📚 IB AQA Physics Formula Handbook | IB AQA 物理：公式汇总手册
This comprehensive handbook compiles the essential formulas you need to master for the IB AQA Physics course. Use it as your quick-reference guide while solving problems, revising key topics, and preparing for exams. Each section focuses on a core area of the syllabus, presenting the most frequently examined equations with clear notation and brief contextual notes.
这本全面的手册汇总了你在 IB AQA 物理课程中必须掌握的核心公式。你可以将它作为解题、复习重点以及备考时的快速参考指南。每一节聚焦考纲的一个核心领域，列出最常考的方程，并配以清晰的符号说明和简要的语境注释。
1. Waves | 波
The speed of a wave is linked to its frequency and wavelength. This fundamental relationship applies to all wave types, including sound, water, and light travelling through a medium.
波速与频率和波长相关。这一基本关系适用于所有类型的波，包括声波、水波以及在介质中传播的光波。
v = f λ
- v = wave speed / 波速 (m s⁻¹)
- f = frequency / 频率 (Hz)
- λ = wavelength / 波长 (m)
Snell's law describes how a wave bends when it passes from one medium into another with a different refractive index. It is crucial for understanding lenses, optical fibres, and phenomena such as total internal reflection.
斯涅耳定律描述了波从一种介质进入另一种具有不同折射率的介质时如何发生弯曲。这对于理解透镜、光纤以及全内反射等现象至关重要。
n₁ sinθ₁ = n₂ sinθ₂
- n₁, n₂ = refractive indices / 折射率
- θ₁ = angle of incidence / 入射角
- θ₂ = angle of refraction / 折射角
For a single-slit diffraction experiment, the angle to the first minimum gives information about the wavelength of the light and the width of the slit. The formula is used to demonstrate the wave nature of light.
对于单缝衍射实验，第一级暗纹的角度反映了光的波长和缝宽的信息。该公式用于展示光的波动性。
θ ≈ λ / b
- θ = angle to first minimum / 第一级暗纹的角度 (rad)
- b = slit width / 缝宽 (m)
2. Electricity and Circuits | 电与电路
Ohm's law defines the relationship between potential difference, current, and resistance for an ohmic conductor at constant temperature. It is the starting point for most DC circuit analysis.
欧姆定律定义了在温度恒定时，欧姆导体两端电势差、电流和电阻之间的关系。它是大多数直流电路分析的起点。
V = I R
- V = potential difference / 电势差 (V)
- I = current / 电流 (A)
- R = resistance / 电阻 (Ω)
Power dissipated in a circuit component can be calculated using any of three equivalent forms. These are essential for analyzing energy transfer and efficiency in electrical systems.
电路元件消耗的功率可以用三个等效公式中的任意一个来计算。这些公式对于分析电系统中的能量传递和效率至关重要。
P = V I = I² R = V² / R
- P = power / 功率 (W)
When resistors are combined in series or parallel, their total resistance changes predictably. These rules help simplify complex circuits.
当电阻串联或并联组合时，其总电阻的变化有规律可循。这些规则有助于简化复杂电路。
| Series / 串联 | Rtotal = R₁ + R₂ + R₃ + ... |
| Parallel / 并联 | 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ... |
3. Mechanics | 力学
The SUVAT equations model motion under uniform acceleration in a straight line. They are used to solve problems involving free fall, vehicle braking, and projectile trajectories.
SUVAT 方程对匀加速直线运动进行建模。它们用于解决涉及自由落体、车辆制动和抛体轨迹的问题。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
- s = displacement / 位移 (m)
- u = initial velocity / 初速度 (m s⁻¹)
- v = final velocity / 末速度 (m s⁻¹)
- a = acceleration / 加速度 (m s⁻²)
- t = time / 时间 (s)
Newton's second law quantifies how the net force on an object produces acceleration. It is a vector law, meaning direction must always be considered.
牛顿第二定律量化了物体的净力如何产生加速度。这是一个矢量定律，意味着必须始终考虑方向。
F = m a
- F = net force / 净力 (N)
- m = mass / 质量 (kg)
Momentum is conserved in all isolated systems, making it a powerful tool for analyzing collisions and explosions. The impulse-momentum theorem links force to the rate of change of momentum.
