📚 Edexcel Pre-U Physics: Core Knowledge Review | Edexcel Pre-U 物理：核心知识点梳理
This revision guide summarises the key concepts across the Edexcel Pre-U Physics specification, covering mechanics, fields, waves, thermodynamics, and modern physics. Each topic is distilled into essential definitions, equations, and principles to aid consolidation before the examination. Equations are presented in centred bold text, using Unicode symbols for clarity, and every explanation is given in both English and Chinese to support bilingual learners.
本复习指南梳理了 Edexcel Pre-U 物理考试大纲的核心概念，涵盖力学、场、波、热力学和现代物理等主题。每个主题都提炼出基本定义、方程和原理，帮助考前巩固。方程以居中加粗的格式呈现，并使用 Unicode 符号确保清晰，每个解释均以中英双语给出，方便双语学习者参考。
1. Kinematics and Dynamics | 运动学与动力学
Motion with constant acceleration is described by the SUVAT equations. For an initial velocity u, final velocity v, acceleration a, displacement s, and time t, the key relations are: v = u + at and s = ut + ½at². These apply to linear motion and to each independent component of projectile motion.
匀加速运动由 SUVAT 方程组描述。对于初速度 u、末速度 v、加速度 a、位移 s 和时间 t，核心关系式为：v = u + at 和 s = ut + ½at²。这些公式既适用于直线运动，也适用于抛体运动各独立分量。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
Newton’s laws of motion establish the link between force and momentum. The resultant force on an object equals its rate of change of momentum: F = Δp/Δt. For constant mass, this reduces to F = ma. Momentum p = mv is conserved in isolated systems, making it a powerful tool for collision and explosion analysis.
牛顿运动定律建立了力与动量之间的联系。物体所受合外力等于其动量变化率：F = Δp/Δt。当质量恒定时，简化为 F = ma。动量 p = mv 在孤立系统中守恒，这使其成为分析碰撞和爆炸问题的有力工具。
Projectile motion is modelled by resolving velocity into horizontal and vertical components. The horizontal component remains constant (neglecting air resistance), while the vertical component accelerates downward at g = 9.81 m s⁻². The trajectory is parabolic, and time of flight depends solely on vertical motion.
抛体运动通过将速度分解为水平和竖直分量来建模。水平分量保持不变（忽略空气阻力），而竖直分量以 g = 9.81 m s⁻² 向下加速。轨迹呈抛物线，飞行时间只取决于竖直运动。
2. Work, Energy and Power | 功、能与功率
Work done W by a constant force F displacing an object by s at an angle θ is W = F s cosθ. When work is done, energy is transferred. The kinetic energy of a mass m moving at speed v is KE = ½mv², and the change in kinetic energy equals the net work done on the object.
恒力 F 使物体沿与力成 θ 角的方向位移 s，所做的功为 W = F s cosθ。做功的过程伴随着能量转移。质量为 m、速度为 v 的物体的动能 KE = ½mv²，动能变化量等于物体所受合外力做的净功。
KE = ½mv² GPE = mgh W = F s cosθ
Gravitational potential energy near Earth’s surface is GPE = mgh, where h is the height above a reference level. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between stores. Power is the rate of energy transfer: P = ΔE/Δt = F v for a constant force and velocity in the same direction.
地球表面附近的重力势能 GPE = mgh，其中 h 是相对于参考平面的高度。能量守恒定律指出能量既不会创生也不会消灭，只在不同储存之间传递。功率是能量传递的速率：P = ΔE/Δt；当力与速度同向且恒定时，P = F v。
Efficiency is the ratio of useful output energy or power to total input energy or power, often expressed as a percentage. In real systems, some energy is always dissipated as thermal energy due to friction or resistance.
效率是有用输出能量或功率与总输入能量或功率的比值，通常以百分比表示。在真实系统中，由于摩擦或电阻，总有一部分能量以热能形式耗散。
3. Circular Motion | 圆周运动
An object moving in a circle of radius r at constant speed v experiences a centripetal acceleration directed toward the centre: a = v²/r = ω²r, where ω is the angular speed in rad s⁻¹. The period T = 2π/ω. Although speed is constant, the velocity is continuously changing direction, so the object is accelerating.
