📚 Pre-U CIE Physics: Essential Core Knowledge | Pre-U CIE 物理：核心知识点梳理
The Cambridge Pre-U Physics syllabus builds a deep, interconnected understanding of the physical world, from the subatomic to the cosmic scale. Mastering the core concepts is essential for success in the examination, as questions frequently require you to link ideas across different topics. This article distills the fundamental knowledge points that underpin the course, presented in a clear bilingual format to support your revision and consolidate your grasp of key principles.
剑桥 Pre-U 物理课程构建了一个从亚原子到宇宙尺度的深刻且相互关联的物理世界认知。掌握核心概念对考试成功至关重要，因为试题经常要求你将不同主题的思想联系起来。本文提炼了支撑该课程的基础知识点，以清晰的中英双语形式呈现，旨在支持你的复习并巩固你对关键原理的理解。
1. Kinematics and Dynamics | 运动学与动力学
Scalar quantities, such as distance and speed, have magnitude only, while vector quantities, such as displacement, velocity and acceleration, require both magnitude and direction. Motion in one dimension with constant acceleration is described by the SUVAT equations.
标量，如路程和速率，仅有大小；而矢量，如位移、速度和加速度，则需要大小和方向。匀加速直线运动由 SUVAT 方程描述。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
The displacement–time, velocity–time and acceleration–time graphs provide visual representations of motion; the gradient of a displacement–time graph gives velocity, the gradient of a velocity–time graph gives acceleration, and the area under a velocity–time graph gives displacement. Newton's three laws form the foundation of dynamics: the first law defines inertia, the second law F = ma links resultant force to rate of change of momentum, and the third law states that forces occur in equal and opposite pairs. Linear momentum p = mv is conserved in a closed system, and impulse FΔt = Δp equals the change in momentum.
位移–时间、速度–时间和加速度–时间图提供了运动的可视化表示；位移–时间图的斜率给出速度，速度–时间图的斜率给出加速度，速度–时间图下的面积给出位移。牛顿三定律构成了动力学的基础：第一定律定义惯性，第二定律 F = ma 将合力与动量变化率联系起来，第三定律指出力成对出现，大小相等方向相反。线动量 p = mv 在封闭系统中守恒，冲量 FΔt = Δp 等于动量的变化。
2. Work, Energy and Power | 功、能与功率
Work done by a constant force is W = Fs cosθ, where θ is the angle between the force and displacement. The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between forms. Kinetic energy is Eₖ = ½mv² and gravitational potential energy near the Earth's surface is ΔEₚ = mgΔh. Power is the rate of doing work: P = W/t = Fv for constant force and velocity in the same direction.
恒力做功为 W = Fs cosθ，θ 为力与位移间的夹角。能量守恒定律指出能量不能被创造或消灭，只能在不同形式间转化。动能为 Eₖ = ½mv²，地球表面附近的重力势能变化为 ΔEₚ = mgΔh。功率是做功的速率：当力与速度同向时，P = W/t = Fv。
Efficiency is the ratio of useful output power (or energy) to total input power, often expressed as a percentage. In many physical systems, energy is dissipated as thermal energy due to friction or resistance, and the total mechanical energy is only conserved when non‑conservative forces do no net work.
效率是有用输出功率（或能量）与总输入功率之比，常用百分比表示。在许多物理系统中，能量因摩擦或电阻而耗散为热能，只有当非保守力不做净功时总机械能才守恒。
3. Circular Motion and Gravitation | 圆周运动与引力
An object moving in a circle of radius r at constant speed v experiences a centripetal acceleration directed towards the centre: a = v²/r = rω², where ω is the angular speed. The centripetal force required is F = mv²/r = mrω². The period of circular motion is T = 2π/ω.
以恒定速率 v 在半径 r 的圆周上运动的物体，具有始终指向圆心的向心加速度：a = v²/r = rω²，其中 ω 为角速度。所需的向心力为 F = mv²/r = mrω²。圆周运动的周期为 T = 2π/ω。
Newton's law of gravitation states that the force between two point masses is F = Gm₁m₂/r², where G is the gravitational constant. The gravitational field strength g at a point is the force per unit mass: g = F/m = GM/r². Gravitational potential V at a distance r from a point mass is V = −GM/r, and the work done to move a mass between two points is mΔV. For planets and satellites, equating centripetal force to gravitational force yields relationships such as v = √GM/r and Kepler's third law T² ∝ r³.
