📚 Edexcel Physics: Last-Minute Revision Notes | 爱德思物理：考前冲刺笔记
These concise revision notes cover the essential concepts, equations and common pitfalls across the Edexcel A Level Physics syllabus. Use them to consolidate key topics rapidly before your exam, focusing on the most frequently assessed ideas in mechanics, materials, waves, electricity, particle physics, fields, thermodynamics, oscillations, gravitation and astrophysics. Each section pairs an English explanation with its Chinese equivalent so you can reinforce understanding in both languages.
这份精华冲刺笔记覆盖了Edexcel A Level物理考纲的核心概念、公式和常见易错点。考前可用它快速回顾重点，聚焦力学、材料、波、电学、粒子物理、场、热力学、振动、引力和天体物理等高频考点。每部分均采用中英文对照讲解，帮助你在双语环境中巩固理解。
1. Mechanics: Kinematics & Dynamics | 力学：运动学与动力学
The four suvat equations describe uniformly accelerated motion: v = u + at, s = ut + 1/2 at², v² = u² + 2as, s = 1/2 (u+v)t. Always choose a positive direction and assign signs consistently. For free-fall near Earth’s surface, acceleration due to gravity g = 9.81 m s⁻² acts downwards.
四个 suvat 方程描述匀加速运动：v = u + at，s = ut + ½at²，v² = u² + 2as，s = ½(u+v)t。务必选定正方向并统一符号。在地表附近自由落体时，重力加速度 g = 9.81 m s⁻²，方向向下。
Projectile motion is analysed by separating horizontal and vertical components. Horizontally, velocity is constant (a = 0). Vertically, the object accelerates at g. Time of flight links both components and is the key to solving projectile problems. Use s = ut + ½at² and v = u + at separately.
分析抛体运动时需分解水平和竖直分量。水平方向速度恒定（加速度为零），竖直方向以 g 加速。飞行时间是连接两分量的关键，解题时独立运用 s = ut + ½at² 和 v = u + at。
Newton’s second law, F = ma, gives net force proportional to acceleration. Momentum p = mv is conserved in isolated systems. Impulse = FΔt = Δp, equal to area under a force–time graph. In collisions, whether elastic or inelastic, total momentum is conserved, but kinetic energy is only conserved in perfectly elastic collisions.
牛顿第二定律 F = ma 表明合力与加速度成正比。动量 p = mv 在孤立系统中守恒。冲量 = FΔt = Δp，等于力-时间图下的面积。无论是弹性还是非弹性碰撞，总动量均守恒，但动能仅在完全弹性碰撞中守恒。
2. Materials | 材料
Hooke’s law states that extension ΔL is proportional to applied force F up to the limit of proportionality: F = kΔL, where k is the stiffness constant. Stress σ = F/A, strain ε = ΔL/L. Young’s modulus E = σ/ε = (FL)/(AΔL). The elastic limit is the point beyond which permanent deformation occurs.
胡克定律指出在比例极限内，伸长量 ΔL 与外力 F 成正比：F = kΔL，k 为劲度系数。应力 σ = F/A，应变 ε = ΔL/L。杨氏模量 E = σ/ε = (FL)/(AΔL)。超过弹性极限后材料发生永久形变。
Stress–strain graphs reveal material properties: a steep linear region gives high Young’s modulus; the area under the graph relates to elastic potential energy stored per unit volume, E = ½σε for linear region. For a ductile material like copper, a large plastic region appears before fracture. For a brittle material, fracture occurs soon after the elastic limit. The energy stored in an elastic spring is E = ½FΔL = ½k(ΔL)².
应力-应变图可揭示材料性质：陡峭的线性区表明杨氏模量大；曲线下的面积与单位体积储存的弹性势能相关，线性区有 E = ½σε。韧性材料（如铜）在断裂前有较大塑性区；脆性材料在弹性极限后很快断裂。弹簧中储存的弹性能为 E = ½FΔL = ½k(ΔL)²。
3. Waves | 波
Wave speed v = fλ, period T = 1/f. Transverse waves oscillate perpendicular to energy transfer (e.g. light); longitudinal waves oscillate parallel (e.g. sound). Polarisation is only possible for transverse waves and provides evidence for their nature.