物体以恒定速率 v 在半径为 r 的圆周上运动时，受到指向圆心的向心加速度：a = v²/r = ω²r，其中 ω 是以 rad s⁻¹ 为单位的角速度。周期 T = 2π/ω。虽然速率恒定，但速度方向不断变化，因此物体在做加速运动。
a = v²/r = ω²r F = mv²/r = mω²r ω = 2π/T
The centripetal force required to keep an object in uniform circular motion is given by F = mv²/r = mω²r. This force is always perpendicular to the velocity and does no work. In common applications, it is provided by tension (e.g., a mass on a string), friction (a car rounding a bend), or gravity (orbiting satellites).
维持物体做匀速圆周运动所需的向心力为 F = mv²/r = mω²r。该力始终垂直于速度，不做功。常见实例中，向心力由张力（如绳端小球）、摩擦力（过弯汽车）或引力（轨道卫星）提供。
At the top of a vertical circular path, the resultant force toward the centre is mg + N = mv²/r, while at the bottom it is N – mg = mv²/r. For a passenger to feel weightless at the top, the contact force N = 0, so the speed must satisfy v² = rg.
在竖直圆周轨道最高点，指向圆心的合力为 mg + N = mv²/r，在最低点则为 N – mg = mv²/r。若乘客在最高点感到失重，支持力 N = 0，因此速度必须满足 v² = rg。
4. Simple Harmonic Motion | 简谐运动
Simple harmonic motion (SHM) occurs when the restoring force on an object is directly proportional to its displacement from equilibrium and acts toward equilibrium: F = -kx. The acceleration is a = -ω²x, where ω = 2πf is the angular frequency. The solution to the equation of motion is x = A sin(ωt) or x = A cos(ωt), where A is the amplitude.
当回复力与偏离平衡位置的位移成正比且指向平衡位置时，物体做简谐运动：F = -kx。加速度为 a = -ω²x，其中 ω = 2πf 是角频率。运动方程的解为 x = A sin(ωt) 或 x = A cos(ωt)，A 为振幅。
a = -ω²x x = A sin(ωt) T = 2π√(m/k) T = 2π√(l/g)
The velocity in SHM is v = ±ω√(A² – x²), and the maximum speed vmax = ωA occurs at equilibrium. Energy continuously interchanges between kinetic and potential forms while the total mechanical energy remains constant: Etotal = ½mω²A². For a mass-spring system, T = 2π√(m/k); for a simple pendulum, T = 2π√(l/g).
简谐运动的速度为 v = ±ω√(A² – x²)，最大速度 vmax = ωA 出现在平衡位置。动能和势能持续转化，而总机械能保持不变：Etotal = ½mω²A²。对于弹簧振子，周期 T = 2π√(m/k)；对于单摆，T = 2π√(l/g)。
Damping removes energy from the system, reducing amplitude over time. Light damping slightly lengthens the period; critical damping brings the system to equilibrium in the shortest time without oscillation; heavy damping results in a slow return without oscillation. Resonance occurs when a periodic driving force matches the natural frequency, causing large-amplitude oscillations.
阻尼会消耗系统能量，使振幅逐渐减小。轻阻尼稍稍增长周期；临界阻尼使系统在最短时间内返回平衡且不振荡；重阻尼则使系统缓慢返回而无振动。当周期性驱动力频率等于固有频率时发生共振，振幅急剧增大。
5. Electric Fields | 电场
Electric fields arise from charged particles and exert forces on other charges. Coulomb’s law gives the force between two point charges Q and q separated by distance r: F = kQq/r², where k = 1/(4πε₀). The electric field strength E at a point is the force per unit positive charge: E = F/q. For a point charge, E = kQ/r².