牛顿万有引力定律指出，两个质点之间的引力为 F = Gm₁m₂/r²，G 为引力常量。某点的引力场强度 g 是单位质量所受的力：g = F/m = GM/r²。距离点质量 r 处的引力势为 V = −GM/r，将质量从一点移动到另一点所做的功为 mΔV。对于行星和卫星，将向心力与引力相等，可导出关系式如 v = √GM/r 和开普勒第三定律 T² ∝ r³。
4. Oscillations | 振动
Simple harmonic motion (SHM) occurs when the acceleration is directly proportional to the displacement from equilibrium and always directed towards it: a = −ω²x. The displacement varies sinusoidally: x = x₀ sin(ωt) or x = x₀ cos(ωt), where x₀ is the amplitude. The period for a mass‑spring system is T = 2π√m/k and for a simple pendulum of length L is T = 2π√L/g.
简谐运动（SHM）发生在加速度与偏离平衡的位移成正比且总是指向平衡位置时：a = −ω²x。位移按正弦变化：x = x₀ sin(ωt) 或 x = x₀ cos(ωt)，x₀ 为振幅。弹簧振子的周期为 T = 2π√m/k，摆长为 L 的单摆周期为 T = 2π√L/g。
Energy in SHM continuously interconverts between kinetic and potential; the total energy is E = ½mω²x₀². Damping reduces amplitude over time, and critical damping returns the system to equilibrium in the shortest time without oscillation. Forced oscillations can lead to resonance when the driving frequency matches the natural frequency, causing maximum amplitude.
简谐运动中的能量在动能与势能之间连续转换；总能量为 E = ½mω²x₀²。阻尼随时间减小振幅，临界阻尼使系统在不振荡的情况下用最短时间回到平衡。受迫振动当驱动频率等于固有频率时会发生共振，导致振幅最大。
5. Thermal Physics | 热物理
The kinetic model of an ideal gas assumes that particles undergo elastic collisions, occupy negligible volume, and exert no forces except during collisions. The equation of state for an ideal gas is pV = nRT = NkT, where R is the molar gas constant and k is the Boltzmann constant. The average translational kinetic energy of a gas particle is directly proportional to the absolute temperature: ⟨Eₖ⟩ = ₃⁄₂ kT for a monatomic gas.
理想气体的动力学模型假定粒子发生弹性碰撞，所占体积可忽略，且除碰撞瞬间外无相互作用力。理想气体状态方程为 pV = nRT = NkT，R 为摩尔气体常量，k 为玻尔兹曼常量。气体粒子的平均平动动能与绝对温度成正比：对单原子气体，⟨Eₖ⟩ = ₃⁄₂ kT。
The first law of thermodynamics expresses energy conservation: ΔU = Q + W d Q = −W; for an adiabatic process, Q = 0 and ΔU = W. The specific heat capacity c and latent heat L are defined by Q = mcΔθ and Q = mL respectively.
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。等温过程中 ΔU = 0 且 Q = −W；绝热过程中 Q = 0 且 ΔU = W。比热容 c 和潜热 L 的定义分别为 Q = mcΔθ 与 Q = mL。
6. Waves and Superposition | 波与叠加
A progressive wave transfers energy without net transfer of matter. The relationship between speed, frequency and wavelength is v = fλ. Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel. The intensity of a wave is proportional to the square of its amplitude, I ∝ A².
行波传递能量而不发生物质的净转移。波速、频率和波长之间的关系为 v = fλ。横波的振动方向与能量传递方向垂直；纵波的振动方向与之平行。波的强度与振幅的平方成正比，I ∝ A²。
When two or more waves meet, they superpose. Constructive interference occurs when the path difference is an integer multiple of the wavelength, and destructive interference when it is an odd multiple of half the wavelength. For Young's double‑slit experiment, the fringe spacing is given by Δy = λD/d, where d is the slit separation and D is the slit‑to‑screen distance. Diffraction gratings produce sharp maxima at angles satisfying d sinθ = nλ. Stationary waves form when two identical progressive waves travel in opposite directions, producing nodes (zero displacement) and antinodes (maximum displacement).