波速 v = fλ，周期 T = 1/f。横波振动方向与能量传播方向垂直（如光）；纵波振动方向与之平行（如声）。只有横波才能偏振，偏振现象是横波的证据。
Refraction obeys Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. Refractive index n = c/v. Total internal reflection occurs when the angle of incidence exceeds the critical angle C, where sin C = 1/n (for light leaving the denser medium). Optical fibres use this principle.
折射遵循斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂。折射率 n = c/v。当入射角大于临界角 C 时发生全内反射，sin C = 1/n（光从光密介质射出）。光纤就利用了该原理。
Two-source interference for light: fringe spacing Δx = λL/d (double-slit), where d is slit separation and L is distance to screen. Diffraction grating: d sin θ = nλ, where n is the order number. Sharper, brighter maxima are obtained. A white-light grating spectrum shows a continuous rainbow with central white maximum.
光的双源干涉：条纹间距 Δx = λL/d（双缝），d 为缝间距，L 为到屏距离。衍射光栅：d sin θ = nλ，n 为级次。光栅产生更锐利明亮的最大值。白光光栅光谱呈现连续彩虹，中央为白色极大。
4. Electricity | 电学
Current I = ΔQ/Δt. Potential difference V = W/Q. Ohm’s law V = IR holds for ohmic conductors at constant temperature. Resistance R = ρL/A, where ρ is resistivity. I–V characteristics: ohmic conductor gives straight line through origin; filament lamp curves as temperature rises; diode conducts only in forward bias after threshold voltage.
电流 I = ΔQ/Δt，电势差 V = W/Q。欧姆定律 V = IR 在恒温下适用于欧姆导体。电阻 R = ρL/A，ρ 为电阻率。I-V 特性：欧姆导体为过原点直线；灯丝随温度升高而弯曲；二极管仅在正向偏置超过阈值电压后导通。
In series circuits, current is constant, voltage is divided. In parallel, voltage is constant, current divides. Kirchhoff’s first law: Σ I_in = Σ I_out (charge conservation). Second law: Σ e.m.f. = Σ IR around any closed loop (energy conservation). Emf ε = I(R + r), where r is internal resistance. Lost volts = Ir. Power P = IV = I²R = V²/R.
串联电路中电流处处相等、电压分配；并联电路中电压相等、电流分配。基尔霍夫第一定律：流入节点电流 = 流出节点电流（电荷守恒）。第二定律：任意闭合回路中 Σ 电动势 = Σ IR（能量守恒）。电动势 ε = I(R + r)，r 为内阻，内阻压降为 Ir。功率 P = IV = I²R = V²/R。
5. Particle Physics & Nuclear Physics | 粒子物理与核物理
An atom consists of a nucleus containing protons and neutrons (nucleons) surrounded by electrons. Nuclide notation: ᴬZX, where A = mass number, Z = atomic number, X = symbol. Isotopes share the same Z but differ in A. The strong nuclear force binds nucleons at short range.
原子由含质子和中子（核子）的原子核及核外电子构成。核素符号：ᴬZX，A 为质量数，Z 为原子序数，X 为元素符号。同位素 Z 相同而 A 不同。强相互作用力在极短程内约束核子。
Radioactive decay: α-decay reduces Z by 2, A by 4 (⁴₂He nucleus). β⁻ decay: neutron → proton + electron + anti-electron-neutrino, Z increases by 1. β⁺ decay: proton → neutron + positron + electron-neutrino, Z decreases by 1. γ radiation is an electromagnetic wave, often accompanying α/β decay; no change in A or Z. In all decays, mass–energy, charge, momentum and nucleon number are conserved.
