📚 AQA A-level Physics Unit 4 Insert January 2020: Essential Revision Guide | AQA A-Level物理第四单元2020年1月考试资料：复习要点指南
The January 2020 insert for AQA A-level Physics Unit 4 is a powerful resource that many students underuse. It contains the key formulae and data needed for the entire paper, from circular motion to electromagnetic induction. Understanding what is in the insert and how to navigate it quickly can make the difference between a pass and a top grade.
2020年1月的AQA物理第四单元考试资料页是一份许多学生没有充分利用的强力资源。它包含了整张试卷所需的关键公式和数据，从圆周运动到电磁感应。理解资料页中的内容并快速查阅它，往往是及格与高分之间的分水岭。
This guide breaks down the main topics of Unit 4, links each topic to the equations on the insert, and provides practical advice for using the insert effectively in the real exam.
本指南分解第四单元的主要主题，将每个主题与资料页上的方程对应起来，并提供在真实考试中有效使用资料页的实用建议。
1. The Insert: Know What Is Provided | 资料页：了解提供了什么
The AQA Unit 4 insert is a clean, double-sided sheet. On the front, you will typically find the fundamental constants: gravitational constant G, Coulomb constant k, elementary charge e, Planck’s constant h, the mass of the electron and proton, and Avogadro’s constant. On the back, the equations are grouped by topic, such as mechanics, fields, capacitor circuits and electromagnetic induction.
AQA第四单元资料页是一张干净的双面页。通常在正面你会找到基本常数：万有引力常量G、库仑常量k、基本电荷e、普朗克常量h、电子和质子质量，以及阿伏伽德罗常量。在背面，方程按主题分组，如力学、场、电容器电路和电磁感应。
In the January 2020 paper, the insert had the same layout as the specimen materials. If you have practised with an official insert before, you will already know where to look. Do not try to memorise every equation; instead, become an expert at finding the right equation in seconds.
在2020年1月的试卷中，资料页的布局与样题材料相同。如果你以前用官方资料页练习过，你就已经知道该去哪里找。不要试图记住每个方程；相反，要成为快速找到正确方程的专家。
2. Circular Motion and Centripetal Force | 圆周运动与向心力
The insert lists the angular speed definition and the centripetal acceleration/force equations. These are essential for any question about an object moving in a circle, whether it is a car going around a bend, a particle in a particle accelerator, or a planet in orbit.
资料页列出了角速度定义以及向心加速度/力的方程。这些对于任何涉及物体做圆周运动的问题都是必不可少的，无论是汽车转弯、粒子加速器中的粒子，还是轨道上的行星。
ω = Δθ / Δt, v = rω, a = rω² = v²/r, F = m r ω² = m v²/r
For example, if a question gives you the radius and the period T, you can compute ω = 2π/T and then use v = rω. Always remember that the centripetal acceleration always points towards the centre of the circle. In the January 2020 Unit 4 paper, this topic appeared in a multi-step question about a satellite. The insert gave the gravitational field equation, but you still had to combine it with circular motion to find the orbital speed.
例如，如果问题给出半径和周期T，你可以计算ω = 2π/T，然后用v = rω。始终记住向心加速度总是指向圆心。在2020年1月的第四单元试卷中，这个话题出现在一个关于卫星的多步计算问题中。资料页给出了引力场方程，但你仍然需要将其与圆周运动结合才能求出轨道速度。
3. Simple Harmonic Motion (SHM) | 简谐运动
Unit 4 also covers simple harmonic motion. The insert provides the standard SHM equations, including the relationship between acceleration, displacement and angular frequency, as well as the variation of displacement, velocity and acceleration with time.
第四单元还涉及简谐运动。资料页提供标准SHM方程，包括加速度、位移和角频率之间的关系，以及位移、速度和加速度随时间变化的方程。
x = A cos(ωt + φ), v = -Aω sin(ωt + φ), a = -ω²x
The key condition for SHM is that the acceleration is proportional to the displacement and always directed towards the equilibrium position. The insert does not tell you this — you must know it. For the January 2020 exam, you may have been asked to identify SHM from a graph or to calculate the maximum speed and acceleration of an oscillator. Remember that v_max = Aω and a_max = Aω². The insert often lists these separately, so locate them quickly.
简谐运动的关键条件是加速度与位移成正比，且始终指向平衡位置。资料页不会告诉你这一点——你必须知道。对于2020年1月的考试，你可能被要求从图像中识别SHM，或者计算振荡器的最大速度和最大加速度。记住 v_max = Aω 和 a_max = Aω²。资料页通常会将它们分别列出，所以请快速找到它们。
4. Gravitational Fields | 引力场
Gravitational fields form a major part of Unit 4. The insert contains Newton’s law of gravitation and the equation for gravitational field strength.
引力场是第四单元的主要部分。资料页包含牛顿万有引力定律和引力场强度的方程。
F = G m₁m₂ / r², g = F/m = GM / r²
For a point mass, the gravitational potential V is also listed, usually in the form V = -GM/r. The negative sign indicates that the potential is zero at infinity and decreases as the mass approaches. Many candidates lose marks by ignoring this negative sign when calculating the energy required to move an object from one radius to another.
对于点质量，引力势V也会列出，通常形式为 V = -GM/r。负号表示势能在无穷远处为零，并随着距离质量越来越近而减小。许多考生在计算将物体从一个半径移动到另一个半径所需的能量时，因忽略这个负号而失分。
In the January 2020 insert, the equations for gravitation were placed next to the circular motion equations. This is a deliberate signal: you will often need to combine them. For instance, to find the orbital period of a satellite, set GMm/r² = m r ω², then simplify to get Kepler’s third law: T² ∝ r³.
