📚 A-Level Edexcel Physics: Last-Minute Revision Notes | A-Level Edexcel 物理：考前冲刺笔记
This set of last-minute revision notes distils the essential concepts, key formulas and common exam pitfalls from the Edexcel A-Level Physics specification. Each section pairs concise English explanations with Chinese translations to reinforce understanding across mechanics, waves, electricity, fields, quantum physics, thermodynamics and oscillations.
这套考前冲刺笔记提炼了 Edexcel A-Level 物理大纲的核心概念、关键公式和常见考试陷阱。每个小节都以简洁的英文讲解搭配中文翻译，帮助你巩固力学、波动、电学、场、量子物理、热力学和振动等模块的理解。
1. Kinematics and Dynamics | 运动学与动力学
The four SUVAT equations (v = u + at, s = ut + ½at², s = ½(u+v)t, v² = u² + 2as) are only valid when acceleration is constant. Always define the positive direction before substituting values.
四个 SUVAT 方程 (v = u + at, s = ut + ½at², s = ½(u+v)t, v² = u² + 2as) 仅在加速度恒定时有效。代入数值前必须先规定正方向。
For projectiles, split the initial velocity into horizontal (u cosθ) and vertical (u sinθ) components. The horizontal motion has zero acceleration, while the vertical acceleration is g = 9.81 m s⁻² downward.
对于抛体运动，将初速度分解为水平分量 (u cosθ) 和竖直分量 (u sinθ)。水平方向加速度为零，竖直方向加速度为向下的 g = 9.81 m s⁻²。
Newton’s second law in vector form ΣF = ma must be applied by resolving all forces along chosen axes. Action–reaction pairs act on different bodies and are equal in magnitude but opposite in direction.
牛顿第二定律的矢量形式 ΣF = ma 需要沿选定轴分解所有力。作用力与反作用力作用在不同物体上，大小相等、方向相反。
v² = u² + 2as
2. Momentum, Energy and Power | 动量、能量与功率
Linear momentum p = mv is a vector quantity. The impulse FΔt equals the change in momentum Δp. In collisions, total momentum is conserved provided no external resultant force acts.
线动量 p = mv 是矢量。冲量 FΔt 等于动量的变化 Δp。只要无外合力作用，碰撞中总动量守恒。
Kinetic energy Eₖ = ½mv², gravitational potential energy ΔEₚ = mgΔh. The work done by a force is W = Fd cosθ, where θ is the angle between force and displacement.
动能 Eₖ = ½mv²，重力势能变化 ΔEₚ = mgΔh。力做的功为 W = Fd cosθ，其中 θ 是力与位移的夹角。
Power is the rate of energy transfer: P = W/t. For a constant force moving at constant velocity, P = Fv. Efficiency = (useful energy output)/(total energy input).
功率是能量传递的速率：P = W/t。对于以恒定速度运动的恒力，P = Fv。效率 = (有用能量输出)/(总能量输入)。
Elastic collisions conserve kinetic energy; inelastic collisions do not, although momentum is still conserved. Always check if a collision is perfectly inelastic (objects stick together).
弹性碰撞动能守恒；非弹性碰撞动能不守恒，但动量仍守恒。务必检查碰撞是否为完全非弹性（物体粘在一起）。
3. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
Hooke’s law states that extension ΔL is proportional to the applied force F, up to the limit of proportionality: F = kΔL. The spring constant k depends on the material and dimensions.
胡克定律指出，在比例极限内，伸长量 ΔL 与作用力 F 成正比：F = kΔL。弹簧常数 k 取决于材料和尺寸。
Tensile stress σ = F/A, tensile strain ε = ΔL/L. The Young modulus E = σ/ε, with units N m⁻² or Pa. It measures a material’s stiffness and is independent of sample dimensions.
拉应力 σ = F/A，拉应变 ε = ΔL/L。杨氏模量 E = σ/ε，单位为 N m⁻² 或 Pa。它衡量材料的刚度，与样品尺寸无关。
The force–extension graph shows an initial linear region, then an elastic limit beyond which plastic deformation occurs. Area under the graph gives work done (elastic strain energy = ½FΔx).