动量在所有孤立系统中守恒，这使其成为分析碰撞和爆炸的强大工具。动量定理将力与动量的变化率联系起来。
p = m v
F Δt = Δp
- p = momentum / 动量 (kg m s⁻¹)
- Δt = time interval / 时间间隔 (s)
Work done by a force is the product of the force and the displacement in its direction. Kinetic and gravitational potential energy are two key mechanical energy stores.
力做的功是力与其方向上位移的乘积。动能和重力势能是两种关键的机械能储存。
W = F s cosθ
Ek = ½ m v²
ΔEp = m g Δh
- W = work done / 功 (J)
- Ek = kinetic energy / 动能 (J)
- ΔEp = change in gravitational potential energy / 重力势能变化量 (J)
- g = gravitational field strength / 重力场强度 (9.81 N kg⁻¹)
4. Thermal Physics | 热物理
The specific heat capacity determines how much energy is needed to raise the temperature of a material. Latent heat describes the energy needed for a phase change without a change in temperature.
比热容决定了使材料升温所需的能量。潜热描述的是在温度不变的情况下发生相变所需的能量。
Q = m c ΔT
Q = m L
- Q = thermal energy / 热量 (J)
- c = specific heat capacity / 比热容 (J kg⁻¹ K⁻¹)
- ΔT = temperature change / 温度变化 (K 或 °C)
- L = specific latent heat / 比潜热 (J kg⁻¹)
The ideal gas law connects the macroscopic state variables of a gas: pressure, volume, temperature, and amount. It is built upon the assumptions of kinetic theory.
理想气体定律将气体的宏观状态变量——压强、体积、温度和数量联系起来。它是建立在动力学理论假设之上的。
p V = n R T
- p = pressure / 压强 (Pa)
- V = volume / 体积 (m³)
- n = number of moles / 摩尔数 (mol)
- R = molar gas constant / 摩尔气体常数 (8.31 J mol⁻¹ K⁻¹)
- T = absolute temperature / 绝对温度 (K)
5. Circular Motion and Gravitation | 圆周运动与引力
An object moving in a circular path experiences an acceleration directed towards the centre, which is sustained by a centripetal force. The linear velocity remains constant in magnitude but changes continuously in direction.
沿圆周路径运动的物体会产生指向圆心的加速度，该加速度由向心力维持。线速度的大小保持不变，但方向不断变化。
a = v² / r = ω² r
F = m v² / r = m ω² r
- a = centripetal acceleration / 向心加速度 (m s⁻²)
- F = centripetal force / 向心力 (N)
- v = linear speed / 线速度 (m s⁻¹)
- ω = angular speed / 角速度 (rad s⁻¹)
- r = radius / 半径 (m)
Newton's law of gravitation describes the attractive force between any two masses. In a uniform radial field, the gravitational field strength follows an inverse-square law.
牛顿万有引力定律描述了任意两个质量之间的吸引力。在均匀辐射场中，重力场强度遵循平方反比定律。
F = G M m / r²
g = F / m = G M / r²
- G = gravitational constant / 引力常量 (6.67 × 10⁻¹¹ N m² kg⁻²)
- M, m = masses / 质量 (kg)
- g = gravitational field strength / 重力场强度 (N kg⁻¹)
6. Nuclear and Quantum Physics | 核与量子物理
Einstein's famous mass-energy equivalence shows that mass can be converted into energy and vice versa. This principle underpins nuclear fission, fusion, and particle-antiparticle annihilation.
爱因斯坦著名的质能等价关系表明质量可以转化为能量，反之亦然。这一原理是核裂变、核聚变以及正反粒子湮灭的基础。
E = m c²
- E = energy / 能量 (J)
- c = speed of light in a vacuum / 真空中光速 (3.00 × 10⁸ m s⁻¹)
The radioactive decay law predicts the number of undecayed nuclei after a given time. Half-life is the time taken for half the radioactive nuclei in a sample to decay.