在2020年1月的资料页中，引力方程被放在圆周运动方程旁边。这是一个刻意的提示：你经常需要把它们结合起来。例如，要求卫星的轨道周期，可令 GMm/r² = m r ω²，然后化简得到开普勒第三定律：T² ∝ r³。
5. Electric Fields | 电场
Electric fields are very similar to gravitational fields, but with charges instead of masses. The insert gives Coulomb’s law and the electric field strength for point charges, as well as the uniform field equation.
电场与引力场非常相似，但用电荷代替质量。资料页给出库仑定律和点电荷的电场强度，以及匀强电场方程。
F = k Q₁Q₂ / r², E = F/Q, E = kQ / r², E = V/d
Here, the constant k is derived from the permittivity of free space: k = 1/(4πε₀). On the AQA insert, the value of ε₀ is given, so you may need to calculate k yourself in some questions. Be careful with the sign of charges: the force between opposite charges is attractive, while the force between like charges is repulsive. The electric field direction is defined as the direction of the force on a positive test charge.
这里的常量k由真空介电常数推导而来：k = 1/(4πε₀)。在AQA资料页中会给出ε₀的值，所以在某些问题中你可能需要自己计算k。注意电荷的符号：异种电荷之间的力是吸引力，同种电荷之间的力是排斥力。电场方向定义为正检验电荷所受力的方向。
For the January 2020 paper, a typical question asked you to compare the electric field strength at different points between two charged plates. Using E = V/d, you could directly calculate the uniform field, as long as you converted all distances to metres.
在2020年1月的试卷中，一个典型问题要求比较两块带电板之间不同点的电场强度。使用 E = V/d，你可以直接计算匀强电场，只要将所有距离转换为米。
6. Capacitance and Charge/Discharge | 电容与充放电
Capacitors are an important part of Unit 4, and the insert includes both the basic capacitance equation and the exponential decay equations for a capacitor discharging through a resistor.
电容器是第四单元的重要组成部分，资料页既包含基本电容方程，也包含电容器通过电阻放电时的指数衰减方程。
C = Q/V, E = ½ QV = ½ CV², Q = Q₀ e^(-t/RC), V = V₀ e^(-t/RC), I = I₀ e^(-t/RC)
The time constant τ = RC is a key idea. When t = RC, the remaining charge is 37% of the initial value. The insert gives the equations, but you should also know how to use the natural logarithm to linearise the decay. For example, from Q = Q₀ e^(-t/RC), take ln of both sides: ln Q = ln Q₀ – t/RC. This means a graph of ln Q against t is a straight line with gradient -1/RC.
时间常数 τ = RC 是关键概念。当 t = RC 时，剩余电荷为初始值的37%。资料页给出方程，但你还应知道如何使用自然对数将衰减线性化。例如，由 Q = Q₀ e^(-t/RC)，两边取对数：ln Q = ln Q₀ – t/RC。这意味着 ln Q 对 t 的图像是一条直线，斜率为 -1/RC。
In the January 2020 Unit 4 paper, the capacitor question gave a graph of voltage against time. Many students correctly used the graph to find the time constant at 37% of the initial voltage, but then forgot to multiply by the resistance to check a value. The insert provides the equations, not the method — you must practise interpreting graphs.
在2020年1月的第四单元试卷中，电容题给了电压-时间图像。许多学生正确地利用图像在初始电压的37%处找到时间常数，但之后忘记乘以电阻来检验数值。资料页提供方程，而非方法——你必须练习解读图像。
7. Magnetic Fields | 磁场
Magnetic fields act on moving charges and current-carrying conductors. The insert lists the force equations for both cases.
磁场作用于运动电荷和载流导线。资料页列出这两种情况的力方程。
F = BIl sinθ, F = Bqv sinθ
When a charged particle moves perpendicularly to a uniform magnetic field, it travels in a circle. The radius of that circle is found by equating the magnetic force to the centripetal force: Bqv = mv²/r, which gives r = mv/(Bq). This equation is not always printed on the insert, so you must derive it. Check the insert: it will give F = Bqv and the circular motion equations, so you can combine them.
当带电粒子垂直于匀强磁场运动时，它做圆周运动。该圆半径可通过磁力等于向心力而求得：Bqv = mv²/r，得到 r = mv/(Bq)。这个方程不一定印在资料页上，所以你必须自己推导。查看资料页：它会给出 F = Bqv 和圆周运动方程，因此你可以将它们组合起来。
The direction of the force on a positive charge is given by Fleming’s left-hand rule. The insert does not provide this rule, so you must practise applying it before the exam. In the January 2020 paper, a question involved a beam of electrons moving through a magnetic field; you had to determine the direction of the force or the shape of the path.
正电荷所受力的方向由楞次定则（左手定则）确定。资料页不提供这个规则，所以你必须在考试前练习应用它。在2020年1月的试卷中，有一道题涉及电子束穿过磁场；你必须判断力的方向或路径的形状。
8. Electromagnetic Induction | 电磁感应
Electromagnetic induction is a fundamental topic that relies on Faraday’s law and Lenz’s law. The insert provides the equation for induced emf.
电磁感应是一个基本主题，依赖于法拉第定律和楞次定律。资料页提供感应电动势的方程。
E = NΔΦ/Δt, |E| = NΔΦ/Δt (with sign for Lenz’s law)
The negative sign in the full version of Faraday’s law represents Lenz’s law: the induced emf is directed so that it opposes the change in magnetic flux that produced it. The AQA insert often writes the
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