力–伸长图显示初始线性区，然后是弹性极限，超过后发生塑性形变。图线下的面积表示做功（弹性应变能 = ½FΔx）。
4. Waves: Wave Equation, Polarisation and Refraction | 波动：波方程、偏振与折射
The wave equation v = fλ links speed, frequency and wavelength. Transverse waves have oscillations perpendicular to energy transfer; longitudinal waves have oscillations parallel.
波方程 v = fλ 将波速、频率和波长联系起来。横波的振动方向与能量传递方向垂直；纵波的振动方向平行于传播方向。
Polarisation can only occur for transverse waves. A polarising filter transmits only the component of the wave parallel to its transmission axis, reducing intensity according to Malus’s law: I = I₀ cos²θ.
偏振只有横波才能发生。偏振片只透过与透振轴平行的分量，光强按马吕斯定律 I = I₀ cos²θ 减小。
Refraction is described by Snell’s law: n₁ sinθ₁ = n₂ sinθ₂. The refractive index n = c/v, where c is the speed of light in vacuum. Total internal reflection occurs when the angle of incidence exceeds the critical angle.
折射遵循斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂。折射率 n = c/v，c 为真空光速。当入射角大于临界角时发生全内反射。
v = fλ
5. Superposition, Interference and Stationary Waves | 叠加、干涉与驻波
When two coherent waves meet, superposition leads to constructive interference (path difference nλ) or destructive interference (path difference (n+½)λ). Phase difference is key.
两列相干波相遇时，叠加产生相长干涉（波程差 nλ）或相消干涉（波程差 (n+½)λ）。相位差是关键。
In Young’s double-slit experiment, fringe spacing Δx = λD/a, where D is slit-to-screen distance and a is slit separation. For a diffraction grating, d sinθ = nλ gives maxima angles.
在杨氏双缝实验中，条纹间距 Δx = λD/a，D 为缝屏距，a 为缝间距。对于衍射光栅，d sinθ = nλ 给出主极大角度。
Stationary waves form when two identical waves travel in opposite directions. Nodes have zero displacement, antinodes have maximum amplitude. For a string fixed at both ends, λₙ = 2L/n.
驻波由两列相同的波相向传播形成。波节位移为零，波腹振幅最大。对于两端固定的弦，λₙ = 2L/n。
6. Electricity: Current, Resistance and Circuits | 电学：电流、电阻与电路
Current I = ΔQ/Δt. Ohm’s law V = IR holds for ohmic conductors at constant temperature. Resistivity ρ = RA/L, linking resistance to material and geometry.
电流 I = ΔQ/Δt。欧姆定律 V = IR 在恒温下适用于欧姆导体。电阻率 ρ = RA/L，将电阻与材料和几何尺寸联系起来。
Kirchhoff’s first law: ΣI into a junction = ΣI out (charge conservation). Second law: ΣEMF = Σpd around any closed loop (energy conservation). Use these to solve multi-loop circuits.
基尔霍夫第一定律：进入节点的电流之和等于流出电流之和（电荷守恒）。第二定律：闭合回路中 Σ电动势 = Σ电压降（能量守恒）。用它们解多回路电路。
A potential divider gives V_out = V_in (R₂/(R₁+R₂)). EMF ε = I(R+r), terminal pd V = ε – Ir, where r is internal resistance. Plotting V against I yields gradient –r and intercept ε.
分压器输出电压 V_out = V_in (R₂/(R₁+R₂))。电动势 ε = I(R+r)，端电压 V = ε – Ir，其中 r 为内阻。作 V-I 图，斜率为 –r，截距为 ε。
P = I²R = V²/R
7. Quantum Physics: Photoelectric Effect, Energy Levels & de Broglie | 量子物理：光电效应、能级与德布罗意波
The photoelectric effect cannot be explained by wave theory. Photons carry energy E = hf = hc/λ. Electrons are emitted only if hf > Φ (work function), with maximum kinetic energy K_max = hf – Φ.
光电效应无法用波动理论解释。光子携带能量 E = hf = hc/λ。仅当 hf > Φ（逸出功）时电子才能逸出，最大动能 K_max = hf – Φ。
Stopping potential V_s relates to K_max by eV_s = K_max. Threshold frequency f₀ = Φ/h. The graph of K_max vs frequency gives slope h and x-intercept f₀.
遏止电势 V_s 满足 eV_s = K_max。截止频率 f₀ = Φ/h。K_max 对频率的图线斜率为 h，与横轴截距为 f₀。
Electrons in atoms exist in discrete energy levels. Emission or absorption of a photon occurs when an electron transitions, with hf = |E₂ – E₁|. Ionisation energy is the energy to remove an electron from ground state.
