📚 Year 10 CAIE Physics: Quick Formula & Theorem Reference | Year 10 CAIE物理公式定理速查手册
This quick reference handbook collects the essential formulas, equations and key theorems required for the Year 10 CAIE Physics syllabus. Each section pairs a concise explanation in English with its Chinese equivalent, followed by the relevant mathematical expressions. Use this guide to revise effectively and to clarify how each law connects measurable quantities.
这本速查手册汇总了Year 10 CAIE物理课程所需的核心公式、方程和重要定理。每个小节先给出简明的英文讲解，再提供对应的中文释义，并列出相关的数学表达式。使用本手册可以有效复习，并帮助理清每条定律如何将可测量量联系在一起。
1. Kinematics | 运动学
Kinematics describes the motion of objects without reference to the forces causing it. For an object moving in a straight line with constant acceleration, four equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). These are often called the suvat equations.
运动学描述物体的运动而不涉及引发运动的力。对于在直线方向上做匀加速运动的物体，四个方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系在一起。这些方程常被称为 suvat 方程。
Equation 1 gives the final velocity after accelerating uniformly for time t.
方程1给出了匀加速时间 t 后的末速度。
v = u + at
Equation 2 gives the displacement when initial velocity, time and acceleration are known.
方程2给出了已知初速度、时间和加速度时的位移。
s = ut + ½at²
Equation 3 relates final velocity squared to initial velocity squared and displacement without using time.
方程3将末速度的平方与初速度的平方和位移联系起来，不涉及时间。
v² = u² + 2as
Equation 4 uses the average velocity to calculate displacement when time is known.
方程4利用平均速度在已知时间时计算位移。
s = ½(u + v)t
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s laws of motion are the foundation for understanding how forces affect motion. The first law describes inertia, while the second law quantifies the effect of a net force, and the third law deals with action–reaction pairs. Weight is a force caused by gravity acting on mass.
牛顿运动定律是理解力如何影响运动的基础。第一定律描述了惯性，第二定律量化了合力的作用，第三定律涉及作用力与反作用力对。重量是重力作用在质量上产生的力。
Newton’s second law states that the net force on an object equals its mass multiplied by its acceleration.
牛顿第二定律指出，物体受到的合力等于其质量乘以加速度。
F = m a
The weight of an object near the Earth’s surface is the product of mass and gravitational field strength (g). On Earth, g is approximately 9.8 N/kg or 10 N/kg for simplified calculations.
地球表面附近物体的重量等于质量与重力场强度 (g) 的乘积。地球上 g 约为 9.8 N/kg，简化计算时常取 10 N/kg。
W = m g
When two objects interact, the force exerted by object A on object B is equal in magnitude and opposite in direction to the force exerted by B on A. This is Newton’s third law.
当两个物体相互作用时，A 对 B 施加的力与 B 对 A 施加的力大小相等、方向相反。这就是牛顿第三定律。
3. Momentum | 动量
Momentum is the product of an object’s mass and its velocity. It is a vector quantity. The impulse–momentum theorem links the impulse of a force to the change in momentum, and the principle of conservation of momentum applies to closed systems with no external forces.
动量是物体质量与速度的乘积，是一个矢量。冲量–动量定理将力的冲量与动量的变化联系起来，而动量守恒定律适用于无外力的封闭系统。
Momentum p is defined as mass times velocity.
动量 p 定义为质量与速度的乘积。
p = m v
The impulse experienced by an object equals the average net force multiplied by the time during which it acts, and this equals the change in momentum.
物体受到的冲量等于平均合力乘以作用时间，也等于动量的变化量。
F Δt = Δp
In collisions and explosions where no external forces act, the total momentum before the event equals the total momentum after the event. This is the conservation of momentum.
在没有外力作用的碰撞和爆炸中，事件前的总动量等于事件后的总动量。这就是动量守恒。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force. Energy is the capacity to do work and can be stored as kinetic energy or gravitational potential energy. Power measures the rate of doing work or transferring energy.
当力使物体沿力的方向移动时，就做了功。能量是做功的本领，可以储存为动能或重力势能。功率衡量做功或能量传递的快慢。
Work done W equals the product of the force and the displacement moved in the direction of the force.
做的功 W 等于力与沿力方向的位移的乘积。
W = F d
Kinetic energy is the energy a body possesses due to its motion.
动能是物体由于运动而具有的能量。
Eₖ = ½mv²
Gravitational potential energy gained by an object raised through a height h is proportional to its mass, g and the height.
物体被举高 h 所增加的重力势能与质量、g 和高度成正比。
∆Eₚ = m g h
Power P is the work done per unit time, or the energy transferred per unit time.
功率 P 是单位时间内做的功，或是单位时间内转移的能量。
P = W / t
5. Density and Pressure | 密度和压强
Density describes how much mass is contained in a unit volume. Pressure quantifies how concentrated a force is over an area. In fluids, pressure increases with depth due to the weight of the fluid above.
密度描述单位体积内所含质量的多少。压强量化了力在面积上的集中程度。在流体中，由于上方流体的重量，压强随深度增加。
Density ρ is mass per unit volume.
密度 ρ 是质量除以体积。
ρ = m / V
Pressure acting on a surface is force per unit area.
作用在表面上的压强是单位面积上所受的力。
p = F / A
In a column of liquid of uniform density, the pressure at a depth h is given by the weight of the liquid above.
