Year 13 AQA Physics: Core Concepts Summary | Year 13 AQA 物理：核心知识点梳理

📚 Year 13 AQA Physics: Core Concepts Summary | Year 13 AQA 物理：核心知识点梳理

Welcome to this comprehensive revision guide covering the essential topics of Year 13 AQA Physics. This article summarises key principles, equations, and practical insights for Further Mechanics, Fields, Capacitance, Nuclear Physics, and Thermal Physics, equipping you with a concise yet thorough review for your exams.

欢迎阅读这份涵盖 Year 13 AQA 物理核心主题的综合复习指南。本文概述了进一步力学、场、电容、核物理和热物理的关键原理、公式和实验见解，为你提供简洁而透彻的考前回顾。

1. Circular Motion | 圆周运动

Angular velocity ω is the rate of change of angular displacement. For uniform circular motion, ω = 2π/T = 2πf, and the linear speed is v = ωr. The period T is the time for one complete revolution.

角速度 ω 是角位移的变化率。在匀速圆周运动中，ω = 2π/T = 2πf，线速度满足 v = ωr。周期 T 是完成一整圈的时间。

Centripetal acceleration a = v²/r = ω²r always points towards the centre. The resultant force providing this acceleration is the centripetal force F = mv²/r = mrω². It is not a separate ‘new’ force but the net inward force from tension, friction, gravity, etc.

向心加速度 a = v²/r = ω²r 始终指向圆心。提供该加速度的合力是向心力 F = mv²/r = mrω²。它并非一种单独的‘新’力，而是由拉力、摩擦力、引力等提供的净指向圆心的合力。

At the top of a vertical loop, the condition for just maintaining contact is that the normal reaction N = 0, giving mg = mv²/r, and thus the critical speed v = √(gr). Similar ideas apply to cars rounding banked curves and satellites orbiting planets.

在竖直圆周顶部，刚好保持接触的条件是支撑力 N = 0，则 mg = mv²/r，临界速度为 v = √(gr)。类似思路适用于汽车过弯道和行星的卫星轨道。

2. Simple Harmonic Motion (SHM) | 简谐运动

An oscillation is simple harmonic if the acceleration a is directly proportional to the displacement x from the equilibrium position and always directed towards it: a = -ω²x, where ω is the angular frequency.

若加速度 a 与相对平衡位置的位移 x 成正比且始终指向平衡位置，则振动为简谐运动：a = -ω²x，其中 ω 为角频率。

The displacement can be written as x = A cos(ωt) or x = A sin(ωt) with phase difference. The velocity at any position is v = ±ω√(A² – x²), and the maximum speed is vₘₐₓ = ωA. The period T = 2π/ω is independent of amplitude for true SHM.

位移可表示为 x = A cos(ωt) 或 x = A sin(ωt)，二者存在相位差。任意位置的速度为 v = ±ω√(A² – x²)，最大速度 vₘₐₓ = ωA。周期 T = 2π/ω，在真正的简谐运动中与振幅无关。

The total mechanical energy E = ½ m ω² A² is conserved, continuously exchanging between kinetic and potential forms. In a mass-spring system, T = 2π√(m/k); for a simple pendulum, T = 2π√(L/g) (small angles).

总机械能 E = ½ m ω² A² 守恒，在动能与势能之间不断转化。弹簧振子中 T = 2π√(m/k)；单摆中 T = 2π√(L/g)（小角度）。

Damping removes energy, reducing amplitude over time. Resonance occurs when the driving frequency matches the natural frequency, causing maximum amplitude; sharpness of resonance is described by the quality factor Q.

阻尼消耗能量，使振幅随时间衰减。当驱动频率等于固有频率时发生共振，振幅最大；共振的尖锐程度由品质因数 Q 描述。

3. Gravitational Fields | 引力场

Newton’s law of gravitation states that the force between two point masses is F = Gm₁m₂/r². The gravitational field strength g = F/m. For a spherical mass, g = GM/r², directed radially inward.

牛顿引力定律指出，两点质量间的引力为 F = Gm₁m₂/r²。引力场强 g = F/m。对于球形质量，g = GM/r²，方向沿径向指向中心。

Gravitational potential V = -GM/r is the work done per unit mass to bring a test mass from infinity to that point. The equipotential surfaces are spheres. Gravitational potential energy is Ep = -GMm/r.

引力势 V = -GM/r 是将单位质量从无穷远处移至该点所做的功。等势面为球面。引力势能为 Ep = -GMm/r。

For orbital motion, equate gravitational force to centripetal force: GMm/r² = mv²/r → v = √(GM/r). This yields Kepler’s third law T² ∝ r³. The escape velocity from a body of radius R is vₑₛ = √(2GM/R).

在轨道运动中，令引力等于向心力：GMm/r² = mv²/r → v = √(GM/r)。由此推导出开普勒第三定律 T² ∝ r³。从半径为 R 的天体逃逸的速度为 vₑₛ = √(2GM/R)。

4. Electric Fields | 电场

Coulomb’s law: the force between two point charges is F = kQ₁Q₂/r², where k = 1/(4πε₀). Electric field strength E = F/q. For a point charge, E = kQ/r², radially outward from a positive charge.

库仑定律：两点电荷之间的作用力为 F = kQ₁Q₂/r²，其中 k = 1/(4πε₀)。电场强度 E = F/q。对于点电荷，E = kQ/r²，方向从正电荷沿径向向外。

Electric potential V = kQ/r; the potential difference between two points is the work done per unit charge. In a uniform electric field, such as between parallel plates, E = V/d, where d is the plate separation.

电势 V = kQ/r；两点间的电势差是单位电荷移动所做的功。在平行板产生的匀强电场中，E = V/d，

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