原子中电子处于离散能级。电子跃迁时发射或吸收光子，hf = |E₂ – E₁|。电离能是从基态移走一个电子所需的能量。
de Broglie wavelength λ = h/p shows wave–particle duality. Electrons can be diffracted, e.g. by graphite, providing evidence for matter waves.
德布罗意波长 λ = h/p 体现了波粒二象性。电子可被石墨等晶体衍射，为物质波提供证据。
8. Circular Motion and Gravitational Fields | 圆周运动与引力场
For an object moving in a circle at constant speed, centripetal acceleration a = v²/r = ω²r, and centripetal force F = mv²/r = mω²r. The force is always directed towards the centre.
物体匀速圆周运动时，向心加速度 a = v²/r = ω²r，向心力 F = mv²/r = mω²r。该力始终指向圆心。
Newton’s law of gravitation: F = GMm/r². Gravitational field strength g = F/m, and for a point mass g = GM/r². Gravitational potential V = –GM/r, and g = –dV/dr.
万有引力定律：F = GMm/r²。引力场强度 g = F/m，对于质点 g = GM/r²。引力势 V = –GM/r，且 g = –dV/dr。
Kepler’s third law T² ∝ r³ for planets moving around the Sun can be derived from equating gravitational and centripetal forces. Satellites in geostationary orbit have T = 24 h and orbit above the equator.
行星绕太阳运动的开普勒第三定律 T² ∝ r³ 可由引力等于向心力推导。地球同步轨道卫星周期为 24 h，轨道位于赤道上方。
9. Electric Fields and Capacitors | 电场与电容器
Coulomb’s law: F = kQq/r², where k = 1/(4πε₀). Electric field strength E = F/q; for a point charge E = Q/(4πε₀r²). In a uniform field between parallel plates, E = V/d.
库仑定律：F = kQq/r²，其中 k = 1/(4πε₀)。电场强度 E = F/q；点电荷电场 E = Q/(4πε₀r²)。平行板间的匀强电场 E = V/d。
Electric potential V = Q/(4πε₀r) for a point charge. Work done in moving a charge q through ΔV is W = qΔV. Equipotential surfaces are perpendicular to field lines.
点电荷的电势 V = Q/(4πε₀r)。移动电荷 q 经过电势差 ΔV 做的功为 W = qΔV。等势面与电场线垂直。
A capacitor stores charge Q = CV. For a parallel-plate capacitor, C = ε₀A/d. Energy stored = ½QV = ½CV² = ½Q²/C. Time constant τ = RC governs exponential charging and discharging: Q = Q₀ e⁻ᵗ/ʳᶜ.
电容器储存电荷 Q = CV。平行板电容器 C = ε₀A/d。储存能量 = ½QV = ½CV² = ½Q²/C。时间常数 τ = RC 决定指数充放电规律：Q = Q₀ e⁻ᵗ/ʳᶜ。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A current-carrying wire in a magnetic field experiences a force F = BIL sinθ (Fleming’s left-hand rule). A moving charge experiences F = Bqv sinθ; circular motion results if v ⟂ B.
载流导线在磁场中受力 F = BIL sinθ（弗莱明左手定则）。运动电荷受力 F = Bqv sinθ；若 v ⟂ B，电荷做圆周运动。
Magnetic flux Φ = BA cosθ, flux linkage = NΦ. Faraday’s law: induced EMF ε = –d(NΦ)/dt. Lenz’s law states the induced current opposes the change that produced it.
磁通量 Φ = BA cosθ，磁通匝链数 = NΦ。法拉第定律：感应电动势 ε = –d(NΦ)/dt。楞次定律指出，感应电流的方向总是阻碍引起感应的变化。
A transformer changes voltage according to Vₛ/Vₚ = Nₛ/Nₚ. For an ideal transformer, power input equals power output: IₚVₚ = IₛVₛ. Efficiency is reduced by eddy currents and flux leakage.
变压器按 Vₛ/Vₚ = Nₛ/Nₚ 变压。理想变压器输入输出功率相等：IₚVₚ = IₛVₛ。涡流和磁通泄漏会降低效率。
11. Nuclear Physics: Decay, Mass–Energy
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