📚 Pre-U CAIE Physics: Core Concepts Summary | Pre-U CAIE 物理：核心知识点梳理
The Pre-U Cambridge Physics course demands a deep and connected understanding of fundamental principles, spanning classical mechanics, electromagnetism, waves, quantum phenomena and nuclear physics. This article structures the essential core knowledge to support focused revision, linking mathematical models with physical intuition. Each section pairs key points in English and Chinese to reinforce bilingual comprehension.
Pre-U剑桥物理课程要求学生对基本原理有深入且完整的理解，涵盖经典力学、电磁学、波动、量子现象与核物理。本文梳理了核心必备知识，以支持有针对性地复习，将数学模型与物理直觉紧密结合。每个小节都以英文与中文配对呈现，强化双语理解。
1. Kinematics and Dynamics | 运动学与动力学
Kinematics describes how objects move using displacement, velocity and acceleration without reference to the causes of motion. Dynamics introduces Newton’s laws of motion to relate these quantities to forces and momentum, forming the bedrock of classical mechanics.
运动学利用位移、速度和加速度描述物体的运动方式，而不涉及运动的原因。动力学引入牛顿运动定律，将这些量与力和动量关联起来，构成了经典力学的基础。
The equations of uniformly accelerated motion allow calculation of one unknown from known initial velocity u, final velocity v, acceleration a, displacement s and time t. These are valid only when acceleration is constant. A typical equation is:
匀加速直线运动的方程允许从已知的初速度u、末速度v、加速度a、位移s和时间t中计算未知量。这些方程仅在加速度恒定时成立。一个典型的方程为：
v² = u² + 2a s
Newton’s second law states that the net force F on a body equals the rate of change of its momentum p. For constant mass, this simplifies to F = m a. This vector relationship underpins all force–acceleration problems, including free‑body diagrams and connected particles.
牛顿第二定律指出，物体所受的净合力F等于其动量p的时间变化率。在质量不变的情况下，可简化为F = m a。这一矢量关系是所有力–加速度问题的基础，包括受力分析和连接体问题。
Momentum is conserved in a closed system with no external forces. Impulse, defined as the change in momentum, equals the product of the average force and the time interval, essential for analysing collisions and recoil.
在无外力作用的封闭系统中，动量守恒。冲量定义为动量的变化，等于平均力与时间间隔的乘积，这对分析碰撞和反冲至关重要。
2. Work, Energy and Power | 功、能与功率
Work is done when a force moves its point of application in the direction of the force. Energy is the capacity to do work, appearing in kinetic, potential, thermal and other forms. Power quantifies the rate of energy transfer.
当力使其作用点沿力的方向移动时，力做了功。能量是做功的能力，表现为动能、势能、热能等形式。功率则量化了能量传递的速率。
The work done by a constant force F acting over a displacement s at an angle θ is W = F s cos θ. For a varying force, work is obtained from the area under a force–displacement graph.
恒力F在位移s上且力与位移夹角为θ时所做的功为W = F s cos θ。对于变力，功可由力–位移图下的面积求得。
K = ½ m v² and ΔU = m g Δh
The principle of conservation of energy is a universal tool: total energy in a closed system remains constant, though it can transform between forms. Inelastic collisions lose kinetic energy to thermal and sound energy, whereas elastic collisions conserve kinetic energy.
能量守恒定律是一个普适工具：封闭系统的总能量保持不变，尽管它可以在不同形式之间转化。非弹性碰撞将部分动能转化为热能和声能，而弹性碰撞则保持动能守恒。
Power P can be expressed as P = W / t or, for a constant force acting on a body moving with velocity v, as P = F v. Efficiency is the ratio of useful output power to total input power.
功率P可表示为P = W / t，若恒力作用在速度为v的物体上，也可表示为P = F v。效率是有用输出功率与总输入功率之比。
3. Circular Motion and Gravitational Fields | 圆周运动与引力场
Uniform circular motion requires a net centripetal force directed towards the centre, continually changing the direction of velocity without changing its speed. Gravitational fields provide a natural context, with planets and satellites moving under Newton’s law of gravitation.
匀速圆周运动需要一个指向圆心的净向心力，该力不断改变速度的方向而不改变其大小。引力场提供了一个天然场景，行星和卫星在牛顿引力定律作用下运动。
For an object moving with speed v on a circular path of radius r, the centripetal acceleration is a = v² / r = r ω². The corresponding centripetal force is F = m v² / r = m r ω².
物体以速度v在半径为r的圆周上运动时，向心加速度为a = v² / r = r ω²。相应的向心力为F = m v² / r = m r ω²。
Newton’s law of gravitation: F = G m₁ m₂ / r². The gravitational field strength g at a point is the force per unit mass, g = G M / r². Near the Earth’s surface g ≈ 9.81 m s⁻², and it can be considered uniform for nearby heights.
牛顿引力定律：F = G m₁ m₂ / r²。一点的引力场强度g是单位质量所受的力，g = G M / r²。在地球表面附近，g ≈ 9.81 m s⁻²，在邻近高度下可视为匀强场。
Orbital period T of a satellite can be derived by equating gravitational force to centripetal force, leading to Kepler’s third law: T² ∝ r³ for circular orbits. Geostationary satellites have a period of 24 hours and orbit above the equator.
