📚 Year 10 CAIE Physics: Formula & Theorem Quick Reference Handbook | 十年级 CAIE 物理：公式定理速查手册
This handbook provides a concise summary of the essential formulas and theorems required for the Year 10 CAIE Physics course. Each formula is clearly stated, and the key principles are explained in both English and Chinese to support bilingual learning and quick revision.
本手册简明扼要地总结了十年级 CAIE 物理课程必备的公式与定理。每条公式均清晰列出，核心原理以中英双语对照解释，便于双语学习与快速复习。
1. Motion and Kinematics | 运动与运动学
Average speed is the total distance travelled divided by the total time taken.
v = s ÷ t
平均速率等于总路程除以总时间。
Acceleration is the rate of change of velocity, calculated from the change in velocity over time.
a = (v – u) ÷ t
加速度是速度的变化率，等于速度变化量除以时间。
For uniformly accelerated motion, the final velocity squared is related to the initial velocity, acceleration, and displacement.
v² = u² + 2as
在匀加速直线运动中，末速度的平方等于初速度的平方加上 2 倍的加速度与位移的乘积。
Displacement during uniformly accelerated motion can be found using the product of average velocity and time, or from initial velocity, acceleration, and time.
s = ½(u + v)t = ut + ½at²
匀加速运动的位移可用平均速度乘时间求出，也可由初速度、加速度和时间计算。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s Second Law states that the resultant force acting on an object is equal to the product of its mass and acceleration.
F = m × a
牛顿第二定律表明，作用在物体上的合力等于物体的质量乘以加速度。
The weight of an object near the Earth’s surface is the gravitational force exerted on it, proportional to its mass.
W = m × g
物体在地表附近的重量是地球对它的引力，与质量成正比（g 取 9.8 N/kg 或 10 N/kg）。
Hooke’s Law describes the extension of a spring as directly proportional to the applied force, up to the limit of proportionality.
F = k × x
胡克定律指出，在弹性限度内，弹簧的伸长量与所受拉力成正比（k 为劲度系数）。
The moment (turning effect) of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action.
Moment = F × d
力对转轴的矩等于力与力臂（转轴到力作用线的垂直距离）的乘积。
For an object in equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments.
Σ Fcw dcw = Σ Facw dacw
物体平衡时，对于任意支点，顺时针力矩之和等于逆时针力矩之和。
3. Momentum | 动量
Momentum is the product of mass and velocity. It is a vector quantity.
p = m × v
动量是质量与速度的乘积，是一个矢量。
The impulse of a force equals the change in momentum of the object on which it acts.
F Δt = Δp = m(v – u)
冲量等于物体动量的变化量，即力与作用时间的乘积。
In a closed system, the total momentum before a collision or explosion is equal to the total momentum after the event.
m&sub1;u&sub1; + m&sub2;u&sub2; = m&sub1;v&sub1; + m&sub2;v&sub2;
在封闭系统中，碰撞或爆炸前后总动量守恒。
4. 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.
W = F × d
力对物体做的功等于力与物体在力的方向上移动的距离的乘积。
Kinetic energy is the energy possessed by a moving object due to its motion.
Ek = ½mv²
动能是物体由于运动而具有的能量，等于二分之一质量乘以速度的平方。
Gravitational potential energy is the energy stored in an object due to its position above the ground.
Ep = mgh
重力势能是物体因被举高而储存的能量，等于质量、重力加速度与高度的乘积。
Power is the rate at which work is done or energy is transferred.
P = W ÷ t = E ÷ t
功率是做功或能量转换的速率，等于功或能量除以时间。
Efficiency is the ratio of useful output energy (or power) to total input energy (or power), often expressed as a percentage.
Efficiency = (useful output ÷ total input) × 100%
效率是有用输出能量（或功率）与总输入能量（或功率）之比，常用百分数表示。
5. Density and Pressure | 密度与压强
Density is the mass per unit volume of a substance.
ρ = m ÷ V
密度是物质单位体积的质量。
Pressure is defined as the force acting per unit area.
p = F ÷ A
压强是单位面积上受到的压力。
The pressure exerted by a liquid column is proportional to its height, density, and the gravitational field strength.
p = h ρ g
液体压强等于液柱的高度、液体密度与重力加速度的乘积，与容器形状无关。
6. Thermal Physics | 热物理
Temperature is measured in degrees Celsius (°C) or Kelvin (K). The conversion between the two scales is given by:
T (K) = θ (°C) + 273
温度以摄氏度或开尔文度量，换算关系为 T (K) = θ (°C) + 273。
The thermal energy required to raise the temperature of a substance is directly proportional to its mass, specific heat capacity, and temperature change.