电场由带电粒子产生并对其他电荷施加力。库仑定律给出两点电荷 Q 与 q 相距 r 时的作用力：F = kQq/r²，其中 k = 1/(4πε₀)。某点的电场强度 E 是单位正电荷所受的力：E = F/q。对于点电荷，E = kQ/r²。
F = kQq/r² E = F/q = kQ/r² E = V/d V = kQ/r
Electric potential V is the work done per unit charge in bringing a positive test charge from infinity to that point, giving V = kQ/r. The potential difference ΔV between two points equals the work done per unit charge. In a uniform electric field between parallel plates, E = V/d, where d is plate separation.
电势 V 是将单位正电荷从无穷远移至该点所做的功，有 V = kQ/r。两点之间的电势差 ΔV 等于单位电荷移动时所做的功。在平行板产生的匀强电场中，E = V/d，d 为板间距。
Charged particles in electric fields experience a force F = qE. When an electron is accelerated through a potential difference V, it gains kinetic energy ½mv² = eV. This principle is used in particle accelerators and electron guns. Field lines radiate outward from positive charges and terminate at negative charges, with line density indicating field strength.
电荷在电场中受到力 F = qE。电子经电势差 V 加速后获得动能 ½mv² = eV。这一原理应用于粒子加速器和电子枪。电场线从正电荷发出终止于负电荷，线密度表示电场强度。
6. Capacitance | 电容
Capacitance C is the charge stored per unit potential difference: C = Q/V. The unit of capacitance is the farad (F). A capacitor stores energy in the electric field between its plates, with energy W = ½QV = ½CV² = ½Q²/C. For a parallel-plate capacitor, C = εA/d, where ε is the permittivity of the dielectric and d is the plate separation.
电容 C 是单位电势差下储存的电荷量：C = Q/V。单位是法拉 (F)。电容器在极板间电场中储存能量，能量为 W = ½QV = ½CV² = ½Q²/C。对平行板电容器，C = εA/d，ε 为介质介电常数，d 为板间距。
C = Q/V W = ½CV² C = εA/d τ = RC
During charging and discharging through a resistor R, the voltage and current change exponentially. The time constant τ = RC is the time for the voltage to fall to 37% (1/e) of its initial value during discharging, or to rise to 63% of the supply voltage during charging. Equations: V = V₀ e−t/RC and I = I₀ e−t/RC for discharge.
通过电阻 R 充放电时，电压和电流呈指数变化。时间常数 τ = RC，是放电时电压降至初始值 37% (1/e) 或充电时升至电源电压 63% 所需的时间。放电方程：V = V₀ e−t/RC，I = I₀ e−t/RC。
In series, the reciprocal of the total capacitance is the sum of reciprocals: 1/Ctot = 1/C₁ + 1/C₂ + …. In parallel, total capacitance is the sum of individual capacitances: Ctot = C₁ + C₂ + …. Practical uses include energy storage, smoothing circuits in power supplies, and timing circuits.
串联时，总电容的倒数为各电容倒数之和：1/Ctot = 1/C₁ + 1/C₂ + …；并联时，总电容为各电容之和：Ctot = C₁ + C₂ + …。实际应用包括储能、电源平滑电路和定时电路。
7. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A magnetic field exerts a force on a moving charge or a current-carrying conductor. For a straight conductor of length L carrying current I at angle θ to a uniform magnetic flux density B, the force is F = BIL sinθ. Fleming’s left-hand rule gives the direction. For a single charge q moving at speed v, F = qvB sinθ.
磁场对运动电荷或载流导线有力的作用。长 L 的直导线通以电流 I，与均匀磁通密度 B 成 θ 角时，受力 F = BIL sinθ。弗莱明左手定则确定方向。对单个电荷 q 以速度 v 运动，F = qvB sinθ。
F = BIL sinθ F = qvB sinθ ε = –N ΔΦ/Δt Φ = BA cosθ
Electromagnetic induction occurs when the magnetic flux Φ = BA cosθ through a circuit changes. Faraday’s law states that the magnitude of the induced e.m.f. ε equals the rate of change of flux linkage NΦ: ε = –N ΔΦ/Δt. Lenz’s law, indicated by the negative sign, states that the induced current opposes the change in flux that produced it.
