A-Level Physics: Core Formulas and Physical Quantities | A-Level 物理：核心公式与物理量关系梳理

📚 A-Level Physics: Core Formulas and Physical Quantities | A-Level 物理：核心公式与物理量关系梳理

Physics at A-Level is not about memorising isolated equations — it is about understanding how physical quantities relate to one another through fundamental laws. This guide consolidates the core formulas across the CIE syllabus into a structured revision map, connecting each equation to the concept it represents and the conditions under which it applies.

A-Level 物理不是靠死记硬背孤立的公式，而是要理解物理量如何通过基本定律相互联系。本指南将 CIE 考纲中的核心公式整合为一张结构化复习地图，把每个方程与它代表的概念及适用条件对应起来，帮助你在考试中快速、准确地调用。

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1. Kinematics: Describing Motion | 运动学：描述运动

The three SUVAT equations form the backbone of linear kinematics. They apply only to motion with constant acceleration, so always check this condition before substituting values.

三条 SUVAT 方程是直线运动学的核心。它们只适用于匀加速运动，代入数值前务必确认这一条件。

v = u + at

s = ut + ½at²

v² = u² + 2as

Here, u is initial velocity, v is final velocity, a is acceleration, t is time and s is displacement. These equations are vectors — direction matters, so assign a sign convention before solving.

其中 u 是初速度，v 是末速度，a 是加速度，t 是时间，s 是位移。这些都是矢量——方向很重要，解题前先规定正方向。

• For projectile motion, resolve into horizontal (constant velocity) and vertical (constant acceleration g) components.
• 抛体运动中，将运动分解为水平方向（匀速）和竖直方向（匀加速 g）两个分量。
• Velocity-time graph gradient gives acceleration; area under the graph gives displacement.
• 速度-时间图像的斜率给出加速度；图像与时间轴围成的面积给出位移。

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2. Dynamics: Forces and Newton's Laws | 动力学：力与牛顿定律

Newton' net force to the rate of change of momentum. For constant mass, this simplifies to F = ma.

牛顿第二定律将合外力与动量变化率联系起来。当质量恒定时，简化为 F = ma。

F = ma

F = Δp/Δt

specific force: W = mg, where g is the gravitational field strength (9.81 N kg⁻¹ on Earth's surface). Distinguish mass (scalar, kg) from weight (vector, N) — a common exam trap.

重力是一种特殊力：W = mg，其中 g 是重力场强度（地球表面约为 9.81 N kg⁻¹）。注意区分质量（标量，kg）和重量（矢量，N）——这是常见的考试陷阱。

• Newton's third law pairs act on different bodies — they never cancel each other.
• 牛顿第三定律中的作用力与反作用力作用在不同物体上——它们永远不会相互抵消。
• When analysing connected particles, draw separate free-body diagrams for each mass.
• 分析连接体问题时，对每个物体分别画受力分析图。

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3. Work, Energy and Power | 功、能量与功率

Work done is the product of force and displacement in the direction of the force. Energy is the capacity to do work, and the principle of conservation of energy governs all mechanical processes.

功等于力与沿力方向位移的乘积。能量是做功的本领，能量守恒定律支配所有力学过程。

W = Fd cos θ

KE = ½mv²

PE = mgh

P = W/t = Fv

useful for problems involving vehicles moving at constant speed against resistive forces.

功率是能量转移的速率。公式 P = Fv 特别适合处理车辆以恒定速度克服阻力行驶的问题。

• Efficiency = useful output energy ÷ total input energy (× 100%).
• 效率 = 有用输出能量 ÷ 总输入能量（× 100%）。
• In a closed system, total energy remains constant; energy may transform between kinetic, potential, thermal and other forms.
• 在封闭系统中，总能量保持不变；能量可以在动能、势能、内能及其他形式之间转化。

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4. Momentum and Collisions | 动量与碰撞

Momentum is a vector quantity defined as the product of mass and velocity. The principle of conservation of linear momentum states that total momentum remains constant in an isolated system.

动量是定义质量与速度乘积的矢量。动量守恒定律指出：孤立系统中总动量保持不变。

p = mv

In collisions, distinguish elastic (kinetic energy conserved) from inelastic (kinetic energy not conserved). For a perfectly inelastic collision, the objects stick together and move with a common velocity.

