📚 Year 11 CAIE Physics: Quick Reference Handbook of Formulas & Theorems | Year 11 CAIE 物理：公式定理速查手册
This handbook collates the essential formulas, theorems and principles for the CAIE IGCSE Physics (0625) syllabus – a rapid revision companion for Year 11 students. Every equation is presented with its units and a brief note on application, followed immediately by the Chinese equivalent to support bilingual learners.
本手册整理了 CAIE IGCSE 物理 (0625) 课程中的核心公式、定理与原理，是 Year 11 学生的快速复习伴侣。每个方程都配有单位和应用说明，并立即附上对应的中文解释，以便双语学习。
1. Kinematics – Motion in a Straight Line | 直线运动学
Kinematics deals with the description of motion without considering its causes. The four standard equations of uniformly accelerated motion are the backbone of this topic.
运动学只描述物体的运动，不涉及引起运动的原因。四个匀加速直线运动的基本方程是本节的核心。
v = u + at
Where v = final velocity (m/s), u = initial velocity (m/s), a = acceleration (m/s²), t = time (s).
其中 v 为末速度 (m/s)，u 为初速度 (m/s)，a 为加速度 (m/s²)，t 为时间 (s)。
s = ut + ½at²
Here s is the displacement (m). This formula gives the distance travelled under constant acceleration.
这里 s 代表位移 (m)。该公式用于计算匀加速直线运动中的位移。
v² = u² + 2as
Useful when time is not given. Always remember that acceleration can be negative (deceleration).
在时间未知时很有用。请牢记加速度可取负值（减速）。
average speed = total distance / total time
For non-uniform motion, this defines the overall rate of movement.
对于非匀速运动，此式定义了整体的运动快慢。
2. Forces and Newton’s Laws | 力与牛顿定律
Forces govern the interaction between objects. Newton’s three laws provide the framework for understanding resultant forces and equilibrium.
力支配着物体之间的相互作用。牛顿三定律为我们理解合力与平衡提供了框架。
F = ma
Newton’s Second Law. F is the resultant force in newtons (N), m is mass in kg, a is acceleration in m/s². This vector equation means acceleration is in the direction of the net force.
牛顿第二定律。F 为合力 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。这是一个矢量方程，加速度方向与合外力方向一致。
W = mg
Weight is the gravitational force on a mass. g is the gravitational field strength (≈ 9.8 N/kg on Earth).
重力是作用在物体上的万有引力。g 为重力场强度（地球表面约为 9.8 N/kg）。
Hooke’s Law: F = kx
Extension x (m) of a spring is directly proportional to the applied force F, up to the limit of proportionality. k is the spring constant (N/m).
弹簧的伸长量 x (m) 与外力 F 成正比，此关系在弹性限度内成立。k 为劲度系数 (N/m)。
Moment = Force × perpendicular distance from pivot
The principle of moments states that for a body in rotational equilibrium, total clockwise moment = total anticlockwise moment.
力矩 = 力 × 支点到力作用线的垂直距离。力矩原理指出，处于转动平衡的物体满足顺时针力矩之和等于逆时针力矩之和。
3. Momentum | 动量
Momentum helps analyse collisions and explosions. It is conserved in all isolated systems.
动量用于分析碰撞与爆炸过程，在任何孤立系统中动量守恒。
p = mv
Momentum p (kg·m/s) is the product of mass and velocity. It is a vector quantity.
动量 p (kg·m/s) 是质量与速度的乘积，为矢量。
F = Δp / Δt
Newton’s Second Law in terms of momentum: resultant force equals rate of change of momentum. This leads to the impulse equation.
用动量表述的牛顿第二定律：合力等于动量的变化率。由此可导出冲量方程。
Impulse = FΔt = Δ(mv)
Impulse (N·s) equals change in momentum. The area under a force–time graph gives impulse.
冲量 (N·s) 等于动量的变化量。力–时间图像下的面积表示冲量。
Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In the absence of external forces, total momentum before a collision equals total momentum after.
在没有外力作用时，碰撞前的总动量等于碰撞后的总动量。
4. Energy, Work and Power | 能量、功与功率
Energy can be stored or transferred. The principle of conservation of energy underpins all these calculations.
能量可以被储存或传递。能量守恒定律是所有这些计算的基础。
Work done = Fd cosθ
When a force moves an object through a displacement d in the direction of the force, work is done. In IGCSE, often θ = 0° and cosθ = 1. Unit: joule (J).
当力使物体沿力的方向移动一段位移 d 时，力做功。在 IGCSE 中，通常 θ = 0°，cosθ = 1。单位：焦耳 (J)。
Kinetic Energy: KE = ½mv²
Energy of a moving object.
