Year 13 OCR Physics: Core Concepts Review | Year 13 OCR 物理：核心知识点梳理

📚 Year 13 OCR Physics: Core Concepts Review | Year 13 OCR 物理：核心知识点梳理

Welcome to the ultimate revision guide for Year 13 OCR Physics. This article walks you through the most important concepts from Newtonian world, astrophysics, particles and medical physics, all condensed into clear bilingual summaries. Use it to reinforce your understanding and boost your exam confidence.

欢迎来到 Year 13 OCR 物理核心知识点梳理。本文以中英双语形式为你逐一总结 A2 阶段的关键主题，涵盖牛顿世界、天体物理、粒子与医学物理等内容，帮助你厘清概念、高效备考。

1. Thermal Physics | 热物理

The internal energy of a substance is the sum of the randomly distributed kinetic and potential energies of its particles. When heating a substance, the relationship Q = mcΔθ applies where no phase change occurs, while Q = mL is used during melting or boiling, with L representing the specific latent heat.

物质的内能是其粒子随机分布的动能与势能之和。加热物质时，若无相变则使用 Q = mcΔθ；若发生熔化或沸腾，则用 Q = mL，其中 L 为比潜热。

For an ideal gas, the equation of state is pV = nRT = NkT, and the kinetic theory model gives the average translational kinetic energy of a molecule as ½ m<c²> = ³⁄₂ kT. This links macroscopic temperature to microscopic motion.

对于理想气体，状态方程为 pV = nRT = NkT，而根据分子动理论，单分子平均平动动能为 ½ m<c²> = ³⁄₂ kT，从而将宏观温度与微观运动联系起来。

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2. Circular Motion | 圆周运动

An object moving in a circle at constant speed experiences a centripetal acceleration directed towards the centre. The angular speed ω = Δθ/Δt is related to linear speed by v = ωr. The centripetal acceleration can be expressed as a = v²/r = ω²r.

做匀速圆周运动的物体具有指向圆心的向心加速度。角速度 ω = Δθ/Δt，与线速度的关系为 v = ωr。向心加速度可表示为 a = v²/r = ω²r。

The net force causing this acceleration is the centripetal force F = mv²/r = mω²r. Common examples include tension in a string, friction on a banked track, or gravity for orbiting bodies. Understanding the force that provides the centripetal component is crucial.

产生该加速度的合力即为向心力 F = mv²/r = mω²r。常见实例包括绳子的张力、倾斜弯道上的摩擦力或轨道运动中的引力。明确向心力的来源是解题关键。

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3. Simple Harmonic Motion | 简谐运动

Simple harmonic motion (SHM) is defined by an acceleration that is directly proportional to displacement from equilibrium and always directed towards it: a = −ω²x. The displacement can be written as x = A cos(ωt) or x = A sin(ωt), with A the amplitude and ω the angular frequency.

简谐运动（SHM）的定义是加速度与相对平衡位置的位移成正比且方向相反：a = −ω²x。位移方程可写为 x = A cos(ωt) 或 x = A sin(ωt)，其中 A 为振幅，ω 为角频率。

The velocity at any displacement is v = ±ω√(A² − x²), and maximum speed is ωA at the equilibrium position. The total mechanical energy in an undamped system remains constant: E = ½ mω²A², shared between kinetic and potential forms.

任意位移处的速度为 v = ±ω√(A² − x²)，平衡位置时达到最大速度 ωA。无阻尼系统中总机械能守恒：E = ½ mω²A²，在动能与势能之间相互转换。

Free oscillations gradually lose energy due to damping, which reduces amplitude. Forced oscillations can lead to resonance when the driving frequency matches the natural frequency, resulting in maximum amplitude transfer. Critical damping returns the system to equilibrium in the shortest time without oscillating.

自由振动因阻尼而逐渐损失能量，振幅减小。受迫振动中，当驱动频率接近固有频率时发生共振，振幅达到最大。临界阻尼可使系统在不振荡的情况下最短时间内回到平衡位置。

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4. Gravitational Fields | 引力场

Newton’s law of gravitation states that any two point masses attract each other with a force F = Gm₁m₂/r². The gravitational field strength g at a point is the force per unit mass, g = F/m. For a spherical mass, the field outside the sphere is identical to that of a point mass: g = GM/r².

牛顿引力定律指出，任意两质点间的吸引力为 F = Gm₁m₂/r²。某点的引力场强度 g 定义为单位质量所受的力，g = F/m。在均匀球体外部，场等同于质量集中于球心的质点，g = GM/r²。

Gravitational potential V is the work done per unit mass to bring a mass from infinity to that point; V = −GM/r. The potential gradient gives the field strength: g = −dV/dr. For satellites, combining centripetal force and gravity yields orbital speed v = √(GM/r) and period T² ∝ r³ (Kepler’s third law).

