📚 Year 9 CAIE Physics Quick Reference Handbook: Formulas & Principles | Year 9 CAIE 物理公式定理速查手册
This handbook provides a concise collection of key formulas and principles for Year 9 CAIE Physics. Designed as a revision tool, it covers motion, forces, energy, thermal physics, waves, optics, electricity and magnetism. Each section presents essential equations with clear explanations to help you master the syllabus and solve problems efficiently.
本手册为 Year 9 CAIE 物理课程汇集了关键公式与定理的简明总结，是一份高效的复习工具，涵盖运动、力、能量、热学、波、光学、电学和磁学等内容。每个部分提供核心方程与概念，并附有清晰解释，助你掌握考纲要点并高效解题。
1. Motion: Speed, Velocity and Acceleration | 运动：速率、速度与加速度
Speed is a scalar quantity that describes how fast an object moves. Average speed v is the total distance s divided by the total time t taken. Velocity is a vector; it is the rate of change of displacement and includes direction. Acceleration a is the rate of change of velocity, calculated as the change in velocity divided by time.
v = s / t
速率是标量，描述物体运动快慢。平均速率 v 等于总路程 s 除以总时间 t。速度为矢量，是位移随时间的变化率，具有方向。加速度 a 是速度的变化率，等于速度变化量除以时间。
a = (v – u) / t
其中 u 为初速度，v 为末速度，t 为时间。加速度的方向与速度变化方向相同。
When acceleration is constant, three equations of uniformly accelerated motion link initial velocity u, final velocity v, acceleration a, displacement s and time t.
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
当加速度恒定时，三个匀加速运动方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系在一起。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s first law states that an object remains at rest or moves with constant velocity unless acted upon by a resultant force. Newton’s second law defines the relationship between force, mass and acceleration. Newton’s third law expresses that for every action there is an equal and opposite reaction.
牛顿第一定律：若物体不受外力或所受合力为零，则保持静止或匀速直线运动。牛顿第二定律定义了力、质量与加速度的关系。牛顿第三定律表明，每一个作用力都有一个大小相等、方向相反的反作用力。
The resultant force F acting on an object is equal to the product of its mass m and its acceleration a. Weight W is the gravitational force on a mass, where g is the gravitational field strength (approximately 9.8 m/s² on Earth).
F = m × a
W = m × g
物体所受的合力 F 等于其质量 m 与加速度 a 的乘积。重量 W 是作用在质量上的重力，g 为重力场强度（地球上约为 9.8 N/kg）。
3. Momentum | 动量
Momentum p is the product of an object’s mass and its velocity. It is a vector quantity, pointing in the same direction as the velocity. The law of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision or explosion, provided no external forces act.
p = m × v
动量 p 等于物体的质量与速度的乘积，是矢量，方向与速度相同。动量守恒定律指出，在没有外力作用的封闭系统中，碰撞或爆炸前后的总动量保持不变。
4. Energy, Work and Power | 能量、功和功率
Energy exists in many forms, and it can be transferred or transformed but never destroyed – the principle of conservation of energy. Kinetic energy (KE) is the energy of motion, and gravitational potential energy (GPE) is the energy stored due to an object’s height above a reference level.
能量有多种形式，可以转移或转化，但不可创造或消灭——即能量守恒定律。动能 (KE) 是物体由于运动而具有的能量，重力势能 (GPE) 是物体因被举高而储存的能量。
KE = ½ m v²
GPE = m g h
其中 m 为质量，v 为速度，g 为重力场强度，h 为高度。
Work W is done when a force moves an object. Power P is the rate of doing work. Efficiency compares useful energy output to total energy input.
W = F × d
P = W / t
Efficiency = (useful energy output / total energy input) × 100%
功 W 等于力 F 与在力方向上移动的距离 d 的乘积。功率 P 为做功的快慢。效率指有用能量输出与总能量输入的百分比。
5. Density and Pressure | 密度与压强
Density ρ is the mass per unit volume of a substance. Pressure p is the force acting perpendicularly per unit area. In a liquid, pressure increases with depth due to the weight of the fluid above.
ρ = m / V
p = F / A
p = ρ g h (in a liquid)
密度 ρ 是物质单位体积的质量。压强 p 是垂直作用在单位面积上的力。在液体中，压强随深度增加，p = ρ g h，其中 h 为深度，ρ 为液体密度，g 为重力场强度。
6. Thermal Properties | 热学性质
When a substance is heated, its temperature rise depends on its mass, specific heat capacity c, and the energy supplied. The specific heat capacity is the energy required to raise the temperature of 1 kg of the substance by 1 °C. During a change of state (melting, boiling), energy is absorbed or released without a change in temperature; this is called latent heat.
当物体吸热时，其温度升高取决于质量、比热容 c 及所供能量。比热容是使 1 kg 物质温度升高 1 °C 所需的能量。在物态变化（熔化、沸腾）过程中，物质吸收或放出能量而温度不变，这部分能量称为潜热。
Q = m c Δθ
Q = m L
Q 为热量，m 为质量，c 为比热容，Δθ 为温度变化，L 为比潜热（熔化或汽化）。
7. Waves | 波
A wave transfers energy without transferring matter. The speed v of a wave is related to its frequency f and wavelength λ. Frequency is the number of complete oscillations per second and is the reciprocal of the period T.
v = f λ
f = 1 / T
波传播能量而不传递物质。波速 v 与频率 f 和波长 λ 相关：v = f λ。频率为每秒振动的次数，是周期 T 的倒数。
8. Optics | 光学
When light passes from one medium to another, it changes speed and direction – refraction. Snell’s law relates the angles of incidence i and refraction r to the refractive indices n of the two media.
n₁ sin i = n₂ sin r
当光从一种介质进入另一种介质时，速度与方向改变——折射。斯涅耳定律将入射角 i 和折射角 r 与两种介质的折射率 n 联系起来。
For a thin lens, the focal length f, object distance u and image distance v are connected by the lens equation. Linear magnification m is the ratio of image height to object height, equal to v/u.
1 / f = 1 / u + 1 / v
m = v / u
对于薄透镜，焦距 f、物距 u 和像距 v 满足薄透镜公式。线性放大率 m 为像高与物高之比，也等于 v / u。
9. Electricity | 电学
Ohm’s law states that the current I through a conductor is directly proportional to the potential difference V across it, provided temperature remains constant. Resistance R is the ratio of voltage to current. Electrical power P can be expressed in several forms.
V = I × R
P = I V = I² R = V² / R
欧姆定律指出，在温度不变时，通过导体的电流 I 与两端电压 V 成正比。电阻 R 等于电压与电流之比。电功率 P 有多种表示法。
The total charge Q passing a point is the product of current and time. In series circuits, resistances add; in parallel circuits, the reciprocal of total resistance equals the sum of the reciprocals of individual resistances.
Q = I t
Rₜ (series) = R₁ + R₂ + …
1/Rₜ (parallel) = 1/R₁ + 1/R₂ + …
通过导体截面的电荷 Q 等于电流与时间的乘积。串联电路中总电阻等于各电阻之和；并联电路中总电阻的倒数等于各支路电阻倒数之和。
10. Magnetism and Electromagnetism | 磁学与电磁学
A current-carrying conductor creates a magnetic field. In an ideal transformer, the ratio of the primary voltage Vₚ to the secondary voltage Vₛ equals the ratio of the number of turns Nₚ to Nₛ.
Vₚ / Vₛ = Nₚ / Nₛ
载流导体在其周围产生磁场。在理想变压器中，原边电压 Vₚ 与副边电压 Vₛ 之比等于原副线圈匝数 Nₚ 与 Nₛ 之比。
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