物体由于运动而具有的能量。
Gravitational Potential Energy: GPE = mgh
Energy stored due to an object’s height h above a reference level.
物体因被举高 h 而储存的能量。
Efficiency = (useful energy output / total energy input) × 100%
Efficiency can also be calculated from power: (useful power output / total power input) × 100%.
效率也可用功率计算：（有用输出功率 / 输入总功率）× 100%。
Power = work done / time taken = energy transferred / time
Power P is measured in watts (W). 1 W = 1 J/s.
功率 P 的单位是瓦特 (W)。1 W = 1 J/s。
5. Pressure and Density | 压强与密度
Pressure is the force exerted per unit area. Density links mass and volume, and appears frequently in fluid statics.
压强是单位面积上受到的压力。密度将质量与体积联系起来，在流体静力学中经常出现。
Pressure p = F / A
Unit: pascal (Pa); 1 Pa = 1 N/m². The same force produces a higher pressure when the area is smaller.
单位：帕斯卡 (Pa)；1 Pa = 1 N/m²。相同作用力下，受力面积越小，压强越大。
Pressure in a liquid: p = ρgh
ρ = density (kg/m³), g = gravitational field strength, h = depth (m). This pressure acts equally in all directions at a given depth.
ρ 为液体密度 (kg/m³)，g 为重力场强度，h 为深度 (m)。在同一深度，液体向各个方向的压强相等。
Density ρ = m / V
Mass per unit volume. Units: kg/m³ or g/cm³.
单位体积的质量。单位：kg/m³ 或 g/cm³。
6. Thermal Physics | 热物理学
Temperature, heat and the behaviour of gases are governed by simple yet powerful relationships. Absolute temperature (kelvin) must be used in gas law calculations.
温度、热量和气体行为受一些简单而强大的关系支配。使用气体定律计算时必须采用绝对温度（开尔文）。
Specific heat capacity: Q = mcΔθ
Q is the thermal energy (J), m mass (kg), c specific heat capacity (J/(kg·°C) or J/(kg·K)), Δθ temperature change.
Q 为热量 (J)，m 为质量 (kg)，c 为比热容 (J/(kg·°C) 或 J/(kg·K))，Δθ 为温度变化。
Specific latent heat: Q = mL
During a change of state (melting/freezing, boiling/condensation), temperature stays constant. L is latent heat (J/kg).
在物态变化（熔化/凝固、沸腾/液化）过程中，温度保持不变。L 为潜热 (J/kg)。
Boyle’s Law: p₁V₁ = p₂V₁ (constant T)
For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.
对于一定质量的气体，在温度不变时，压强与体积成反比。
Charles’ Law: V₁/T₁ = V₂/T₂ (constant p)
Volume is directly proportional to absolute temperature when pressure is constant.
在压强不变时，体积与绝对温度成正比。
Pressure Law: p₁/T₁ = p₂/T₂ (constant V)
Pressure is directly proportional to absolute temperature at fixed volume.
在体积不变时，压强与绝对温度成正比。
Combined gas equation: pV/T = constant
For a fixed mass of gas, (p₁V₁)/T₁ = (p₂V₂)/T₂. Remember T must be in kelvin (K = °C + 273).
对于一定质量的气体，(p₁V₁)/T₁ = (p₂V₂)/T₂。注意温度单位必须为开尔文 (K = °C + 273)。
7. Wave Properties | 波的性质
Waves transfer energy without transferring matter. The universal wave equation links speed, frequency and wavelength.
波传递能量而不传递物质。通用波动方程将波速、频率和波长联系起来。
v = fλ
Wave speed v (m/s) = frequency f (Hz) × wavelength λ (m). This holds for all types of waves.
波速 v (m/s) = 频率 f (Hz) × 波长 λ (m)。此式适用于所有类型的波。
Frequency f = 1/T
The period T is the time for one complete oscillation (s).
周期 T 是完成一次全振动所需的时间 (s)。
For reflection, the angle of incidence equals the angle of reflection. Refraction obeys Snell’s law: n₁ sin i = n₂ sin r, but in IGCSE the qualitative relationships and critical angle calculations are key.
对于反射，入射角等于反射角。折射遵循斯涅尔定律：n₁ sin i = n₂ sin r，但 IGCSE 重点考察定性关系以及临界角的计算。
Critical angle: sin c = 1/n
n is the refractive index of the medium when light travels from the medium to air. Total internal reflection occurs when the angle of incidence exceeds the critical angle.
n 为光从该介质射向空气时的折射率。当入射角大于临界角时，发生全内反射。
8. Light and Lenses | 光与透镜
Lenses form real or virtual images. The magnification equation is essential for ray diagram verification.