引力势 V 是将单位质量从无穷远处移至该点所做的功，V = −GM/r。势的梯度给出场强：g = −dV/dr。对于卫星，由向心力与万有引力相等可得轨道速度 v = √(GM/r)，并导出周期规律 T² ∝ r³（开普勒第三定律）。

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5. Astrophysics & Cosmology | 天体物理与宇宙学

Stars are born from collapsing clouds of gas and dust, spending most of their lives on the main sequence where hydrogen fuses into helium. A star’s position on the Hertzsprung-Russell (HR) diagram depends on its luminosity and surface temperature. After the main sequence, low-mass stars become red giants and then white dwarfs, while massive stars may undergo supernova explosions, leaving behind neutron stars or black holes.

恒星诞生于气体尘埃云的坍缩，主序星阶段通过氢聚变为氦维持稳定。赫罗图（HR图）以光度和表面温度为坐标，低质量恒星在脱离主序后演化为红巨星再成为白矮星，大质量恒星则可能发生超新星爆发，留下中子星或黑洞。

The cosmological principle states that the universe is homogeneous and isotropic on large scales. Observations of redshifted light from distant galaxies show that they are moving away, with the redshift defined as z = Δλ/λ₀ ≈ v/c. Hubble’s law v = H₀d implies the universe is expanding, and the cosmic microwave background radiation provides strong evidence for the Big Bang theory.

宇宙学原理认为，在大尺度上宇宙是均匀且各向同性的。遥远星系的谱线红移表明它们正在远离，红移定义为 z = Δλ/λ₀ ≈ v/c。哈勃定律 v = H₀d 揭示宇宙正在膨胀，而宇宙微波背景辐射为“大爆炸”理论提供了有力证据。

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6. Capacitors | 电容器

Capacitance C is defined as the charge stored per unit potential difference: C = Q/V. For a parallel-plate capacitor, C = ε₀εᵣA/d, where εᵣ is the relative permittivity of the dielectric. Energy stored can be expressed as E = ½ QV = ½ CV² = ½ Q²/C, and this energy is released when the capacitor discharges.

电容 C 定义为单位电势差所储存的电荷量：C = Q/V。对于平行板电容器，有 C = ε₀εᵣA/d，其中 εᵣ 为电介质的相对介电常数。电容储存的能量可写为 E = ½ QV = ½ CV² = ½ Q²/C，并在放电时释放。

In RC circuits, the time constant τ = RC determines the rate of charging or discharging. The charge on a discharging capacitor follows Q = Q₀ e^−t/τ, while charging is described by Q = Q₀(1 − e^−t/τ). The initial current is V₀/R, and after one time constant the voltage drops to about 37% of its initial value.

在 RC 电路中，时间常数 τ = RC 决定了充放电的快慢。放电时的电荷变化遵循 Q = Q₀ e^−t/τ，充电时则为 Q = Q₀(1 − e^−t/τ)。初始电流为 V₀/R，经过一个时间常数后电压约降至初始值的 37%。

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7. Electric Fields | 电场

Coulomb’s law describes the force between two point charges: F = kQ₁Q₂/r² (k = 1/(4πε₀)). Electric field strength E is the force per unit positive charge, E = F/q. For a point charge, E = kQ/r², and for a uniform field between parallel plates, E = V/d.

库仑定律描述两点电荷间的力：F = kQ₁Q₂/r²（k = 1/(4πε₀)）。电场强度 E 定义为单位正电荷所受的力，E = F/q。对于点电荷，E = kQ/r²；在平行板产生的匀强电场中，E = V/d。

Electric potential V at a distance r from a point charge is V = kQ/r. Charged particles moving in electric fields experience acceleration, and the work done by the field equals qΔV. This principle is used in particle accelerators and to determine the deflection of electron beams in cathode ray tubes.

距离点电荷 r 处的电势为 V = kQ/r。带电粒子在电场中运动时受到加速，电场力做功等于 qΔV。这一原理广泛应用于粒子加速器，并可用来分析电子束在阴极射线管中的偏转。

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8. Magnetic Fields & Electromagnetic Induction | 磁场与电磁感应

A magnetic field exerts a force on a moving charge: F = BQv sinθ, where θ is the angle between velocity and the field. For a current-carrying conductor, F = BIL sinθ. Fleming’s left-hand rule gives the direction of the force, which is exploited in electric motors.

