📚 AQA A-Level Physics Year 13 Core Concepts | AQA 物理 A-Level Year 13 核心知识点梳理
The second year of AQA A-Level Physics delves into advanced mechanics, fields, thermal physics, and nuclear physics, building a comprehensive foundation for further study. Mastering these core principles is essential for success in examinations and for appreciating the physical world.
AQA 物理 A-Level 第二年课程深入探讨高等力学、场论、热物理与核物理，为进一步深造打下坚实基础。掌握这些核心原理是考试成功的关键，也是理解物理世界的重要途径。
1. Circular Motion | 圆周运动
In circular motion, an object moves along a circular path at constant speed, but its velocity changes due to the changing direction.
在圆周运动中，物体以恒定速率沿圆形路径运动，但由于方向不断变化，速度矢量持续改变。
The angular displacement θ is measured in radians; angular velocity ω = Δθ/Δt (rad s⁻¹), and it relates to linear speed via v = ωr.
角位移 θ 以弧度衡量；角速度 ω = Δθ/Δt (单位 rad s⁻¹)，线速度与角速度的关系为 v = ωr。
a = v² / r = ω² r
F = m v² / r = m ω² r
Centripetal acceleration a is always directed towards the centre and does not change the speed, only direction.
向心加速度 a 始终指向圆心，只改变速度方向而不改变速率。
The centripetal force does no work because it acts perpendicular to the displacement. It can be provided by tension, gravity, or friction.
向心力不做功，因为它与位移垂直。向心力可由张力、重力或摩擦力提供。
2. Simple Harmonic Motion | 简谐运动
Simple harmonic motion (SHM) occurs when the acceleration is directly proportional to the displacement from equilibrium and always directed towards that equilibrium point.
当加速度与偏离平衡位置的位移成正比且始终指向平衡点时，物体做简谐运动。
a = -ω² x
The solutions for displacement are x = A cos(ωt) or x = A sin(ωt), where A is the amplitude and ω the angular frequency.
位移的解为 x = A cos(ωt) 或 x = A sin(ωt)，其中 A 为振幅，ω 为角频率。
Velocity in SHM can be expressed as v = ±ω √(A² – x²), with maximum speed vmax = ωA at the equilibrium position.
简谐运动的速度可表示为 v = ±ω √(A² – x²)，在平衡位置处速度最大 vmax = ωA。
The period T = 2π/ω. For a mass-spring system T = 2π√(m/k); for a simple pendulum T = 2π√(l/g).
周期 T = 2π/ω。弹簧振子的周期 T = 2π√(m/k)，单摆的周期 T = 2π√(l/g)。
The total mechanical energy in undamped SHM is constant and equals ½ m ω² A². Energy continually interchanges between kinetic and potential forms.
无阻尼简谐运动中总机械能守恒，等于 ½ m ω² A²。能量在动能与势能之间不断转换。
3. Resonance and Damping | 共振与阻尼
Free vibrations occur at the natural frequency of a system without external driving; forced vibrations occur when a periodic driving force is applied.
自由振动以系统的固有频率发生，无外部驱动；当施加周期性的驱动力时，系统作受迫振动。
Resonance happens when the driving frequency matches the natural frequency, causing a dramatic increase in amplitude.
当驱动频率与固有频率相等时发生共振，振幅急剧增大。
Damping removes energy from the system, reducing amplitude. Light damping leads to a gradual decay, critical damping returns the system to equilibrium most quickly without oscillation, and overdamping results in a slow return.
阻尼消耗系统能量，减小振幅。轻阻尼导致振幅缓慢衰减；临界阻尼使系统最快回到平衡位置且不振荡；过阻尼则使返回变得非常缓慢。
Damping also widens and lowers the resonance peak. Phase difference between driver and oscillator approaches π/2 at resonance.
阻尼还会使共振峰变宽变低。共振时，驱动力与振子之间的相位差趋近于 π/2。
4. Gravitational Fields | 引力场
Newton’s law of universal gravitation states that the force between two point masses is F = G m₁ m₂ / r², where G is the gravitational constant.
牛顿万有引力定律指出，两质点间的引力为 F = G m₁ m₂ / r²，G 为引力常量。
The gravitational field strength g at a point is the force per unit mass: g = F/m = G M / r² for a radial field due to mass M.
引力场强度 g 定义为单位质量的受力：g = F/m。对于质量为 M 的质点产生的径向场，g = G M / r²。
Gravitational potential V is the work done per unit mass to bring a test mass from infinity to that point; for a radial field V = – G M / r.
引力势 V 是将单位质量的检验质量从无穷远处移至该点所做的功；对于径向场 V = – G M / r。
The change in gravitational potential energy is ΔU = m ΔV. The escape velocity from a planet’s surface is v_esc = √(2GM/R).