Q = m c Δθ
物质升温吸收的热量等于质量、比热容与温度变化量的乘积。
During a change of state, the thermal energy transferred does not change the temperature and is called latent heat.
Q = m L
物态变化时吸收或放出的热量称为潜热，等于质量与比潜热的乘积（L 为熔化比潜热或汽化比潜热）。
For a fixed mass of an ideal gas at constant temperature, pressure is inversely proportional to volume (Boyle’s Law).
pV = constant
一定质量的气体在温度不变时，压强与体积成反比（玻意耳定律）。
For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature (Charles’ Law).
V ÷ T = constant
一定质量的气体在压强不变时，体积与绝对温度成正比（查理定律）。
7. Wave Properties | 波的性质
The speed of a wave is the product of its frequency and wavelength. This applies to all types of waves.
v = f λ
波速等于频率与波长的乘积，适用于所有波动。
Frequency is the reciprocal of the period, which is the time taken for one complete oscillation.
f = 1 ÷ T
频率是周期的倒数，周期是完成一次全振动所需的时间。
The refractive index of a medium is the ratio of the sine of the angle of incidence in vacuum (or air) to the sine of the angle of refraction.
n = sin i ÷ sin r
介质的折射率等于真空中入射角的正弦与折射角的正弦之比。
The critical angle for total internal reflection is related to the refractive indices of the two media. When light passes from a denser to a less dense medium:
sin c = 1 ÷ n
全反射的临界角满足 sin c = 1/n（光从光密介质射向光疏介质时）。
8. Electricity | 电学
Electric charge is the product of current and time. The unit of charge is the coulomb (C).
Q = I t
电荷量等于电流与时间的乘积，单位为库仑。
Ohm’s Law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant.
V = I R
欧姆定律：在温度不变的条件下，导体中的电流与两端的电压成正比，电阻是比例常量。
Electrical power is the rate at which electrical energy is transferred, and can be expressed in several forms.
P = I V = I² R = V² ÷ R
电功率等于电流与电压的乘积，也等于 I²R 或 V²/R。
The electrical energy dissipated in a circuit component depends on power and time.
E = I V t
用电器消耗的电能等于电功率乘以时间，E = I V t。
For resistors connected in series, the total resistance is the sum of individual resistances.
Rtotal = R&sub1; + R&sub2; + …
串联电路的总电阻等于各分电阻之和。
For resistors connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
1 ÷ Rtotal = 1 ÷ R&sub1; + 1 ÷ R&sub2; + …
并联电路总电阻的倒数等于各支路电阻的倒数之和。
9. Magnetism and Electromagnetism | 磁学与电磁学
When a current-carrying conductor is placed in a magnetic field, it experiences a force whose direction is given by Fleming’s left-hand rule. The magnitude is:
F = B I L
通电导线在磁场中会受到力的作用，力的方向由左手定则判断，大小 F = BIL（导线与磁场垂直时）。
An ideal transformer changes the voltage of an alternating current according to the ratio of turns in the primary and secondary coils.
Vp ÷ Vs = Np ÷ Ns
理想变压器的电压比等于原副线圈的匝数比：Vp / Vs = Np / Ns。
For a 100% efficient transformer, input power equals output power, leading to an inverse relationship between voltage and current.
Vp Ip = Vs Is
理想变压器输入功率等于输出功率，因此电压与电流成反比。
10. Nuclear and Atomic Physics | 核物理与原子物理
Nuclear equations represent the changes in atomic nuclei during radioactive decay. Both mass number (upper) and proton number (lower) are conserved.
Alpha decay: ²³&sup8;₉₂U → ²³⁰₉₀Th + ⁴₂He
核反应方程表示放射性衰变中原子核的变化，质量数（上标）和质子数（下标）守恒。示例为 α 衰变：铀-238 衰变为钍-234 和 α 粒子（氦核）。
Beta decay involves the emission of an electron and an antineutrino, with the proton number increasing by one while the mass number remains unchanged.
¹⁰₂₆C → ¹⁰₃₇N + ⁰ₓ₇e + ν̅
β 衰变中，一个中子转变为质子和电子（β 粒子），质子数加 1，质量数不变。示例：碳-14 衰变为氮-14。
The half-life of a radioactive isotope is the time taken for half of the unstable nuclei in a sample to decay. The remaining fraction after n half-lives is:
Remaining fraction = (½)n
半衰期是放射性原子核有半数发生衰变所需的时间。经 n 个半衰期后未衰变的分数为 (½)n。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply