📚 Year 13 OCR Physics: Core Concepts Summary | A2物理核心知识点梳理
As Year 13 students prepare for their OCR Physics A-Level examinations, a systematic review of the essential topics from Modules 5 and 6 is crucial. This article consolidates key principles, equations and revision pointers for the Newtonian world, astrophysics, particles and medical physics.
对于 Year 13 学生来说，系统梳理模块5和6的核心知识对备考至关重要。本文总结了牛顿世界、天体物理、粒子物理和医学物理等重点内容，包含关键公式和复习要点。
1. Thermal Physics & Ideal Gases | 热物理与理想气体
Temperature is a measure of the average random kinetic energy of particles. The internal energy of a system is the sum of the random kinetic and potential energies of its molecules. Specific heat capacity c = ΔQ/(mΔθ) and specific latent heat L = Q/m define energy transfer during heating or phase changes.
温度是粒子平均无规则动能的量度。系统的内能是所有分子无规则动能与势能的总和。比热容 c = ΔQ/(mΔθ) 和比潜热 L = Q/m 描述了加热或相变过程中的能量转移。
The ideal gas laws are linked by the equation of state pV = nRT = NkT, where R = 8.31 J mol⁻¹ K⁻¹ and k = 1.38×10⁻²³ J K⁻¹. Molecular kinetic theory gives the relationship between mean square speed and temperature:
理想气体状态方程 pV = nRT = NkT 联系了宏观量，气体常量 R = 8.31 J mol⁻¹ K⁻¹，玻尔兹曼常数 k = 1.38×10⁻²³ J K⁻¹。分子动理论给出了方均速率与温度的关系：
½ m<c²> = (3/2) kT
This shows that the average translational kinetic energy of a molecule depends only on temperature.
这反映了分子的平均平移动能仅取决于温度。
2. Circular Motion | 圆周运动
An object moving at constant speed v in a circle of radius r has an angular speed ω = v/r. Its velocity is always tangential, and the acceleration (centripetal) is directed towards the centre: a = v²/r = ω²r.
物体以恒定速率 v 在半径 r 的圆周上运动时，角速度 ω = v/r。速度方向始终沿切线，加速度（向心加速度）指向圆心：a = v²/r = ω²r。
The resultant force providing this acceleration is the centripetal force F = mv²/r = mω²r. This force is not a new kind of force; it is provided by tension, friction, gravity or the normal reaction, depending on the context.
提供该加速的合力即为向心力 F = mv²/r = mω²r。向心力不是新的力，它可由绳的张力、摩擦力、引力或支持力等提供。
3. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when acceleration a is directly proportional to displacement x from equilibrium and always directed towards that point: a = -ω²x. The frequency is f = 1/T, angular frequency ω = 2πf.
当加速度 a 与离开平衡位置的位移 x 成正比且始终指向平衡点时，物体做简谐运动：a = -ω²x。频率 f = 1/T，角频率 ω = 2πf。
Key equations include x = A cos(ωt) or x = A sin(ωt), v_max = ωA, a_max = ω²A. For a mass-spring system T = 2π√(m/k), and for a simple pendulum T = 2π√(l/g) for small amplitudes. Total energy E_total = ½ m ω² A² remains constant in undamped SHM.
关键方程：x = A cos(ωt) 或 x = A sin(ωt)，v_max = ωA，a_max = ω²A。对于弹簧振子 T = 2π√(m/k)，单摆小角度时 T = 2π√(l/g)。无阻尼简谐运动中的总能量 E_total = ½ m ω² A² 恒定。
Resonance occurs when the driving frequency matches the natural frequency, causing a dramatic increase in amplitude. Damping reduces the amplitude and shifts the resonance peak.
当驱动力频率与系统固有频率相同时发生共振，振幅急剧增大。阻尼使振幅减小并使共振峰变宽、偏移。
4. Gravitational Fields | 引力场
Newton’s law of universal gravitation: F = -GMm/r², where G = 6.67×10⁻¹¹ N m² kg⁻². The gravitational field strength g = F/m = GM/r². Near the Earth’s surface, g is approximately 9.81 N kg⁻¹.
万有引力定律：F = -GMm/r²，G = 6.67×10⁻¹¹ N m² kg⁻²。引力场强度 g = F/m = GM/r²。在地球表面附近 g 约为 9.81 N kg⁻¹。
Gravitational potential V = -GM/r, so the work done to move a mass m from infinity to a point is mV. Escape velocity from a body of mass M and radius R is v_esc = √(2GM/R). Kepler’s third law states T² ∝ r³ for planetary orbits.
引力势 V = -GM/r，将质量 m 从无穷远处移至该点需做的功为 mV。从质量为 M、半径为 R 的天体逃逸的速度为 v_esc = √(2GM/R)。开普勒第三定律指出行星轨道周期的平方与轨道半径的立方成正比 T² ∝ r³。
5. Cosmology & Astrophysics | 宇宙学与天体物理
The Hertzsprung-Russell diagram plots stellar luminosity against temperature, revealing the main sequence, giants and white dwarfs. A star spends most of its life on the main sequence fusing hydrogen into helium, and its evolutionary path depends on initial mass.
赫罗图以恒星的光度对温度作图，展示了主序星、巨星和白矮星的分布。恒星一生的大部分时间在主序阶段通过氢聚变为氦，演化路径取决于其初始质量。
The universe is expanding; Hubble’s law v = H₀ d shows that the recession velocity of galaxies is proportional to their distance, with H₀ ≈ 70 km s⁻¹ Mpc⁻¹. The cosmic microwave background radiation and the relative abundance of light elements provide strong evidence for the Big Bang model.