穿过回路的磁通量 Φ = BA cosθ 发生变化时产生电磁感应。法拉第定律指出感应电动势 ε 的大小等于磁链 NΦ 的变化率：ε = –N ΔΦ/Δt。楞次定律（负号反映）指出感应电流的方向总是阻碍引起感应的磁通量变化。
A transformer changes voltage based on the turns ratio: Vs/Vp = Ns/Np. For an ideal transformer, primary and secondary power are equal: Ip Vp = Is Vs. Eddy currents in the core are minimised by lamination. Applications include the a.c. generator, in which a coil rotates in a magnetic field, producing a sinusoidal e.m.f.: ε = NBAω sin(ωt).
变压器依据匝数比改变电压：Vs/Vp = Ns/Np。对于理想变压器，原副边功率相等：Ip Vp = Is Vs。通过叠片铁心减少涡流。应用包括交流发电机，线圈在磁场中旋转，产生正弦电动势：ε = NBAω sin(ωt)。
8. Thermodynamics and Ideal Gases | 热力学与理想气体
The ideal gas equation links pressure p, volume V, temperature T in kelvin, and amount n (mol): pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹. It can also be written as pV = NkT, with N the number of molecules and k the Boltzmann constant. Boyle’s law (p ∝ 1/V), Charles’s law (V ∝ T), and the pressure law (p ∝ T) are special cases.
理想气体状态方程联系压强 p、体积 V、开氏温度 T 和物质的量 n (mol)：pV = nRT，R = 8.31 J mol⁻¹ K⁻¹。也可写为 pV = NkT，N 为分子数，k 为玻尔兹曼常数。玻意耳定律 (p ∝ 1/V)、查理定律 (V ∝ T) 和压强定律 (p ∝ T) 是其特例。
pV = nRT ΔU = Q + W pV = ⅓Nm⟨c²⟩ KEavg = ³⁄₂kT
The first law of thermodynamics expresses energy conservation: ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done on the system (Edexcel sign convention). For an ideal gas, internal energy depends only on temperature. In an isothermal process ΔU = 0, so Q = -W; in an adiabatic process Q = 0, so ΔU = W; at constant volume, W = 0 and ΔU = Q.
热力学第一定律表达了能量守恒：ΔU = Q + W，ΔU 为内能变化，Q 为系统吸收的热量，W 为对系统做的功（Edexcel 符号约定）。理想气体的内能只与温度有关。等温过程中 ΔU = 0，故 Q = -W；绝热过程中 Q = 0，故 ΔU = W；等容过程中 W = 0，ΔU = Q。
The kinetic theory model relates microscopic motion to macroscopic pressure: pV = ⅓Nm⟨c²⟩, where ⟨c²⟩ is the mean square speed. The average translational kinetic energy per molecule is ³⁄₂kT, showing that temperature is a measure of random kinetic energy. The root-mean-square speed c_rms = √(3kT/m).
分子动理论模型将微观运动与宏观压强联系起来：pV = ⅓Nm⟨c²⟩，⟨c²⟩ 为速率平方均值。每个分子的平均平动动能为 ³⁄₂kT，说明温度是分子无规则运动动能的量度。方均根速率 c_rms = √(3kT/m)。
9. Nuclear and Particle Physics | 原子核与粒子物理
The nucleus is composed of protons and neutrons held by the strong nuclear force. The mass defect is the difference between the total mass of separate nucleons and the nucleus mass, converted to binding energy via ΔE = Δm c². Binding energy per nucleon peaks at iron-56, making it the most stable nucleus. Nuclear reactions release energy by moving toward higher binding energy per nucleon.