卫星的轨道周期T可通过令引力等于向心力导出，得到开普勒第三定律：对圆轨道有T² ∝ r³。地球同步卫星的周期为24小时，运行时位于赤道上空。
4. Oscillations and Waves | 振动与波
Simple harmonic motion (SHM) is a periodic motion where the restoring force is proportional to the displacement from equilibrium and directed towards it. Waves transfer energy without net transfer of matter and exhibit reflection, refraction, diffraction and interference.
简谐运动是一种周期性运动，其恢复力与离开平衡位置的位移成正比并指向平衡位置。波动传递能量而不伴随物质的净移动，并表现出反射、折射、衍射和干涉。
For SHM: acceleration a = − ω² x, where ω = 2π f. The velocity v at displacement x from amplitude A is v = ± ω√(A² − x²). The total energy of a simple harmonic oscillator is proportional to A².
对于简谐运动：加速度a = − ω² x，其中ω = 2π f。在振幅A下，位移为x时的速度v = ± ω√(A² − x²)。简谐振子的总能量与A²成正比。
Progressive waves are described by the wave equation v = f λ. Transverse waves (e.g. light) oscillate perpendicular to the direction of travel, while longitudinal waves (e.g. sound) oscillate parallel to it.
行波由波动方程v = f λ描述。横波（如光）的振动方向垂直于传播方向，纵波（如声波）的振动方向平行于传播方向。
Superposition leads to constructive interference when waves are in phase and destructive interference when out of phase. Standing waves on a string or in a pipe have nodes and antinodes, with resonant frequencies determined by boundary conditions.
叠加原理使得同相波产生相长干涉，反相波产生相消干涉。弦或管中的驻波具有波节和波腹，其共振频率由边界条件决定。
Two-source interference produces fringes with path difference Δx = n λ for constructive and Δx = (n + ½) λ for destructive interference. Young’s double-slit experiment famously demonstrates this for light.
双源干涉产生的条纹满足：相长干涉时程差Δx = n λ，相消干涉时Δx = (n + ½) λ。杨氏双缝实验经典地展示了光的干涉。
5. Electric Fields | 电场
Electric fields originate from charged particles and exert forces on other charges. The field concept allows analysis of interactions without direct contact, and potential difference drives charge flow in circuits.
电场源于带电粒子并对其他电荷施力。场的概念允许在不直接接触的情况下分析相互作用，电势差则驱动电路中电荷的流动。
Coulomb’s law gives the force between two point charges: F = k Q₁ Q₂ / r², where k = 1 / (4π ε₀). Electric field strength E at a point is the force per unit positive charge, E = F / q.
库仑定律给出两点电荷之间的力：F = k Q₁ Q₂ / r²，其中k = 1 / (4π ε₀)。一点的电场强度E是单位正电荷所受的力，E = F / q。
For a uniform electric field between parallel plates, E = V / d, where V is the potential difference and d the plate separation. The work done moving a charge q through a potential difference V is W = q V.
在平行板之间的匀强电场中，E = V / d，其中V为电势差，d为板间距。将电荷q移动通过电势差V所做的功为W = q V。
Parabolic motion of a charged particle in a uniform electric field mirrors projectile motion, with constant acceleration a = q E / m perpendicular to the field plates.
带电粒子在匀强电场中的抛物线运动与抛体运动类似，垂直于场板的加速度恒为a = q E / m。
6. Capacitance | 电容
Capacitance measures the ability of a system to store charge per unit potential difference. Capacitors are ubiquitous in timing circuits, filters and energy storage.
电容衡量系统在单位电势差下储存电荷的能力。电容器广泛应用于定时电路、滤波器和能量存储中。
Capacitance C = Q / V. For a parallel-plate capacitor, C = ε₀ εᵣ A / d, where εᵣ is the relative permittivity of the dielectric. Combining capacitors: in parallel Ctotal = Σ C; in series 1 / Ctotal = Σ 1 / C.
电容C = Q / V。对平行板电容器，C = ε₀ εᵣ A / d，其中εᵣ是介质的相对介电常数。电容器组合：并联时C总 = Σ C；串联时1 / C总 = Σ 1 / C。
Energy stored in a capacitor: U = ½ Q V = ½ C V² = ½ Q² / C. During charging and discharging through a resistor, the voltage and current change exponentially with time constant τ = R C.
电容器储存的能量：U = ½ Q V = ½ C V² = ½ Q² / C。在通过电阻充放电的过程中，电压和电流以时间常数τ = R C按指数规律变化。
V(t) = V₀ e−t/RC (discharging)
7. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Magnetic fields are produced by moving charges or permanent magnets and exert forces on other moving charges. Electromagnetic induction links time-varying magnetic flux to induced EMF, the principle behind generators and transformers.
磁场由运动电荷或永磁体产生，并对其他运动电荷施力。电磁感应将时变磁通量与感应电动势联系起来，这是发电机和变压器的基础原理。
The force on a current-carrying conductor in a magnetic field is given by F = B I l sin θ (Fleming’s left-hand rule). For a single charge q moving with velocity v, the Lorentz force is F = q v B sin θ.
