📚 AQA Physics A-level Unit 4: Insert (Jan 2019) Masterclass | AQA物理A-level第四单元：2019年1月资料页全解
The January 2019 insert for AQA A-level Physics Unit 4 is more than a sheet of paper — it is your personal formula bank. Unit 4 focuses on fields and further mechanics, and the insert provides every essential equation in a neat grid. This article explains how to use that insert effectively and turns each formula group into a clear revision plan.
2019年1月AQA物理A-level第四单元的资料页不仅仅是一张纸，它是你的个人公式库。第四单元聚焦“场”与“进阶力学”，资料页以清晰表格形式给出所有关键方程。本文会解释如何高效使用资料页，并把每一组公式转化为清晰的复习方案。
1. Understanding the Unit 4 Insert | 理解第四单元资料页
The Unit 4 insert is organised by topic headings: circular motion, simple harmonic motion, gravitational fields, electric fields, capacitors, magnetic fields and electromagnetic induction. You are expected to select the correct equation from the list, substitute values in SI units, and then interpret the answer.
第四单元资料页按主题分类排列：圆周运动、简谐运动、引力场、电场、电容器、磁场与电磁感应。你需要从列表中选出正确公式，代入国际单位制数值，然后解释结果。
Each equation uses standard symbols. For example, ω is angular speed, Φ is magnetic flux, and ε₀ is the permittivity of free space. Do not waste exam time trying to remember every equation; instead, train yourself to match each equation to a scenario.
资料页中的每个公式都使用标准符号。例如，ω 是角速度，Φ 是磁通量，ε₀ 是真空介电常数。不要在考试中浪费时间试图背下所有公式；相反，训练自己将公式与具体情境对应。
Before the exam, practise locating equations quickly on the insert.
考前练习在资料页中快速定位公式。
Circle the quantities you are given and the quantity you need.
在题目中圈出已知量和目标量。
Write down the equation before substituting numbers.
代入数字前先写出公式。
2. Circular Motion | 圆周运动
eriod and f is the frequency. The linear speed is v = ωr, with r the radius of the circle.
匀速圆周运动的特点是速率恒定但速度方向不断改变。资料页给出角速度 ω = 2π/T = 2πf，其中 T 是周期，f 是频率。线速度 v = ωr，r 为圆周半径。
is not an extra force; it is provided by tension, friction, gravity or another real force.
向心加速度始终指向圆心：a = v²/r = ω²r。所需合外力因此为 F = mv²/r = mω²r。这个力不是额外力；它由拉力、摩擦力、重力或其他真实力提供。
Check units: ω is in rad s⁻¹, v in m s⁻¹, and F in N.
检查单位：ω 的单位是 rad s⁻¹，v 是 m s⁻¹，F 是 N。
If a car turns on a flat road, friction is the centripetal force.
如果汽车在平直道路上转弯，摩擦力提供向心力。
3. Simple Harmonic Motion | 简谐运动
the key equation a = −ω²x, where a is acceleration and x is displacement from equilibrium.
简谐运动要求恢复力与位移成正比，并且方向指向平衡位置。资料页列出关键方程 a = −ω²x，其中 a 是加速度，x 是距平衡位置的位移。
For a mass on a spring, T = 2π√m/k, where k is the spring constant. For a pendulum, T = 2π√l/g nsert also gives displacement x = A cos(ωt) for a system starting at maximum displacement.
对于弹簧振子，T = 2π√m/k，其中 k 是劲度系数。对于单摆，T = 2π√l/g，其中 l 是摆长，g 是重力场强度。资料页还给出从最大位移处开始的位移方程 x = A cos(ωt)。
Energy is exchanged between kinetic and potential forms: max speed vmax = Aω and max acceleration amax = Aω². The total energy is ½ mω²A².
能量在动能与势能之间相互转化：最大速度 vmax = Aω，最大加速度 amax = Aω²。总能量为 ½ mω²A²。
4. Gravitational Fields | 引力场
g = GM/r², where M is the mass of the source object and r is the distance from its centre.
万有引力定律为 F = G m₁m₂/r²。引力场强度是 g = GM/r²，其中 M 是中心天体质量，r 是到中心的距离。
nergy is E = −GMm/r. Notice the negative sign; the zero of potential is taken at infinity.
