📚 Complete Physics: Core Concepts Explained | 完整物理核心概念解析
Physics seeks to describe the universe from the smallest subatomic particles to the largest galaxies using a unified set of principles. Mastering its core concepts – mechanics, thermodynamics, waves, electromagnetism, and modern physics – provides the tools to analyse real-world phenomena and solve problems with clarity. This article breaks down these fundamental ideas, pairing each with a simple explanation and the essential equations you need to remember.
物理学试图用统一的原理来描述从微观亚原子粒子到宏观星系的宇宙。掌握力学、热学、波动、电磁学和近代物理的核心概念，能够为你提供清晰分析现实世界问题和解题的工具。本文将逐一解析这些基本观念，每一部分都配有简明解释和你必须掌握的关键方程。
1. Kinematics | 运动学
Kinematics describes motion in terms of displacement, velocity, and acceleration without considering the forces that cause it. When acceleration is constant, three equations link these quantities and time. They are the foundation for analysing projectiles and linear motion.
运动学描述物体的位移、速度和加速度，而不考虑产生运动的力。当加速度恒定时，三个方程将上述物理量与时间联系起来。它们是分析抛体运动和直线运动的基础。
v = u + at
s = ut + ½at²
v² = u² + 2as
Here u is initial velocity, v final velocity, a acceleration, t time, and s displacement. These equations are derived from the definitions of average velocity and acceleration. They apply only when a is constant in magnitude and direction.
其中 u 为初速度，v 为末速度，a 为加速度，t 为时间，s 为位移。这些方程由平均速度和加速度的定义导出，仅当加速度的大小和方向保持不变时才适用。
2. Dynamics and Newton’s Laws | 动力学与牛顿定律
Dynamics relates motion to its causes – forces. Newton’s three laws form the core: an object remains at rest or in uniform motion unless acted upon by a net force (inertia); the net force on an object equals the product of its mass and acceleration (F = ma); and when one object exerts a force on another, the second object exerts an equal and opposite force on the first (action-reaction).
动力学将运动和它的起因——力联系起来。牛顿三定律是核心：物体在不受外力时保持静止或匀速直线运动（惯性）；物体的加速度与所受合外力成正比，与质量成反比（F = ma）；两物体之间的作用力与反作用力大小相等、方向相反。
Free-body diagrams are essential for identifying all forces acting on a system, such as weight, normal reaction, tension, and friction. The net force resolved along chosen axes determines the resulting acceleration.
受力图是确定系统所受全部力（如重力、法向反作用力、张力和摩擦力）的关键工具。将合外力沿选定坐标轴分解后，即可确定加速度。
3. Work, Energy and Power | 功、能与功率
Work is done when a force displaces an object in its direction: W = Fs cos θ. Energy is the capacity to do work and exists in many forms. Kinetic energy (KE = ½mv²) is energy due to motion; gravitational potential energy (GPE = mgh) is energy due to position in a gravitational field. The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
力在位移方向做功：W = Fs cos θ。能量是做功的能力，有多种形式。动能（KE = ½mv²）是因运动而具有的能量；重力势能（GPE = mgh）是因物体在引力场中的位置而具有的能量。能量守恒定律指出，能量不能创生也不能消失，只能从一种形式转化为另一种形式。
Power is the rate of doing work or transferring energy: P = W/t. In mechanics it is also given by P = Fv for a constant force applied in the direction of velocity.
功率是做功或能量转化的快慢：P = W/t。在力学中，若力的方向与速度方向一致，功率也可表示为 P = Fv。
4. Momentum and Impulse | 动量与冲量
Momentum p is defined as the product of mass and velocity: p = mv. It is a vector quantity. Impulse is the change in momentum caused by a force acting over a time interval: impulse = FΔt = Δp. The law of conservation of momentum states that in a closed system with no external forces, total momentum before an interaction equals total momentum after.
动量 p 定义为质量与速度的乘积：p = mv，是矢量。冲量是力在时间上的累积效应，等于动量的变化：冲量 = FΔt = Δp。动量守恒定律指出，在无外力的封闭系统中，相互作用前的总动量等于相互作用后的总动量。
Collisions can be elastic (both momentum and kinetic energy conserved) or inelastic (only momentum conserved, with some KE converted into heat, sound or deformation). Real-world collisions are often partially inelastic.
碰撞分为弹性碰撞（动量和动能均守恒）和非弹性碰撞（仅动量守恒，部分动能转化为热、声或形变）。现实中的碰撞大多是非完全弹性的。
5. Circular Motion and Gravitation | 圆周运动与引力
An object moving in a circle at constant speed experiences a centripetal acceleration directed towards the centre: a = v²/r = ω²r. The required centripetal force is F = mv²/r = mω²r. This force is provided by tension, gravity, friction or the normal reaction depending on the situation.
物体做匀速圆周运动时具有指向圆心的向心加速度：a = v²/r = ω²r。所需的向心力为 F = mv²/r = mω²r。向心力可由张力、引力、摩擦力或法向反作用力提供，视具体情况而定。
Newton’s law of universal gravitation states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = Gm₁m₂/r². Gravitational field strength g at a point is the force per unit mass, and near Earth’s surface it is approximately 9.81 N kg⁻¹.
牛顿万有引力定律指出，任何两个质量都相互吸引，引力大小与两质量的乘积成正比，与它们中心距离的平方成反比：F = Gm₁m₂/r²。引力场强度 g 是单位质量所受的引力，在地球表面附近约为 9.81 N kg⁻¹。
6. Thermal Physics | 热物理学
Temperature measures the average kinetic energy of particles in a substance; heat is the energy transferred due to a temperature difference. Internal energy is the sum of the random kinetic and potential energies of all particles in a system. Heating a substance can raise its temperature (Q = mcΔθ) or change its state (Q = mL), where c is specific heat capacity and L is specific latent heat.
温度是物质粒子平均动能的量度；热量是因温差而传递的能量。内能是系统内所有粒子无规则运动的动能和势能之和。对物体加热可使其温度升高（Q = mcΔθ）或改变物态（Q = mL），其中 c 是比热容，L 是比潜热。
The ideal gas equation relates pressure p, volume V, number of moles n, and absolute temperature T: pV = nRT. Here R is the universal gas constant. Kinetic theory links macroscopic pressure to microscopic particle collisions: pV = ⅓ N m⟨c²⟩, where ⟨c²⟩ is the mean square speed.
理想气体状态方程联系压强 p、体积 V、物质的量 n 和热力学温度 T：pV = nRT，其中 R 是普适气体常数。分子动理论将宏观压强与微观粒子碰撞相联系：pV = ⅓ N m⟨c²⟩，⟨c²⟩ 为方均速率。
7. Waves and Sound | 波动与声学
A wave transfers energy without transferring matter. In transverse waves (e.g. light, water ripples) particle displacement is perpendicular to energy propagation; in longitudinal waves (e.g. sound) displacement is parallel. Wave speed v, frequency f, and wavelength λ are linked by v = fλ.
波动传播能量而不传播物质。横波（如光、水波）中质点位移垂直于能量传播方向；纵波（如声波）中位移平行于传播方向。波速 v、频率 f 和波长 λ 满足 v = fλ。
Superposition occurs when two or more waves meet. Constructive interference gives increased amplitude; destructive interference gives reduced amplitude. Standing waves form when identical waves travel in opposite directions along a bounded medium, producing nodes (zero amplitude) and antinodes (maximum amplitude).
叠加是指两个或多个波相遇。相长干涉导致振幅增大；相消干涉导致振幅减小。当两列相同的波在有限介质中相向传播时形成驻波，产生波节（振幅为零）和波腹（振幅最大）。
8. Optics | 光学
Light can be treated as rays that follow the laws of reflection and refraction. The law of reflection states that the angle of incidence equals the angle of reflection (θᵢ = θᵣ). Refraction is governed by Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index of the medium.
光可看作遵循反射定律和折射定律的光线。反射定律指出入射角等于反射角（θᵢ = θᵣ）。折射服从斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，其中 n 是介质的折射率。
Lenses form images by refraction. Thin lens equation relates object distance u, image distance v, and focal length f: 1/f = 1/u + 1/v. Convex (converging) lenses can produce real or virtual images; concave (diverging) lenses always produce virtual, diminished images.
透镜通过折射成像。薄透镜方程联系物距 u、像距 v 和焦距 f：1/f = 1/u + 1/v。凸透镜（会聚透镜）可成实像或虚像；凹透镜（发散透镜）总是成缩小、正立的虚像。
9. Electric Fields and Circuits | 电场与电路
Electric charge is a fundamental property. Like charges repel; opposite charges attract, described by Coulomb’s law: F = k|q₁q₂|/r². An electric field E is a region where a charge experiences a force: E = F/q. For a uniform field between parallel plates, E = V/d.
电荷是物质基本属性。同种电荷相斥，异种电荷相吸，库仑定律描述这一作用：F = k|q₁q₂|/r²。电场 E 是电荷受力的区域：E = F/q。平行板之间的匀强电场满足 E = V/d。
Current I is rate of flow of charge: I = ΔQ/Δt. Potential difference V is energy transferred per unit charge. Resistance R = V/I, and Ohm’s law (V = IR) holds for ohmic conductors at constant temperature. In series circuits, current is the same everywhere; in parallel circuits, potential difference is the same across each branch.
电流 I 是电荷流动的速率：I = ΔQ/Δt。电势差 V 是单位电荷转移的能量。电阻 R = V/I，欧姆定律（V = IR）适用于恒温下的欧姆导体。串联电路中电流处处相等；并联电路中各支路两端电压相等。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Magnetic fields are produced by moving charges or permanent magnets. A current-carrying wire in a magnetic field experiences a force F = BIL sin θ (for a straight wire) or F = BQv sin θ (for a moving charge). The direction is given by Fleming’s left-hand rule.
磁场由运动电荷或永磁体产生。通电导线在磁场中受力 F = BIL sin θ（直导线），运动电荷受力 F = BQv sin θ。方向由弗莱明左手定则确定。
Faraday’s law states that an induced e.m.f. is proportional to the rate of change of magnetic flux linkage: ε = -N ΔΦ/Δt. Lenz’s law gives the direction of the induced current: it opposes the change that caused it. Together they explain transformers, generators and inductors.
法拉第定律指出，感应电动势与磁通量变化率成正比：ε = -N ΔΦ/Δt。楞次定律给出感应电流的方向：总是阻碍引起感应的变化。二者共同解释了变压器、发电机和电感器的工作原理。
11. Quantum Physics | 量子物理
Quantum physics reveals that energy at the atomic scale is quantised. Photons are discrete packets of electromagnetic energy with energy E = hf, where h is Planck’s constant. The photoelectric effect demonstrates that when light of sufficient frequency strikes a metal surface, electrons are emitted with maximum kinetic energy KEmax = hf – φ, where φ is the work function of the metal.
量子物理学揭示原子尺度的能量是量子化的。光子是电磁能量的分立包，能量为 E = hf，h 是普朗克常数。光电效应表明，当频率足够高的光照射金属表面时，会发射电子，其最大动能为 KEmax = hf – φ，φ 为金属的逸出功。
Atomic energy levels are discrete; electrons can transition between levels by absorbing or emitting photons of precise energy. The line emission and absorption spectra provide evidence for quantised energy levels and allow identification of elements.
原子能级是分立的；电子可以通过吸收或发射特定能量的光子在能级间跃迁。线状发射光谱和吸收光谱为能级的量子化提供了证据，并可用于鉴别元素。
12. Nuclear and Particle Physics | 核与粒子物理
The atomic nucleus contains protons and neutrons (nucleons), held together by the strong nuclear force. Radioactive decay occurs when an unstable nucleus emits alpha, beta, or gamma radiation. Alpha decay reduces mass number by 4 and atomic number by 2; beta decay increases atomic number by 1; gamma emission just releases energy.
原子核由质子和中子（核子）组成，依靠强核力结合在一起。不稳定的原子核会通过发射 α、β 或 γ 射线发生放射性衰变。α 衰变使质量数减 4、原子序数减 2；β 衰变使原子序数加 1；γ 辐射仅释放能量。
The activity A of a radioactive sample decays exponentially: A = λN, and N = N₀ e⁻ᵗ, where λ is the decay constant. Half-life T₁/₂ = ln 2/λ is the time for half the nuclei to decay. Einstein’s mass-energy equivalence E = mc² explains the energy released in nuclear fission and fusion, where a small loss in mass appears as a huge amount of energy.
放射性样品的活度 A 按指数衰减：A = λN，N = N₀ e⁻ᵗ，λ 是衰变常数。半衰期 T₁/₂ = ln 2/λ 是半数核发生衰变所需的时间。爱因斯坦质能方程 E = mc² 解释了核裂变和核聚变释放的巨大能量，微小的质量亏损转化为巨大的能量。
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