放射性衰变定律预测给定时间后尚未衰变的原子核数量。半衰期是样本中一半放射性原子核发生衰变所需的时间。
N = N₀ e−λt
A = λ N
T½ = ln 2 / λ
- N = number of undecayed nuclei / 未衰变原子核数
- N₀ = initial number / 初始数量
- λ = decay constant / 衰变常数 (s⁻¹)
- A = activity / 活度 (Bq)
- T½ = half-life / 半衰期 (s)
The energy of a photon is directly proportional to its frequency. This formula bridges the wave and particle models of light and is critical for explaining the photoelectric effect and atomic spectra.
光子的能量与其频率成正比。该公式连接了光的波动模型与粒子模型，对于解释光电效应和原子光谱至关重要。
E = h f = h c / λ
- h = Planck constant / 普朗克常数 (6.63 × 10⁻³⁴ J s)
7. Electromagnetic Induction | 电磁感应
Faraday's law and Lenz's law together describe how a changing magnetic flux induces an emf. The induced emf opposes the change that caused it, a principle essential for understanding generators and transformers.
法拉第定律和楞次定律共同描述了变化的磁通量如何感应出电动势。感应电动势会阻碍产生它的变化，这一原理对于理解发电机和变压器至关重要。
ε = − N ΔΦ / Δt
- ε = induced emf / 感应电动势 (V)
- N = number of turns / 匝数
- Φ = magnetic flux / 磁通量 (Wb)
- ΔΦ/Δt = rate of change of flux / 磁通量变化率 (Wb s⁻¹)
Magnetic flux is the product of the magnetic flux density and the area it penetrates, taking into account the angle of penetration. The force on a current-carrying wire in a magnetic field is given by the motor effect formula.
磁通量是磁通量密度与其穿透面积的乘积，并考虑了穿透角度。载流导线在磁场中所受的力由电动机效应公式给出。
Φ = B A cosθ
F = B I L sinθ
- B = magnetic flux density / 磁通量密度 (T)
- A = area / 面积 (m²)
- L = length of conductor in field / 在磁场中的导体长度 (m)
8. Oscillations | 振动
Simple harmonic motion occurs when the restoring force is directly proportional to displacement and acts towards the equilibrium position. The time period formulas for a mass-spring system and a simple pendulum are frequently examined.
当回复力与位移成正比并指向平衡位置时，物体做简谐运动。弹簧振子和单摆的周期公式经常被考查。
a = − ω² x
T = 2π√m/k
T = 2π√L/g
- x = displacement from equilibrium / 相对平衡位置的位移 (m)
- T = period / 周期 (s)
- k = spring constant / 弹簧常数 (N m⁻¹)
- L = pendulum length / 摆长 (m)
9. Fields and Potentials | 场与势
The electric force between two point charges follows an inverse-square law analogous to gravitation. Electric field strength is defined as the force per unit charge, and the potential energy in a uniform field depends on the separation of the charges.
两点电荷之间的电力遵循与引力类似的平方反比定律。电场强度定义为单位电荷所受的力，而均匀电场中的势能取决于电荷的间距。
F = k Q q / r²
E = F / q = k Q / r²
V = W / q
E = V / d
- k = Coulomb constant / 库仑常数 (8.99 × 10⁹ N m² C⁻²)
- Q, q = charges / 电荷 (C)
- E = electric field strength / 电场强度 (N C⁻¹ 或 V m⁻¹)
- V = potential difference / 电势差 (V)
- d = separation between plates / 板间距 (m)
10. Energy Production and Transfer | 能量产生与传递
Efficiency measures how much of the input energy or power is usefully transferred. The albedo and emissivity influence the black-body radiation power emitted from a surface, which is key to understanding Earth's energy balance.
效率衡量了输入能量或功率中有多少被有效转移。反照率和发射率影响了表面发射的黑体辐射功率，这是理解地球能量平衡的关键。
η = (useful output / total input) × 100%
P = e σ A T⁴
- η = efficiency / 效率 (%)
- e = emissivity / 发射率 (0 to 1)
- σ = Stefan-Boltzmann constant / 斯特藩-玻尔兹曼常数 (5.67 × 10⁻⁸ W m⁻² K⁻⁴)
- T = absolute temperature / 绝对温度 (K)
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