在碰撞中，区分弹性碰撞（动能守恒）与非弹性碰撞（动能不守恒）。完全非弹性碰撞中，物体粘在一起以共同速度运动。

• For two-body collisions: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (conservation of momentum).
• 两体碰撞中：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂（动量守恒）。
• Impulse FΔt equals the change in momentum — the area under a force-time graph.
• 冲量 FΔt 等于动量变化量——即力-时间图像下的面积。

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5. Circular Motion and Gravitation | 圆周运动与万有引力

Uniform circular motion requires a centripetal force directed toward the centre of the circle. This force changes the direction of velocity but not its magnitude.

匀速圆周运动需要指向圆心的向心力。这个力改变速度的方向，但不改变速度的大小。

a = v²/r = ω²r

F = mv²/r

F = GMm/r²

Newton' al force provides the required centripetal force, leading to the orbital speed formula v = √GM/r.

万有引力定律描述了两个质量之间的引力。对于轨道卫星，万有引力提供所需向心力，从而得出轨道速度公式 v = √GM/r。

• Kepler's third law: T² ∝ r³ for objects orbiting the same central mass.
• 开普勒第三定律：绕同一中心天体运动的物体满足 T² ∝ r³。
• Geostationary satellites have a period of 24 hours and orbit the equator in the same direction as Earth's rotation.
• 地球同步卫星的周期为 24 小时，在赤道上方与地球自转同向运行。

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6. Oscillations and Simple Harmonic Motion | 振动与简谐运动

Simple harmonic motion (SHM) occurs when acceleration is proportional to displacement and directed toward the equilibrium position. The mathematical description involves sinusoidal functions.

简谐运动发生在加速度与位移成正比且指向平衡位置的情况下。其数学描述涉及正弦函数。

a = -ω²x

x = A cos(ωt)

v_max = Aω

T = 2π√m/k (mass-spring)

T = 2π√l/g (simple pendulum)

For a mass-spring system, the period depends on mass and spring constant. For a simple pendulum, the period depends on length and gravitational field strength — notably independent of mass.

对弹簧振子，周期取决于质量和劲度系数。对单摆，周期取决于摆长和重力场强度——值得注意的是与质量无关。

• In SHM, energy continuously transforms between kinetic and potential forms; total energy remains constant for ideal systems.
• 简谐运动中，能量在动能与势能之间持续转化；理想系统中总能量守恒。
• Damping reduces amplitude over time; resonance occurs when driving frequency equals natural frequency.
• 阻尼使振幅随时间减小；当驱动力频率等于固有频率时发生共振。

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7. Waves and Superposition | 波动与叠加原理

Waves transfer energy without transferring matter. Key relationships link wave speed, frequency and wavelength.

波动传递能量而不传递物质。核心关系将波速、频率和波长联系起来。

v = fλ

The Doppler effect describes the apparent change in frequency when a wave source and observer move relative to each other. For sound waves, the observed frequency increases as the source approaches.

多普勒效应描述了波源与观察者相对运动时频率的表观变化。对声波而言，当波源靠近时观察到的频率增大。

f' = f(v + u₀)/(v - u_s) (moving source and observer)

e: constructive (path difference = nλ) and destructive (path difference = (n + ½)λ). Young's double-slit experiment gives fringe spacing x = λD/d.

叠加原理导致干涉：相长干涉（光程差 = nλ）和相消干涉（光程差 = (n + ½)λ）。杨氏双缝实验中条纹间距 x = λD/d。

• Stationary waves form at specific resonant frequencies; nodes are points of zero amplitude.
• 驻波在特定共振频率下形成；波节是振幅为零的点。
• For the diffraction grating: d sin θ = nλ.
• 对于衍射光栅：d sin θ = nλ。

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8. Electric Fields and Circuits | 电场与电路

Coulomb's law describes the force between point charges. The electric field strength is the force per unit charge, and the potential reflects the work done per unit charge.

库仑定律描述了点电荷之间的作用力。电场强度是单位电荷所受的力，电势反映单位电荷所做的功。

F = kQ₁Q₂/r² (k = 1/4πε₀)

E = F/q

E = V/d (uniform field)

For circuits, Ohm's law establishes the relationship between voltage, current and resistance. Resistivity characterises the material itself, independent of the conductor's dimensions.

对电路而言，欧姆定律建立了电压、电流和电阻之间的关系。电阻率描述材料本身的特性，与导体尺寸无关。

V = IR

R = ρL/A

P = VI = I²R = V²/R

• Resistors in series: R_total = R₁ + R₂ + ...; in parallel: 1/R_total = 1/R₁ + 1/R₂ + ...
• 串联电阻：R_total = R₁ + R₂ + ...；并联电阻：1/R_total = 1/R₁ + 1/R₂ + ...
• Kirchhoff's laws: junction rule (current conservation) and loop rule (voltage conservation).
• 基尔霍夫定律：节点规则（电流守恒）和回路规则（电压守恒）。
• A voltmeter has very high resistance; an ammeter has very low resistance.
• 电压表内阻很高；电流表内阻很低。

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9. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应

A moving charge in a magnetic field experiences the Lorentz force. The force on a current-carrying conductor follows Fleming's left-hand rule.