引力势 V 的定义是将单位质量从无穷远处移至某处所做的功：V = −GM/r。相应的势能为 E = −GMm/r。注意负号；势能零点取在无穷远处。
For circular orbits, the orbital speed is v = √GM/r ²r³/(GM). These are direct results from equating gravitational force to centripetal force.
对于圆形轨道，轨道速度 v = √GM/r，周期满足 T² = 4π²r³/(GM)。这些由万有引力等于向心力直接推出。
5. Electric Fields | 电场
rength E is force per unit positive charge: E = F/q, so for a point charge E = Q/(4πε₀r²).
库仑定律为 F = (1/4πε₀)Qq/r²。电场强度 E 是单位正电荷所受的力：E = F/q，因此点电荷的电场强度为 E = Q/(4πε₀r²)。
separation between two parallel plates. The force on a charge q in such a field is F = qE.
在匀强电场中，电势差 V 与场强的关系为 E = V/d，其中 d 是平行板间距。电荷 q 在该场中受力 F = qE。
r) and the energy change when moving charge q through potential difference ΔV is ΔE = qΔV.
点电荷的电势为 V = Q/(4πε₀r)，电荷 q 通过电势差 ΔV 时的能量变化为 ΔE = qΔV。
Use vector signs carefully: electric field lines point from positive to negative.
注意矢量方向：电场线从正电荷指向负电荷。
For uniform fields, the field strength is constant between plates.
对于匀强电场，极板之间场强恒定。
6. Capacitors | 电容器
ifference. For a parallel plate capacitor, C = ε₀εᵣA/d, with εᵣ the relative permittivity.
电容器定义为 C = Q/V，其中 Q 是储存电荷，V 是电势差。对于平行板电容器，C = ε₀εᵣA/d，εᵣ 是相对介电常数。
red is E = ½QV = ½CV² = ½Q²/C. In a charging circuit, the charge increases as Q = Q₀(1 − e−t/RC); in discharging it decays as Q = Q₀e−t/RC.
储存能量为 E = ½QV = ½CV² = ½Q²/C。在充电电路中，电荷按 Q = Q₀(1 − e−t/RC) 增加；放电时按 Q = Q₀e−t/RC 衰减。
The product RC is the time constant; after one time constant, the charge falls to about 37% of its initial value when discharging.
乘积 RC 是时间常数；放电时，经过一个时间常数，电荷约为初始值的37%。
7. Magnetic Fields | 磁场
θ, where B is magnetic flux density, I is current, l is length of wire in the field and θ is the angle between the wire and the field.
载流导线在磁场中受力 F = BIl sinθ，其中 B 是磁通密度，I 是电流，l 是导线在磁场中的长度，θ 是导线与磁场方向的夹角。
n a circle with radius r = mv/(Bq). This equation can be derived by equating Bqv to mv²/r.
对于运动带电粒子，受力为 F = Bqv sinθ。当速度与磁场垂直时，粒子做圆周运动，半径 r = mv/(Bq)。该式由 Bqv 等于 mv²/r 推导得出。
Remember Fleming’s left-hand rule for the direction of force.
用弗莱明左手定则判断力的方向。
The magnetic force on a stationary charge is zero.
静止电荷所受磁场力为零。
8. Electromagnetic Induction | 电磁感应
osθ, where θ is the angle between the normal to the area and the magnetic field. The flux linkage is NΦ, where N is the number of turns.
穿过线圈的磁通量为 Φ = BA cosθ，其中 θ 是面积法线与磁场的夹角。磁通链为 NΦ，N 是匝数。
ve sign represents Lenz’s law: the induced current always opposes the change producing it.
法拉第定律指出：感应电动势 = −N(ΔΦ/Δt)。负号体现楞次定律：感应电流总是阻碍引起它的磁通量变化。
B, the motional EMF is EMF = Blv. This is often easier to use than ΔΦ/Δt in exam problems.
若长度为 l 的导体棒以速度 v 垂直于磁场 B 运动，动生电动势为 EMF = Blv。在考题中这往往比直接使用 ΔΦ/Δt 更便捷。
9. Key Constants from the Jan 2019 Insert | 2019年1月资料页中的关键常数
The insert provides fundamental constants. You are expected to use these values directly from the sheet, but you should still be aware of them.