原子核由质子和中子组成，通过强核力结合在一起。质量亏损是指单独核子总质量与核质量之差，由 ΔE = Δm c² 转换为结合能。每核子平均结合能在铁-56 处达到极大值，使其最为稳定。核反应中向更高每核子结合能转变时会释放能量。
E = Δm c² N = N₀ e−λt A = λN t₁/₂ = ln2/λ
Radioactive decay follows the exponential law N = N₀ e−λt, where λ is the decay constant. The activity A = λN is measured in becquerels (Bq). Half-life t₁/₂ = ln2/λ is the time for half the nuclei to decay. Alpha decay reduces Z by 2 and A by 4; beta-minus decay converts a neutron to a proton, increasing Z by 1; gamma emission releases energy without changing composition.
放射性衰变遵循指数规律：N = N₀ e−λt，λ 为衰变常数。活度 A = λN，单位为贝克勒尔 (Bq)。半衰期 t₁/₂ = ln2/λ 是半数核衰变所需的时间。α 衰变使 Z 减 2、A 减 4；β⁻ 衰变将中子转化为质子，Z 加 1；γ 辐射释放能量但不改变核组成。
In particle physics, hadrons (e.g., protons, neutrons) are made of quarks; leptons (e.g., electrons, neutrinos) are fundamental. Interactions are mediated by gauge bosons: the photon for electromagnetic, W and Z bosons for weak, and gluons for strong. Conservation laws for charge, baryon number, and lepton number apply in all particle interactions.
粒子物理中，强子（如质子、中子）由夸克构成；轻子（如电子、中微子）为基本粒子。相互作用由规范玻色子传递：光子传递电磁作用，W 和 Z 玻色子传递弱作用，胶子传递强作用。所有粒子相互作用中必须遵守电荷数、重子数和轻子数守恒定律。
10. Waves and Optics | 波动与光学
A travelling wave transfers energy without transferring matter. The relationship between wave speed v, frequency f, and wavelength λ is v = fλ. Transverse waves (e.g., electromagnetic) oscillate perpendicular to propagation; longitudinal waves (e.g., sound) oscillate parallel. Phase difference is expressed in radians or degrees, with 2π rad equating to one full cycle.
行波传递能量而不传递物质。波速 v、频率 f 和波长 λ 之间的关系为 v = fλ。横波（如电磁波）振动方向垂直于传播方向；纵波（如声波）振动方向平行于传播方向。相位差以弧度或度表示，2π rad 对应于一个完整周期。
v = fλ d sinθ = nλ n₁ sinθ₁ = n₂ sinθ₂ 1/f = 1/u + 1/v
Superposition leads to interference. For Young’s double-slit experiment, constructive interference occurs when the path difference d sinθ = nλ (n = 0, 1, 2…), producing bright fringes. The fringe spacing Δy = λD/d for small angles. Diffraction grating maxima obey the same condition, with n referred to as the order. A single slit produces a central maximum of angular width 2λ/a and much weaker secondary maxima.
叠加原理导致干涉。杨氏双缝实验中，当光程差 d sinθ = nλ（n = 0, 1, 2…）时发生相长干涉，形成亮条纹。小角度时条纹间距 Δy = λD/d。衍射光栅的极大满足相同条件，n 称为级数。单缝衍射产生角宽度为 2λ/a 的中央明纹和强度很弱的次级明纹。
Refraction is governed by Snell’s law: n₁ sinθ₁ = n₂ sinθ₂. When light enters a medium of higher refractive index, it bends toward the normal. Total internal reflection occurs when the angle of incidence exceeds the critical angle θc = sin⁻¹(n₂/n₁). Thin lenses obey the lens equation 1/f = 1/u + 1/v, with sign conventions specifying real and virtual images. Magnification M = v/u.
折射遵从斯涅耳定律：n₁ sinθ₁ = n₂ sinθ₂。光进入折射率较高的介质时向法线偏折。当入射角大于临界角 θc = sin⁻¹(n₂/n₁) 时发生全内反射。薄透镜遵循透镜方程 1/f = 1/u + 1/v，并通过符号规则区分实像和虚像。放大率 M = v/u。
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