载流导体在磁场中所受的力为F = B I l sin θ（弗莱明左手定则）。对以速度v运动的单个电荷q，洛伦兹力为F = q v B sin θ。
Magnetic flux Φ = B A cos θ; flux linkage = N Φ. Faraday’s law: induced EMF ε = − d (N Φ) / d t. Lenz’s law states that the induced current opposes the change in flux, explaining the negative sign.
磁通量Φ = B A cos θ；磁链 = N Φ。法拉第定律：感应电动势ε = − d (N Φ) / d t。楞次定律表明感应电流阻碍磁通量的变化，解释了式中的负号。
A conductor of length l moving perpendicular to a uniform field with speed v generates a motional EMF ε = B l v. Transformers operate on mutual induction, with voltage ratio Vs / Vp = Ns / Np for an ideal transformer.
长度为l的导体垂直于匀强磁场以速度v运动时，产生的动生电动势为ε = B l v。变压器基于互感原理工作，理想变压器电压比Vs / Vp = Ns / Np。
8. Alternating Currents | 交流电
Alternating current (AC) periodically reverses direction, and a sinusoidal voltage is characterised by its peak value, frequency and phase. Root‑mean‑square (rms) values link AC to equivalent DC heating effects.
交流电周期性地改变方向，正弦电压由峰值、频率和相位表征。均方根值将交流电与等效的直流热效应联系起来。
For a sinusoidal voltage V = V₀ sin ω t, the rms voltage is Vrms = V₀ / √2, and similarly Irms = I₀ / √2. Average power in a resistive load is Pav = Vrms Irms.
对于正弦电压V = V₀ sin ω t，均方根电压为Vrms = V₀ / √2，类似地Irms = I₀ / √2。纯电阻负载的平均功率为Pav = Vrms Irms。
Rectification converts AC to DC. Half‑wave rectification uses a single diode, while full‑wave rectification (using a diode bridge) inverts the negative half‑cycles, and smoothing capacitors reduce ripple.
整流将交流电转换为直流电。半波整流使用单个二极管，全波整流（使用桥式整流）将负半周翻转，平滑电容则减小纹波。
An ideal op‑amp in a circuit with negative feedback provides a virtual earth at the inverting input, enabling summing, integrating and differential operations essential in signal processing.
带有负反馈的理想运放在电路中可在反相输入端提供虚地，从而实现求和、积分和微分运算，这些在信号处理中至关重要。
9. Quantum Physics | 量子物理学
Quantum theory introduces the particle‑like behaviour of light (photons) and the wave‑like behaviour of particles, unifying concepts through the photoelectric effect and electron diffraction.
量子理论引入了光的粒子性（光子）和粒子的波动性，通过光电效应和电子衍射将概念统一起来。
Photon energy E = h f = h c / λ. The photoelectric effect demonstrates that electrons are ejected from a metal surface only when the photon energy exceeds the work function φ; the maximum kinetic energy is Kmax = h f − φ. The stopping potential is independent of intensity, which contradicts classical wave theory.
光子能量E = h f = h c / λ。光电效应表明，仅当光子能量大于金属的逸出功φ时，电子才会从金属表面逸出；最大动能为Kmax = h f − φ。遏止电势差与光强无关，这与经典波动理论相矛盾。
Kmax = e Vs
De Broglie’s hypothesis assigns a wavelength λ = h / p to any particle with momentum p. This explains electron diffraction and the stable electron orbits in the Bohr model of the hydrogen atom: angular momentum is quantised, m v r = n h / (2π).
德布罗意假设将波长λ = h / p赋予动量为p的任何粒子。这解释了电子衍射以及氢原子玻尔模型中稳定的电子轨道：角动量是量子化的，m v r = n h / (2π)。
Emission and absorption line spectra arise from electron transitions between discrete energy levels. The photon energy emitted or absorbed equals the difference between two energy levels, ΔE = h f = E₂ − E₁.
发射和吸收线光谱由电子在离散能级间的跃迁产生。发射或吸收的光子能量等于两能级之差，ΔE = h f = E₂ − E₁。
10. Nuclear Physics | 原子核物理学
Nuclear physics examines the structure of the nucleus, radioactive decay, mass‑energy equivalence and nuclear reactions. It underpins applications in power generation, medical imaging and carbon dating.
原子核物理学研究原子核的结构、放射性衰变、质能等价和核反应。它是发电、医学成像和碳断代等应用的基础。
The unified atomic mass unit u is defined such that 1 u = 1.66 × 10⁻²⁷ kg and 1 u of mass is equivalent to 931.5 MeV of energy (E = m c²). Mass defect is the difference between the mass of a nucleus and the sum of its constituent nucleons; binding energy is the energy required to separate a nucleus into its protons and neutrons.
统一原子质量单位u的定义为1 u = 1.66 × 10⁻²⁷ kg，且1 u的质量相当于931.5 MeV的能量（E = m Published by TutorHao | Pre-U Physics Revision Series | aleveler.com
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