资料页提供基本物理常数。你应当直接使用资料页中的数值，但仍需了解它们。
| Quantity | Symbol | Value |
| Acceleration of free fall | g | 9.81 m s⁻² |
| Gravitational constant | G | 6.67 × 10⁻¹¹ N m² kg⁻² |
| Elementary charge | e | 1.60 × 10⁻¹⁹ C |
| Permittivity of free space | ε₀ | 8.85 × 10⁻¹² F m⁻¹ |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ H m⁻¹ |
| Speed of light | c | 3.00 × 10⁸ m s⁻¹ |
ed on your insert. In many AQA papers, 1/(4πε₀) is written directly as 9.0 × 10⁹ N m² C⁻².
请检查资料页上是否已将 1/(4πε₀) 简化为数值。在许多AQA试卷中，1/(4πε₀) 直接写作 9.0 × 10⁹ N m² C⁻²。
10. Examiner Tips and Common Mistakes | 考官技巧与常见错误
Students often lose marks because they use an equation for the wrong situation. For example, gravitational potential at the surface is negative, but gravitational field strength is a positive magnitude. Do not confuse potential V with potential energy E.
学生常因在错误情境中使用公式而失分。例如，地球表面的引力势为负值，但引力场强度是正的数值。不要将电势 V 与势能 E 混淆。
Always convert cm to m, minutes to seconds, and g to kg.
始终把厘米换算成米、分钟换算成秒、克换算成千克。
In SHM, the acceleration is always opposite in direction to displacement.
在简谐运动中，加速度方向始终与位移方向相反。
For capacitors, use Q = Q₀e−t/RC for discharging, not charging.
对于电容器，放电用 Q = Q₀e−t/RC，不要用于充电。
hen using F = Bqv, note that q can be positive or negative; the direction of foce changes.
使用 F = Bqv 时，注意 q 可正可负；力的方向会改变。
Lenz’s law: the negative sign in Faraday’s law is not optional in explanations.
楞次定律：在解释中不能省略法拉第定律的负号。
11. Putting the Insert to Work in the Exam | 在考试中善用资料页
When you open the paper, quickly read the insert and mark any equations that feel unfamiliar. Then use a step-by-step method for each numerical question.
打开试卷后，快速浏览资料页，并标出不熟悉的公式。然后对每道计算题使用分步法。
Step 1: underline all numerical values with units.
第一步：用下划线标出所有带单位的数值。
Step 2: write down the required formula from the insert.
第二步：从资料页写出所需公式。
Step 3: rearrange to make the target quantity the subject.
第三步：变形以表示出目标量。
Step 4: substitute values, compute and state the unit.
第四步：代入数值，计算结果并写出单位。
This approach prevents “islands” of numbers with no relation to physics. It also helps the examiner see your reasoning for partial marks.
这种方法可避免毫无物理逻辑的零散数字，也能帮助考官看到你的推理过程，从而获得过程分。
12. Final Revision Checklist | 最终复习清单
Use this checklist to confirm you are ready for the Unit 4 exam with the January 2019 insert style.
使用以下清单确认你已为第四单元考试做好准备，并熟悉2019年1月资料页风格。
I can distinguish circular motion from SHM and select the correct equations.
我能区分圆周运动与简谐运动，并选出正确公式。
I can calculate gravitational field strength, potential and orbital values.
我能计算引力场强度、引力势和轨道数值。
I can apply Coulomb’s law and the electric field equations confidently.
我能自信地应用库仑定律和电场方程。
I can solve capacitor charging and discharging problems using exponential equations.
我能使用指数方程解决电容器充电和放电问题。
I know how to use the right-hand rule or left-hand rule for magnetic fields.
我知道如何为磁场问题使用右手定则或左手定则。
I can write Faraday’s law with Lenz’s law direction in words and equations.
我能用文字和方程写出包含楞次定律方向的法拉第定律。
At this point, the insert should feel like a familiar tool rather than a hidden code. Practise with past papers, always keeping the insert beside you, and soon you will know every equation by location and by meaning.
到了这个阶段，资料页应像熟悉的工具，而不是隐藏的密码。练习真题时，始终把资料页放在手边，很快你就会既知道每个公式的位置，也知道它的含义。
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