpendicular to the direction of travel. In longitudinal waves (e.g. sound) vibrations are parallel.
波传递能量而不传递物质。横波（如光、水波）振动方向与传播方向垂直；纵波（如声波）振动方向与传播方向平行。
The wave equation links speed, frequency and wavelength. Frequency is the number of complete waves passing a point per second, measured in hertz (Hz).
波速公式将波速、频率和波长联系起来。频率是每秒通过某点的完整波个数，单位为赫兹 (Hz)。
v = f λ
The period T is the time for one complete wave. It is the reciprocal of frequency.
周期 T 是一个完整波所经历的时间，它是频率的倒数。
f = 1 / T
Reflection, refraction and diffraction are wave behaviours. The law of reflection states that the angle of incidence equals the angle of reflection.
反射、折射和衍射是波的常见行为。反射定律指出入射角等于反射角，即 i = r。
7. Sound | 声
Sound is a longitudinal wave that requires a medium to travel. In air at room temperature, its speed is about 340 m/s. The echo method uses reflection of sound.
声音是一种需要介质传播的纵波，室温下空气中的声速约为 340 m/s。回声法利用了声音的反射。
distance = speed × time / 2 (for an echo)
Pitch depends on frequency: higher frequency gives a higher pitch. Loudness depends on amplitude.
音调由频率决定，频率越高音调越高；响度由振幅决定。
8. Light | 光
medium. Its speed in a vacuum is approximately 3.0 × 10⁸ m/s, the fastest possible speed.
光在同一均匀介质中沿直线传播。真空中的光速约为 3.0 × 10⁸ 米/秒，是宇宙中最快的速度。
The law of reflection applies to light: the angle of incidence equals the angle of reflection, measured from the normal.
光的反射定律：入射角等于反射角，均自法线量起。
i = r
When light passes from one transparent medium to another, it changes speed and bends. This is refraction. A ray entering a denser medium slows down and bends towards the normal.
光从一种透明介质进入另一种时，速度改变并发生偏折，这就是折射。进入光密介质时，光线减速并向法线偏折。
9. Charge, Current and Voltage | 电荷、电流与电压
Electric charge is measured in coulombs (C). Current is the rate of flow of charge. In a metal wire, current is a flow of electrons.
电荷的单位是库仑 (C)。电流是电荷流动的快慢。金属导线中，电流是电子的定向移动。
I = Q / t or Q = I t
Voltage (potential difference) is the energy transferred per unit charge. It drives current through a circuit.
电压（电势差）是单位电荷转移的能量，它推动电流在电路中流动。
V = E / Q
In a series circuit, current is the same everywhere. In a parallel circuit, the total current is the sum of the branch currents.
串联电路中电流处处相等；并联电路中，干路电流等于各支路电流之和。
10. Resistance and Circuits | 电阻与电路
Resistance measures how much a component opposes the flow of current. Ohm's law states that, at constant temperature, the current through a resistor is directly proportional to the voltage across it.
电阻衡量元件对电流的阻碍作用。欧姆定律指出，在温度不变时，通过导体的电流与它两端的电压成正比。
R = V / I
The total resistance in a series circuit is the sum of individual resistances. In a parallel circuit, the reciprocal of the total resistance equals the sum of the reciprocals.
串联电路的总电阻等于各电阻之和；并联电路中，总电阻的倒数等于各电阻倒数之和。
Rtotal = R₁ + R₂ + … (series)
1/Rtotal = 1/R₁ + 1/R₂ (parallel)
Electrical power is the rate at which electrical energy is transferred. It can be calculated using current and voltage.
电功率是电流做功的快慢，可用电流和电压计算。
P = I V also P = I² R
Energy transferred by an electrical device depends on power and time. The kilowatt‑hour is a common unit of energy for mains electricity.
用电器消耗的电能由功率和时间决定。千瓦时是家庭用电中常见的能量单位。
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