引力势能的变化为 ΔU = m ΔV。从行星表面逃逸所需的速度 v_esc = √(2GM/R)。
Kepler’s third law T² ∝ r³ applies to satellites and is consistent with Newton’s law for circular orbits.
开普勒第三定律 T² ∝ r³ 适用于卫星，与牛顿定律在圆轨道下一致。
5. Electric Fields and Capacitors | 电场与电容
Coulomb’s law gives the force between two point charges: F = k Q₁ Q₂ / r², where k = 1/(4πε₀).
库仑定律给出两点电荷间的作用力：F = k Q₁ Q₂ / r²，其中 k = 1/(4πε₀)。
Electric field strength E = F/q. For a uniform field between parallel plates, E = V/d; for a point charge, E = k Q / r².
电场强度 E = F/q。在平行板间的匀强电场中，E = V/d；点电荷电场中，E = k Q / r²。
Capacitance C = Q/V. For a parallel-plate capacitor, C = ε₀ A / d. Dielectrics increase capacitance by reducing the effective field.
电容 C = Q/V。平行板电容器的电容 C = ε₀ A / d，电介质通过削弱有效电场来增大电容。
Energy stored in a capacitor: W = ½ Q V = ½ C V² = ½ Q²/C.
电容器储存的能量：W = ½ Q V = ½ C V² = ½ Q²/C。
During charging or discharging through a resistor, voltage follows V = V₀ e^(-t/RC), where τ = RC is the time constant. The current decays similarly.
通过电阻充放电时，电压按 V = V₀ e^(-t/RC) 变化，其中时间常数 τ = RC。电流也以类似方式衰减。
6. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Magnetic flux density B is a vector field; a charge q moving with velocity v in a magnetic field experiences a force F = B q v sinθ (Lorentz force).
磁通量密度 B 是矢量场；电荷 q 以速度 v 在磁场中运动时，所受洛伦兹力为 F = B q v sinθ。
A current-carrying conductor of length L in a magnetic field experiences a force F = B I L sinθ, where the direction is given by Fleming’s left-hand rule.
载流导体在磁场中所受的安培力为 F = B I L sinθ，方向由左手定则确定。
Magnetic flux Φ = B A cosθ, where θ is the angle between the field lines and the normal to the area.
磁通量 Φ = B A cosθ，其中 θ 为磁感线与面积法线间的夹角。
Faraday’s law: the induced e.m.f. across a conductor is ε = – dΦ/dt. Lenz’s law states that the induced current opposes the change in flux that produced it.
法拉第定律：导体中的感应电动势 ε = – dΦ/dt。楞次定律指出，感应电流的方向总是阻碍引起它的磁通量变化。
The induced e.m.f. for a straight conductor moving perpendicularly through a uniform field is ε = B l v.
直导线垂直切割匀强磁场时的动生电动势为 ε = B l v。
7. Thermal Physics and Ideal Gases | 热物理与理想气体
Internal energy is the sum of the random kinetic energies and potential energies of the particles in a system. Temperature is related to average kinetic energy.
内能是系统内粒子无规则运动的动能与势能之和。温度与平均动能相关。
The first law of thermodynamics: ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added, and W is work done on the system.
热力学第一定律：ΔU = Q + W，ΔU 为内能变化，Q 为系统吸收的热量，W 为外界对系统做的功。
An ideal gas obeys Boyle’s law (pV = constant at constant T), Charles’s law (V ∝ T) and the pressure law (p ∝ T). These combine to give pV = nRT = NkT.
理想气体遵守玻意耳定律（恒温下 pV = 常数）、查理定律（V ∝ T） 和压强定律（p ∝ T）。综合后得到 pV = nRT = NkT。
pV = nRT = NkT
The kinetic model of gases relates macroscopic pressure to molecular motion: pV = 1/3 N m
气体分子运动论将宏观压强与分子运动联系起来：pV = 1/3 N m
The average translational kinetic energy of a molecule is ½ m
分子的平均平动动能 ½ m
8. Nuclear Decay and Radioactivity | 核衰变与放射性
The nucleus consists of protons and neutrons held together by the strong nuclear force. Unstable nuclei undergo radioactive decay, emitting alpha, beta−, beta+, or gamma radiation.
原子核由质子和中子组成，靠强核力结合。不稳定的核会发生放射性衰变，发射 α、β⁻、β⁺ 或 γ 辐射。
The activity A = λN, where λ is the decay constant and N is the number of undecayed nuclei. Activity is measured in becquerels (Bq).
放射性活度 A = λN，λ 为衰变常数，N 为未衰变核的数目。活度的单位是贝克勒尔 (Bq)。
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