当两列或更多波相遇时发生叠加。路程差为波长的整数倍时产生相长干涉，为半波长的奇数倍时产生相消干涉。在杨氏双缝实验中，条纹间距为 Δy = λD/d，d 为缝距，D 为缝到屏的距离。衍射光栅在满足 d sinθ = nλ 的角度产生锐利的极大。驻波由两列相同行波相向传播形成，产生波节（位移为零）和波腹（位移最大）。
7. Electric Fields and Capacitance | 电场与电容
Electric field strength E at a point is the force per unit positive charge: E = F/q. For a uniform field between parallel plates, E = V/d. The force on a charge in an electric field is F = qE. Coulomb's law for the force between two point charges is F = Q₁Q₂ / (4πε₀r²) in free space.
电场强度 E 是某点单位正电荷所受的力：E = F/q。对于平行板间的匀强电场，E = V/d。电荷在电场中所受的力为 F = qE。真空中两点电荷间库仑力为 F = Q₁Q₂ / (4πε₀r²)。
Capacitance C is defined as C = Q/V. The energy stored in a capacitor is E = ½QV = ½CV² = ½Q²/C. For a parallel‑plate capacitor, C = ε₀A/d (dielectric constant κ multiplies ε₀ when a medium is inserted). When charging or discharging through a resistor, the time constant τ = RC governs the exponential change: Q = Q₀ e⁻ᵗ/ᴿᴯ for discharge and Q = Q₀(1 − e⁻ᵗ/ᴿᴯ) for charging.
电容 C 定义为 C = Q/V。电容器储存的能量为 E = ½QV = ½CV² = ½Q²/C。平行板电容器的电容为 C = ε₀A/d（插入介质时介电常数 κ 乘以 ε₀）。当通过电阻充放电时，时间常数 τ = RC 控制指数变化：放电时 Q = Q₀ e⁻ᵗ/ᴿᴰ，充电时 Q = Q₀(1 − e⁻ᵗ/ᴿᴰ)。
8. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A magnetic field exerts a force on a moving charge. The magnetic force on a straight current‑carrying conductor in a uniform field is F = BIL sinθ, where θ is the angle between the current and the field. For a single charge, F = Bqv sinθ. The direction of force is given by Fleming's left‑hand rule.
磁场对运动的电荷施加力。匀强磁场中载流直导线所受的磁力为 F = BIL sinθ，θ 为电流与磁场方向间的夹角。对于单个电荷，F = Bqv sinθ。力的方向由弗莱明左手定则判定。
Magnetic flux Φ through a surface is the product of the magnetic flux density B and the area A perpendicular to the field: Φ = BA cosθ. Faraday's law states that the induced e.m.f. is equal to the negative rate of change of flux linkage: ε = −N ΔΦ/Δt. Lenz's law dictates the direction of induced e.m.f., opposing the change producing it. An a.c. generator produces a sinusoidal e.m.f. ε = BANω sin(ωt). The Hall effect produces a transverse voltage VH = BI/(nqt) where n is the charge carrier density and t is the thickness.
穿过某一平面的磁通量 Φ 是磁通量密度 B 与垂直于磁场的面积 A 的乘积：Φ = BA cosθ。法拉第定律指出，感应电动势等于磁链变化率的负值：ε = −N ΔΦ/Δt。楞次定律规定了感应电动势的方向总是阻碍引起它的变化。交流发电机产生正弦电动势 ε = BANω sin(ωt)。霍尔效应产生横向电压 VH = BI/(nqt)，n 为载流子密度，t 为厚度。
9. Alternating Currents | 交流电
An alternating current (a.c.) varies sinusoidally: I = I₀ sin(ωt), where I₀ is the peak current. The root‑mean‑square (r.m.s.) value relates the a.c. to the equivalent d.c. in terms of power dissipation: Irms = I₀/√2 and Vrms = V₀/√2. For a pure resistor, current and voltage are in phase and the mean power is P = Irms Vrms = Irms²R = Vrms²/R.