放射性衰变：α 衰变使 Z 减少 2、A 减少 4（放出 ⁴₂He 核）。β⁻ 衰变：中子 → 质子 + 电子 + 反电子中微子，Z 增加 1。β⁺ 衰变：质子 → 中子 + 正电子 + 电子中微子，Z 减少 1。γ 辐射是电磁波，常伴随 α/β 衰变，不改变 A 或 Z。所有衰变均遵守质能、电荷、动量和核子数守恒。
Activity A = λN, where λ is decay constant, N is number of undecayed nuclei. Half-life T₁/₂ = ln2/λ. Exponential decay: N = N₀ e⁻λt. The quark model: hadrons (baryons: 3 quarks, e.g. proton uud, neutron udd; mesons: quark–antiquark). Leptons (e.g. electron, neutrino) experience weak interaction. In β⁻ decay, a down quark changes to an up quark: d → u + e⁻ + ν̅ₑ.
放射性活度 A = λN，λ 为衰变常数，N 为未衰变核子数。半衰期 T₁/₂ = ln2/λ。指数衰变规律：N = N₀ e⁻λt。夸克模型：强子（重子：3 个夸克，如质子 uud、中子 udd；介子：夸克-反夸克对）。轻子（如电子、中微子）参与弱相互作用。β⁻ 衰变中下夸克变为上夸克：d → u + e⁻ + ν̅ₑ。
6. Electric & Magnetic Fields | 电场与磁场
Coulomb’s law: F = (1/4πε₀) Q₁Q₂/r². Electric field strength E = F/q (unit: N C⁻¹ or V m⁻¹). For a uniform field between parallel plates, E = V/d. For a point charge, E = (1/4πε₀) Q/r². Electric potential V = (1/4πε₀) Q/r in a radial field; uniform field: ΔV = Ed. Equipotential surfaces are perpendicular to field lines.
库仑定律：F = (1/4πε₀) Q₁Q₂/r²。电场强度 E = F/q（单位：N C⁻¹ 或 V m⁻¹）。平行板间均匀电场：E = V/d。点电荷电场：E = (1/4πε₀) Q/r²。电势：径向场 V = (1/4πε₀) Q/r；均匀场中 ΔV = Ed。等势面与电场线处处垂直。
A magnetic field exerts a force on a current-carrying conductor: F = BIL sin θ, where θ is angle between B and I. For a moving charge: F = BQv sin θ. Fleming’s left-hand rule gives direction. Charged particles in uniform B follow circular paths: BQv = mv²/r, radius r = mv/(BQ).
磁场对载流导线施加力：F = BIL sin θ，θ 为 B 与 I 夹角。运动电荷受力：F = BQv sin θ。用左手定则判定方向。带电粒子在匀强磁场中做圆周运动：BQv = mv²/r，半径 r = mv/(BQ)。
Faraday’s law: induced e.m.f. ε = -N dΦ/dt, where magnetic flux Φ = BA cos θ. Lenz’s law states that the induced current opposes the change producing it, explaining the negative sign. A transformer changes voltages: Vₛ/Vₚ = Nₛ/Nₚ. For an ideal transformer, primary power ≈ secondary power: IₚVₚ = IₛVₛ. Efficiency losses arise from eddy currents, hysteresis and copper losses.
法拉第电磁感应定律：感应电动势 ε = -N dΦ/dt，磁通量 Φ = BA cos θ。楞次定律表明感应电流的方向总是阻碍引起感应的变化，解释了负号。变压器改变电压：Vₛ/Vₚ = Nₛ/Nₚ。理想变压器输入功率约等于输出功率：IₚVₚ = IₛVₛ。涡流、磁滞和铜损导致效率下降。
7. Thermodynamics & Kinetic Theory | 热力学与分子动力论
The first law of thermodynamics, as commonly used in Edexcel, is ΔU = Q – W, where ΔU is increase in internal energy, Q is heat supplied to the system, and W is work done BY the system. For a gas expanding at constant pressure, W = pΔV. If work is done ON the system, the sign of W changes accordingly.