磁场对运动电荷的作用力为 F = BQv sinθ，其中 θ 是速度与磁场方向的夹角。对于载流导线，力的大小为 F = BIL sinθ。左手定则判断受力方向，这一原理应用于电动机。

Faraday’s law states that the induced emf is equal to the rate of change of magnetic flux: ε = −dΦ/dt, and Lenz’s law determines its direction. An AC generator or transformer relies on changing flux to induce voltage. For an ideal transformer, Vₚ/Vₛ = Nₚ/Nₛ and IₚVₚ = IₛVₛ, indicating power conservation.

法拉第定律指出，感应电动势等于磁通量变化率的负值：ε = −dΦ/dt，楞次定律则确定其方向。交流发电机和变压器均利用变化的磁通量产生感应电压。对于理想变压器，Vₚ/Vₛ = Nₚ/Nₛ 且 IₚVₚ = IₛVₛ，体现功率守恒。

The rms values of alternating current and voltage are related to peak values by I_rms = I₀/√2 and V_rms = V₀/√2. Understanding flux linkage, back emf, and the operation of a simple AC generator are essential for electromagnetic applications.

交流电的有效值与峰值关系为 I_rms = I₀/√2 和 V_rms = V₀/√2。掌握磁链、反电动势以及简易交流发电机的工作原理是电磁学应用的关键。

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9. Particle & Nuclear Physics | 粒子与核物理

The Standard Model classifies fundamental particles into quarks, leptons, and gauge bosons. Hadrons are particles made of quarks; baryons (e.g., proton, neutron) consist of three quarks, while mesons (e.g., pion) are quark–antiquark pairs. Leptons, such as electrons and neutrinos, are not subject to the strong interaction.

标准模型将基本粒子分为夸克、轻子和规范玻色子。强子是由夸克组成的粒子，其中重子（如质子、中子）由三个夸克构成，介子（如 π 介子）由一个夸克和一个反夸克组成。轻子（如电子、中微子）不参与强相互作用。

Nuclear decay processes include alpha (α), beta-minus (β⁻), and gamma (γ) emission. The activity A of a radioactive sample is the number of decays per second: A = λN. The half-life t₁/₂ = ln 2/λ is the time for half the nuclei to decay. Exponential decay is described by N = N₀ e^−λt.

核衰变包括 α 衰变、β⁻ 衰变和 γ 辐射。放射性活度 A 是每秒衰变次数：A = λN。半衰期 t₁/₂ = ln 2/λ 是原子核衰变一半所用的时间。指数衰变规律为 N = N₀ e^−λt。

Mass–energy equivalence E = mc² explains the mass defect in nuclei; binding energy is the work needed to separate a nucleus into its individual nucleons. Nuclear fission and fusion both release energy owing to the increase in average binding energy per nucleon, with fusion being the process that powers stars.

质能方程 E = mc² 解释了原子核的质量亏损；结合能是将原子核拆散成核子所需的功。核裂变和核聚变均因平均结合能增大而释放能量，其中聚变是恒星的能量来源。

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10. Medical Physics | 医学物理

X-rays are produced when high-speed electrons strike a metal target, generating bremsstrahlung and characteristic X‑ray spectra. Their attenuation through matter follows I = I₀ e^−μx, where μ is the linear attenuation coefficient. Computed tomography (CT) uses multiple X‑ray projections to create detailed cross‑sectional images.

X 射线由高速电子轰击金属靶产生，形成轫致辐射和特征谱线。X 射线在物质中的衰减遵循 I = I₀ e^−μx，μ 为线性衰减系数。计算机断层扫描（CT）利用多角度投影重建精细的断层图像。

Ultrasound imaging employs high-frequency sound waves that reflect at boundaries between tissues of different acoustic impedance Z = ρc. The reflection coefficient is largest when the impedance mismatch is significant, and a coupling gel is used to minimise air gaps. A‑scans and B‑scans provide distance and cross‑sectional information, respectively, and the Doppler effect detects blood flow velocity.

超声成像利用高频声波在不同声阻抗 Z = ρc 的组织界面发生反射。阻抗差越大反射越强，使用耦合凝胶可消除空气间隙。A 扫描和 B 扫描分别提供距离与断面信息，多普勒效应则用以测量血流速度。

Radioactive tracers such as technetium‑99m emit gamma radiation and are used in medical diagnostics. Positron emission tomography (PET) detects gamma ray pairs produced by electron–positron annihilation, allowing functional imaging of organs. Careful consideration of half‑life, penetration, and toxicity is vital when selecting a medical radioisotope.

锝‑99m 等放射性示踪剂发射 γ 射线，用于医学诊断。正电子发射断层扫描（PET）通过探测正负电子湮灭产生的 γ 光子对，实现器官功能成像。选择医用放射性同位素时必须综合考虑半衰期、穿透能力和生物毒性。

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