交流电（a.c.）按正弦变化：I = I₀ sin(ωt)，I₀ 为峰值电流。方均根（r.m.s.）值将交流电与等效直流电在功率耗散方面联系起来：Irms = I₀/√2，Vrms = V₀/√2。对于纯电阻，电流和电压同相，平均功率为 P = Irms Vrms = Irms²R = Vrms²/R。
Transformers operate on the principle of electromagnetic induction, with Vs / Vp = Ns / Np for an ideal transformer. Power losses occur due to eddy currents, hysteresis in the core, and resistive heating in the windings. Rectification converts a.c. to d.c., with half‑wave and full‑wave rectifiers producing different ripple characteristics, often smoothed by a capacitor.
变压器基于电磁感应原理工作，理想变压器满足 Vs / Vp = Ns / Np。功率损失来源于涡流、磁芯的磁滞以及绕组中的电阻发热。整流将交流转换为直流，半波和全波整流器产生不同的波纹特性，常通过电容器进行平滑。
10. Quantum Physics | 量子物理
Electromagnetic radiation exhibits particle‑like behaviour; the energy of a photon is E = hf = hc/λ. The photoelectric effect demonstrates that electrons are emitted from a metal surface when the incident photon energy exceeds the work function Φ: hf = Φ + KE_max otoelectric emission occurs below f₀ regardless of intensity, supporting the photon model.
电磁辐射表现出粒子性；光子的能量为 E = hf = hc/λ。光电效应表明，当入射光子能量大于功函数 Φ 时，电子从金属表面逸出：hf = Φ + KE_max。阈频率 f₀ 满足 hf₀ = Φ。低于 f₀ 时，无论光强多大均不发生光电发射，这支持了光子模型。
Matter also exhibits wave‑like properties; the de Broglie wavelength of a particle is λ = h/p = h/(mv). Electron diffraction provides experimental evidence for this wave nature. Line spectra arise from electron transitions between discrete energy levels in atoms: ΔE = hf. The energy levels in hydrogen are given by Eₙ = −13.6 eV / n² lmer and Paschen series correspond to transitions ending at n=1, n=2 and n=3 respectively.
物质也表现出波动性；粒子的德布罗意波长为 λ = h/p = h/(mv)。电子衍射为此波动性提供了实验证据。线状光谱源于原子中电子在离散能级间的跃迁：ΔE = hf。氢原子能级由 Eₙ = −13.6 eV / n² 给出，赖曼系、巴耳末系和帕邢系分别对应跃迁到 n=1、n=2 和 n=3 的谱线。
11. Nuclear and Particle Physics | 核与粒子物理
The atomic nucleus consists of protons and neutrons bound by the strong nuclear force. The mass defect, the difference between the mass of the nucleons and the mass of the nucleus, accounts for the binding energy via E = mc². Nuclear fission and fusion release energy when the binding energy per nucleon increases.
原子核由质子和中子通过强核力结合而成。质量亏损，即核子总质量与原子核质量之差，通过 E = mc² 给出了结合能。当每个核子的平均结合能增大时，核裂变和核聚变会释放能量。
Radioactive decay follows the law ΔN/Δt = −λN, and the number of undecayed nuclei decreases exponentially: N = N₀ e⁻λᵗ. The half‑life T₁/₂ is related to the decay constant by T₁/₂ = ln2 / λ. Alpha, beta and gamma emissions are distinguished by their ionising and penetrating abilities. In particle physics, hadrons are composed of quarks; baryons (e.g. protons, neutrons) consist of three quarks, while mesons consist of a quark‑antiquark pair. Leptons, such as electrons and neutrinos, are fundamental. Conservation laws for charge, baryon number, lepton number, and strangeness govern particle interactions.
放射性衰变遵循规律 ΔN/Δt = −λN，未衰变核的数目呈指数衰减：N = N₀ e⁻λᵗ。半衰期 T₁/₂ 与衰变常量关系为 T₁/₂ = ln2 / λ。α、β 和 γ 射线依据其电离和穿透能力加以区分。在粒子物理中，强子由夸克构成；重子（如质子、中子）由三个夸克组成，而介子由一个夸克‑反夸克对组成。轻子，如电子和中微子，是基本粒子。电荷、重子数、轻子数和奇异数守恒定律支配着粒子相互作用。
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