宇宙正在膨胀；哈勃定律 v = H₀ d 表明星系的退行速度与距离成正比，H₀ ≈ 70 km s⁻¹ Mpc⁻¹。宇宙微波背景辐射和轻元素丰度为大爆炸模型提供了有力证据。
6. Capacitors | 电容器
Capacitance C = Q/V, measured in farads (F). For a parallel-plate capacitor, C = ε₀ A/d, where ε₀ = 8.85×10⁻¹² F m⁻¹ is the permittivity of free space. A dielectric material increases capacitance by a factor ε_r.
电容 C = Q/V，单位法拉。对平行板电容器，C = ε₀ A/d，ε₀ 是真空介电常数 8.85×10⁻¹² F m⁻¹。插入电介质可使电容增大 ε_r 倍。
Energy stored in a capacitor is E = ½ QV = ½ CV² = ½ Q²/C. During discharge through a resistor, the charge decreases exponentially: Q = Q₀ e^{-t/RC}, where the time constant τ = RC indicates the time for the charge to fall to 37% of its initial value.
电容器储存的能量 E = ½ QV = ½ CV² = ½ Q²/C。通过电阻放电时，电荷指数衰减：Q = Q₀ e^{-t/RC}，时间常数 τ = RC 表示电荷降至初始值 37% 所需的时间。
7. Electric Fields | 电场
Coulomb’s law: F = kQq/r², where k = 1/(4πε₀). The electric field strength E = F/q; for a point charge E = kQ/r², and for a uniform field between parallel plates E = V/d. Electric field lines point away from positive charges.
库仑定律：F = kQq/r²，其中 k = 1/(4πε₀)。电场强度 E = F/q；点电荷的电场 E = kQ/r²，平行板间的匀强电场 E = V/d。电场线由正电荷指向负电荷。
Electric potential V = kQ/r; equipotential surfaces are perpendicular to field lines. Charged particles are accelerated in electric fields: the work done qV equals the change in kinetic energy ½ mv².
电势 V = kQ/r；等势面与电场线正交。带电粒子在电场中被加速，电场力做功 qV 等于动能的增量 ½ mv²。
8. Magnetic Fields & Electromagnetic Induction | 磁场与电磁感应
Magnetic force on a moving charge: F = BQv sinθ. Fleming’s left-hand rule gives the direction of force for a current-carrying conductor. A charged particle moving perpendicular to a uniform B-field undergoes circular motion with radius r = mv/(BQ).
运动电荷在磁场中受力 F = BQv sinθ。左手定则判断通电导体受力的方向。带电粒子垂直射入匀强磁场时做匀速圆周运动，半径 r = mv/(BQ)。
Magnetic flux Φ = BA cosθ (unit: weber, Wb). Faraday’s law of electromagnetic induction states that the induced emf ε is proportional to the rate of change of flux linkage: ε = -N dΦ/dt. Lenz’s law dictates that the induced current opposes the change causing it.
磁通量 Φ = BA cosθ（单位韦伯）。法拉第电磁感应定律：感应电动势 ε 与磁链变化率成正比：ε = -N dΦ/dt。楞次定律指出感应电流的磁场总是阻碍引起感应电动势的磁通变化。
9. Nuclear & Particle Physics | 核物理与粒子物理
Atomic nuclei are composed of protons and neutrons, bound by the strong nuclear force. The binding energy is the work required to separate a nucleus into its constituents; the graph of binding energy per nucleon peaks at iron-56. Radioactive decay follows the exponential law: N = N₀ e^{-λt}, with activity A = λN.
原子核由质子和中子组成，靠强核力束缚。结合能是将原子核分解为独立核子所需的功；平均结合能曲线在铁-56处达到峰值。放射性衰变遵循指数规律：N = N₀ e^{-λt}，活度 A = λN。
Half-life T₁/₂ = ln2/λ. Particles are classified as hadrons (baryons and mesons, composed of quarks) or leptons (e.g. electrons, neutrinos). Beta-minus decay involves a neutron changing into a proton, emitting an electron and an antineutrino: n → p + e⁻ + ν̅_e.
半衰期 T₁/₂ = ln2/λ。粒子分为强子（重子和介子，由夸克组成）和轻子（如电子、中微子）。β⁻ 衰变中，中子转变为质子，放出一个电子和一个反电子中微子：n → p + e⁻ + ν̅_e。
10. Medical Imaging | 医学成像
X-rays are produced when high-speed electrons strike a metal target; the intensity I after passing through matter of thickness x is I = I₀ e^{-μx}, where μ is the attenuation coefficient. CT scanners combine multiple X-ray images to generate 3D representations.
X 射线由高速电子轰击金属靶产生；穿过厚度为 x 的物质后强度为 I = I₀ e^{-μx}，μ 是衰减系数。CT 扫描结合多个 X 射线图像生成三维影像。
Ultrasound uses high-frequency sound waves; the acoustic impedance difference at boundaries determines reflection. PET scans detect gamma photons from positron-electron annihilation, providing functional imaging. The annihilation produces two 511 keV photons travelling in opposite directions.
超声利用高频声波，界面处声阻抗差异决定反射强弱。PET 扫描探测正电子湮灭产生的 γ 光子，用于功能性成像。正负电子湮灭产生两个能量为 511 keV、反向运动的光子。
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