在密度均匀的液柱中，深度为 h 处的压强取决于上方液体的重量。
p = h ρ g
6. Thermal Physics | 热物理
When thermal energy is transferred to a substance, its temperature may rise or its state may change. Specific heat capacity describes the energy required to raise the temperature of 1 kg of a substance by 1 °C. Specific latent heat describes the energy needed to change the state of 1 kg without temperature change.
当热能传递给物质时，物质的温度可能升高或状态可能改变。比热容描述使 1 kg 物质温度升高 1 ℃ 所需的能量。比潜热描述使 1 kg 物质在不改变温度的情况下改变状态所需的能量。
Energy transferred for a temperature change Δθ is the product of mass, specific heat capacity c and the temperature change.
温度变化 Δθ 所传递的能量等于质量、比热容 c 与温度变化的乘积。
Q = m c Δθ
Energy transferred during a change of state at constant temperature is mass times specific latent heat L.
在恒定温度下发生状态变化时传递的能量等于质量乘以比潜热 L。
Q = m L
7. Waves | 波
Waves transfer energy without transferring matter. The speed of a wave is related to its frequency and wavelength. Frequency and period are reciprocals. These relationships apply to both mechanical and electromagnetic waves, including sound and light.
波传播能量但不转移物质。波速与频率和波长有关。频率和周期互为倒数。这些关系适用于机械波和电磁波，包括声波和光波。
Wave speed v equals frequency f multiplied by wavelength λ.
波速 v 等于频率 f 乘以波长 λ。
v = f λ
Frequency f is the reciprocal of the period T.
频率 f 是周期 T 的倒数。
f = 1 / T
8. Optics | 光学
When light passes from one transparent medium to another, it changes speed and direction. The refractive index n quantifies how much the light slows down and how much it bends. Total internal reflection occurs when the angle of incidence exceeds the critical angle for light traveling from a denser to a less dense medium.
当光从一种透明介质进入另一种时，速度和方向会发生改变。折射率 n 定量描述了光速减慢的程度以及光线的偏折程度。当光从光密介质射向光疏介质且入射角大于临界角时，就会发生全内反射。
Snell’s law relates the angle of incidence i and angle of refraction r to the refractive index n.
斯涅尔定律将入射角 i 和折射角 r 与折射率 n 联系起来。
n = sin i / sin r
Refractive index can also be found from the speed of light in vacuum c and the speed in the medium v.
折射率也可由真空中的光速 c 与介质中的光速 v 求出。
n = c / v
The critical angle c is the angle of incidence for which the angle of refraction is 90°. It is given by sin c = 1/n when the second medium is air or vacuum.
临界角 c 是使折射角为 90° 的入射角。当第二种介质为空气或真空时，sin c = 1/n。
sin c = 1 / n
9. Electricity | 电学
Electric circuits obey the laws of charge conservation and energy conservation. Ohm’s law links voltage, current and resistance for ohmic conductors. Power dissipated in a component can be expressed in several equivalent forms, and energy transfer is charge moved through a potential difference.
电路遵守电荷守恒和能量守恒定律。对于欧姆导体，欧姆定律将电压、电流和电阻联系起来。元件消耗的功率可以用几种等价形式表示，能量转移是电荷在电势差下的移动。
Ohm’s law: the potential difference V across a conductor is directly proportional to the current I through it, with resistance R as the constant of proportionality.
欧姆定律：导体两端的电势差 V 与通过它的电流 I 成正比，比例常数为电阻 R。
V = I R
Electrical power P can be calculated using current and voltage, or by substituting Ohm’s law.
电功率 P 可用电流和电压计算，也可代入欧姆定律变换形式。
P = I V
P = I² R
P = V² / R
Energy transferred E in a circuit is the product of power and time, or charge times voltage.
电路中转移的能量 E 是功率与时间的乘积，或是电荷乘以电压。
E = V I t
Charge Q is current multiplied by time.
电荷 Q 等于电流乘以时间。
Q = I t
For resistors in series, the total resistance is the sum of individual resistances.
电阻串联时，总电阻等于各电阻之和。
Rₜ = R₁ + R₂ + …
For resistors in parallel, the reciprocal of the total resistance is the sum of reciprocals of the individual resistances.
电阻并联时，总电阻的倒数等于各电阻倒数之和。
1/Rₜ = 1/R₁ + 1/R₂ + …
10. Electromagnetism | 电磁学
Transformers change the voltage of alternating current. An ideal transformer conserves power, so the product of voltage and current in the primary coil equals that in the secondary coil. The voltage ratio is related to the turns ratio.
变压器改变交流电的电压。理想变压器保持功率不变，因此初级线圈的电压与电流的乘积等于次级线圈的电压与电流的乘积。电压比与匝数比相关。
For an ideal transformer, the ratio of primary voltage Vp to secondary voltage Vs equals the ratio of the number of turns on the primary coil Np to the number on the secondary coil Ns.
对于理想变压器，初级电压 Vp 与次级电压 Vs 之比等于初级线圈匝数 Np 与次级线圈匝数 Ns 之比。
Vp / Vs = Np / Ns
Under ideal conditions (100% efficiency), input power equals output power, so the current is inversely proportional to the voltage.
在理想情况下（100% 效率），输入功率
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