运动电荷在磁场中会受到洛伦兹力。载流导体所受的力遵循弗莱明左手定则。

F = BIL sin θ

F = qvB sin θ

Faraday's law states that the induced EMF equals the rate of change of magnetic flux linkage. Lenz's law determines the direction of induced current: it opposes the change that produced it.

法拉第定律指出：感应电动势等于磁通链的变化率。楞次定律确定感应电流的方向：感应电流总是阻碍引起它的磁通变化。

ε = -N(ΔΦ/Δt)

Φ = BA cos θ

• The transformer equation: V_s/V_p = N_s/N_p; for an ideal transformer, V_p I_p = V_s I_s.
• 变压器公式：V_s/V_p = N_s/N_p；理想变压器中 V_p I_p = V_s I_s。
• Magnetic flux is measured in webers (Wb); flux density in tesla (T = Wb m⁻²).
• 磁通量单位是韦伯（Wb）；磁感应强度单位是特斯拉（T = Wb m⁻²）。

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10. Thermal Physics and Ideal Gases | 热学与理想气体

Temperature is a measure of average kinetic energy of particles. The kinetic theory of gases connects macroscopic properties (pressure, volume, temperature) to molecular behaviour.

温度是粒子平均动能的量度。气体分子动理论将宏观量（压强、体积、温度）与分子行为联系起来。

pV = nRT (ideal gas equation)

pV = ⅓ Nm⟨c²⟩

⟨KE⟩ = (3/2)kT

Internal energy is the sum of potential and kinetic energies of all particles. For an ideal gas, internal energy depends only on temperature since there are no intermolecular forces.

内能是所有粒子势能与动能之和。对理想气体，由于无分子间作用力，内能仅取决于温度。

• Specific heat capacity relates energy input to temperature rise: Q = mcΔT.
• 比热容将能量输入与温度升高联系起来：Q = mcΔT。
• Latent heat: Q = mL, where L is the specific latent heat of fusion or vaporisation.
• 潜热：Q = mL，其中 L 是熔化或汽化的比潜热。

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11. Nuclear Physics and Radioactive Decay | 核物理与放射性衰变

Einstein' ding. The unified atomic mass unit (u) equals 1.66 × 10⁻²⁷ kg, corresponding to 931.5 MeV.

爱因斯坦的质能等价关系揭示了核结合能中蕴含的巨大能量。原子质量单位（u）等于 1.66 × 10⁻²⁷ kg，对应 931.5 MeV。

E = mc²

ΔE = Δmc² (binding energy)

ows first-order kinetics. The decay constant λ relates to half-life through t₁/₂ = ln 2/λ.

放射性衰变遵循一级动力学。衰变常数 λ 与半衰期的关系为 t₁/₂ = ln 2/λ。

N = N₀e^-λt

A = λN = A₀e^-λt

• Alpha decay reduces mass number by 4 and atomic number by 2; beta decay increases atomic number by 1; gamma emission involves excess energy release.
• α 衰变使质量数减 4、原子序数减 2；β 衰变使原子序数加 1；γ 辐射释放多余能量。
• Binding energy per nucleon indicates nuclear stability — iron-56 has the highest value.
• 每个核子的结合能反映核稳定性——铁-56 具有最高值。

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12. Quantum Physics | 量子物理

Photons are quanta of electromagnetic energy. The photoelectric effect demonstrates the particle nature of light: emission of electrons depends on photon energy exceeding the work function.

光子是电磁能量的量子。光电效应证明了光的粒子性：要使电子逸出，光子能量必须超过逸出功。

E = hf

hf = Φ + KE_max

KE_max = eV_stopping

The de Broglie hypothesis extends wave-particle duality to matter: every moving particle has an associated wavelength. This underlies electron diffraction experiments.

德布罗意假说将波粒二象性扩展到物质：每个运动粒子都有与之关联的波长。这是电子衍射实验的基础。

λ = h/p = h/mv

• Atomic energy levels are quantised; photon emission occurs when electrons transition from higher to lower energy states.
• 原子能级是量子化的；电子从高能级跃迁到低能级时发射光子。
• The uncertainty principle: ΔxΔp ≥ h/4π.
• 不确定性原理：ΔxΔp ≥ h/4π。

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