Edexcel 教材常用的热力学第一定律表达为 ΔU = Q – W。ΔU 是内能增加量，Q 为系统吸收的热量，W 为系统对外做的功。恒压膨胀时，W = pΔV。若外界对系统做功，W 符号作相应变化。
Ideal gas equation: pV = nRT = NkT, where R = 8.31 J mol⁻¹ K⁻¹, k = 1.38 × 10⁻²³ J K⁻¹. Kinetic theory links: pV = ⅓N m⟨c²⟩, hence average translational kinetic energy ½ m⟨c²⟩ = (3/2) kT. The root-mean-square speed cᵣₘₛ = √(⟨c²⟩).
理想气体状态方程：pV = nRT = NkT，R = 8.31 J mol⁻¹ K⁻¹，k = 1.38 × 10⁻²³ J K⁻¹。分子动力论给出：pV = ⅓N m⟨c²⟩，因此平均平动动能 ½ m⟨c²⟩ = (3/2) kT。均方根速率 cᵣₘₛ = √(⟨c²⟩)。
Specific heat capacity: Q = mcΔθ. Specific latent heat: Q = mL (fusion or vaporisation). In a heating experiment, electrical power IV is assumed to transfer entirely to the substance, but cooling corrections are often needed. An adiabatic process occurs with no heat exchange (Q = 0), so ΔU = -W, and pV^γ = constant.
比热容：Q = mcΔθ。比潜热：Q = mL（熔解或汽化）。加热实验中，常假设电功率 IV 全部传递给物质，但往往需要散热修正。绝热过程中无热交换（Q = 0），故 ΔU = -W，且满足 pV^γ = 常数。
8. Simple Harmonic Motion (SHM) | 简谐运动（SHM）
SHM occurs when acceleration a is directly proportional to displacement x and directed towards equilibrium: a = -ω²x. Solutions: x = A sin(ωt) or x = A cos(ωt). Maximum speed v_max = ωA occurs at equilibrium. Speed at displacement x: v = ±ω√(A² – x²). Period T = 2π/ω.
当加速度 a 与位移 x 成正比且指向平衡位置时，物体做简谐运动：a = -ω²x。解为 x = A sin(ωt) 或 x = A cos(ωt)。最大速率 v_max = ωA 出现在平衡位置。位移为 x 时速率 v = ±ω√(A² – x²)。周期 T = 2π/ω。
For a mass–spring system, T = 2π√(m/k). For a simple pendulum, T = 2π√(L/g). Energy in SHM: total energy E_tot = ½kA² = ½mω²A², interchanging between kinetic and potential. Damping reduces amplitude over time. Light damping slightly lowers frequency; critical damping returns the system to equilibrium without overshoot. Resonance occurs when driving frequency matches natural frequency, giving maximum amplitude.
弹簧振子周期 T = 2π√(m/k)，单摆周期 T = 2π√(L/g)。简谐运动中的能量：总能量 E_tot = ½kA² = ½mω²A²，在动能和势能间相互转换。阻尼使振幅逐渐减小。轻阻尼略微降低频率；临界阻尼使系统最快回到平衡位置且无振荡。当驱动频率等于固有频率时发生共振，振幅最大。
9. Gravitational Fields | 引力场
Newton’s law of gravitation: F = G M m / r². Gravitational field strength g = F/m. For a point or spherical mass, g = G M / r². In a radial field, g ∝ 1/r². Gravitational potential V = -G M / r, always negative, representing work done per unit mass to bring a test mass from infinity. Potential gradient dV/dr = -g.
牛顿引力定律：F = G M m / r²。引力场强度 g = F/m。点质量或球体外部：g = G M / r²。径向场中 g ∝ 1/r²。引力势 V = -G M / r，始终为负值，表示将单位质量从无穷远处移至该点所做的功。势梯度 dV/dr = -g。
Satellite orbits: centripetal force is
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