透镜可成实像或虚像。放大率公式是验证光路图的重要工具。
Magnification = image height / object height = image distance / object distance
No sign convention is required in the core syllabus; use absolute distances for convex lens calculations.
核心课程中无需符号约定；凸透镜计算时使用绝对距离。
The principal focus of a converging lens is the point where rays parallel to the principal axis converge. For a diverging lens, they appear to diverge from the principal focus.
凸透镜的焦点是平行于主光轴的光线会聚的点。凹透镜的焦点是平行于主光轴的光线发散后反向延长线会聚的点。
9. Electricity and Circuits | 电与电路
Current, voltage and resistance are linked by Ohm’s law. Mastering series and parallel circuit rules is critical for problem-solving.
电流、电压和电阻由欧姆定律联系。掌握串联和并联电路的规律是解题的关键。
Ohm’s Law: V = IR
Potential difference V (V), current I (A), resistance R (Ω). Applies only when temperature remains constant.
电势差 V (V)、电流 I (A)、电阻 R (Ω)。仅在温度恒定条件下适用。
Resistance: R = V/I
The ratio of voltage to current defines resistance.
电压与电流之比定义为电阻。
Series circuits: Rₜₒₜ = R₁ + R₂ + …
Current is the same everywhere; the supply voltage divides across components.
电流处处相等；电源电压在各元件间分配。
Parallel circuits: 1/Rₜₒₜ = 1/R₁ + 1/R₂ + …
Voltage is the same across each branch; currents add up to the total current.
各支路电压相等；总电流为各支路电流之和。
Electrical power: P = IV = I²R = V²/R
Power in watts (W). The energy transferred is E = Pt = IVt.
功率单位为瓦特 (W)。消耗的电能 E = Pt = IVt。
10. Magnetism and Electromagnetism | 磁学与电磁学
Magnetic fields exert forces on moving charges and current-carrying conductors. Electromagnetic induction is the basis for generators and transformers.
磁场对运动电荷和载流导体会施加作用力。电磁感应是发电机与变压器的基础。
Motor effect force: F = BIL
F = force on a conductor (N), B = magnetic flux density (T), I = current (A), L = length of conductor in the field (m). The direction is given by Fleming’s left-hand rule.
F 为导体所受的力 (N)，B 为磁通密度 (T)，I 为电流 (A)，L 为导体在磁场中的长度 (m)。方向由弗莱明左手定则判定。
Transformer equation: Vₚ/Vₛ = Nₚ/Nₛ
For an ideal transformer, the ratio of primary to secondary voltage equals the turns ratio. Step-up (Nₛ > Nₚ) increases voltage; step-down does the opposite.
对于理想变压器，原、副线圈电压比等于匝数比。升压变压器 (Nₛ > Nₚ) 提高电压，降压变压器则相反。
Transformer power: IₚVₚ = IₛVₛ (ideal)
Since power is conserved, a higher voltage on the secondary side means a smaller current.
由于功率守恒，副边电压升高意味着电流减小。
11. Atomic and Nuclear Physics | 原子与核物理
Radioactive decay follows a statistical law. The half-life concept and equations for nuclear reactions are fundamental.
放射性衰变遵循统计规律。半衰期的概念以及核反应方程是基础。
Alpha decay: A decreases by 4, Z decreases by 2
Example: \u00B2\u00B3\u2078U\u2082\u2082 → \u00B2\u00B3\u2074Th\u2082\u2080 + \u00B2He\u2082. The emitted alpha particle is a helium nucleus.
例如：²³⁸U₉₂ → ²³⁴Th₉₀ + ⁴He₂。发射的 α 粒子是氦原子核。
Beta-minus decay: A unchanged, Z increases by 1
A neutron becomes a proton, emitting a β⁻ particle (electron) and an antineutrino.
一个中子转变成质子，发射出一个 β⁻ 粒子（电子）和一个反中微子。
Half-life: fraction remaining = (1/2)^n, n = number of half-lives
The time taken for the activity (or number of undecayed nuclei) to fall to half its initial value is constant for a given isotope.
给定同位素的活度（或未衰变原子核数）降至初始值一半所需的时间是恒定的。
Nuclear fission and fusion
Fission is the splitting of a heavy nucleus into two lighter nuclei, releasing energy. Fusion is the joining of light nuclei to form a heavier nucleus, which powers the Sun.
裂变是一个重核分裂成两个较轻的核并释放能量。聚变是轻核结合成更重的核，为太阳提供能量。
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