Mastering CIE A-Level Physics Appendix 2: Data, Formulae and Relationships | 掌握 CIE A-Level 物理附录2：数据、公式与关系

📚 Mastering CIE A-Level Physics Appendix 2: Data, Formulae and Relationships | 掌握 CIE A-Level 物理附录2：数据、公式与关系

The CIE A-Level Physics data, formulae and relationships booklet, often called Appendix 2, is supplied in every written theory paper. It contains the essential constants, equations and relationships that you are not expected to memorise, but you must be able to select and apply them accurately under timed conditions.

CIE A-Level 物理的数据、公式与关系小册子，通常称为附录2，会随每份笔试理论试卷提供。它包含你不必记忆但必须在限时条件下准确选择和应用的基本常数、方程式与关系式。

This article breaks down Appendix 2 topic by topic, explains how each formula is used, and gives you a clear bilingual revision guide to turn the booklet into a real exam advantage.

本文将按主题拆解附录2，解释每个公式的使用方法，并为你提供一份清晰的双语复习指南，把小册子变成真正的考试优势。

1. Why Appendix 2 Is Your Best Friend in the Exam | 为什么附录2是你考试中的最佳帮手

Many students treat the formula sheet as a last-minute rescue tool, but top scorers use it actively during revision. Knowing exactly what is printed on the sheet means you can focus your memory on definitions, derivations and experimental skills instead of raw recall.

许多学生把公式表当作考前临时抱佛脚的工具，但高分学生会在复习阶段就主动使用它。清楚知道表上印了什么，你就能把记忆精力放在定义、推导和实验技能上，而不是死记硬背。

In CIE AS and A-Level Physics, Appendix 2 is available in Papers 1, 2 and 4, so you should never waste time trying to memorise every constant or every long equation. Your job is to recognise the relevant formula quickly and substitute values correctly.

在 CIE AS 和 A-Level 物理中，附录2在试卷1、2和4中都会提供，因此你不必浪费时间记住每一个常数或每一条长公式。你的任务是快速识别相关公式并正确代入数值。

Use the formula sheet while doing past papers, not just in the last week. This builds familiarity with where each equation sits and helps you avoid confusing similar expressions such as gravitational potential and gravitational potential energy.

做历年真题时就要使用公式表，而不是最后一周才看。这样可以熟悉每个公式在表中的位置，并避免混淆相似表达式，例如引力势与引力势能。

2. Fundamental Constants You Must Recognise | 必须认识的基本常数

The data section of Appendix 2 gives fundamental constants to a suitable number of significant figures. You do not need to memorise them, but you should know their symbols and standard units because exam questions often use them without explanation.

附录2的数据部分以适当的有效数字给出了基本常数。你不必记住它们，但应认识它们的符号和标准单位，因为试题中经常不加解释地使用这些常数。

Constant / 常数	Symbol / 符号	Value / 数值
Speed of light in free space / 真空中光速	c	3.00 × 10⁸ m s⁻¹
Elementary charge / 元电荷	e	1.60 × 10⁻¹⁹ C
Planck constant / 普朗克常数	h	6.63 × 10⁻³⁴ J s
Gravitational constant / 引力常数	G	6.67 × 10⁻¹¹ N m² kg⁻²
Avogadro constant / 阿伏伽德罗常数	N_A	6.02 × 10²³ mol⁻¹
Boltzmann constant / 玻尔兹曼常数	k	1.38 × 10⁻²³ J K⁻¹
Electron rest mass / 电子静质量	mₑ	9.11 × 10⁻³¹ kg
Proton rest mass / 质子静质量	mₚ	1.67 × 10⁻²⁷ kg
Permittivity of free space / 真空中介电常数	ε₀	8.85 × 10⁻¹² F m⁻¹

Pay close attention to powers of ten. For example, the Planck constant is 10⁻³⁴, while the Boltzmann constant is 10⁻²³, so mixing them up will change an answer by eleven orders of magnitude.

要特别注意10的幂次。例如普朗克常数是10⁻³⁴，而玻尔兹曼常数是10⁻²³，如果混淆它们，结果就会相差十一个数量级。

3. SI Units and Prefixes | 国际单位制与词头

CIE questions regularly require you to express quantities in SI base units or to convert prefixes such as pico, nano, micro and mega. Appendix 2 reminds you of the base units for mass, length, time, current, temperature, amount of substance and luminous intensity.

CIE 试题经常要求你用 SI 基本单位表示物理量，或者换算皮可、纳诺、微、兆等词头。附录2提醒你质量、长度、时间、电流、温度、物质的量和发光强度的基本单位。

The most commonly tested prefixes are p (10⁻¹²), n (10⁻⁹), μ (10⁻⁶), m (10⁻³), c (10⁻²), k (10³), M (10⁶), G (10⁹) and T (10¹²). Always convert values to base units before substituting into equations unless the formula is a ratio.

最常考查的词头是 p（10⁻¹²）、n（10⁻⁹）、μ（10⁻⁶）、m（10⁻³）、c（10⁻²）、k（10³）、M（10⁶）、G（10⁹）和 T（10¹²）。除非公式是比值，否则代入前应始终将数值换算为基本单位。

For example, a wavelength of 650 nm must become 650 × 10⁻⁹ m before using λ = ax/D. A capacitor of 2.2 μF must become 2.2 × 10⁻⁶ F before using C = Q/V.

例如，650 nm 的波长在代入 λ = ax/D 之前必须先转换为 650 × 10⁻⁹ m。2.2 μF 的电容在代入 C = Q/V 之前必须转换为 2.2 × 10⁻⁶ F。

4. Mechanics: Kinematics, Forces and Energy | 力学：运动学、力与能量

Appendix 2 lists the four constant-acceleration equations, often called the SUVAT equations. They only apply when acceleration is constant, so never use them for non-uniform motion.

附录2列出了四个匀加速度方程，通常称为 SUVAT 方程。它们仅适用于加速度恒定的情况，因此切勿在非匀变速运动中使用。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

Newton’s second law appears in two important forms: F = ma and F = Δp/Δt. The second form is more general because it also describes systems with changing mass, such as a rocket ejecting fuel.

牛顿第二定律有两种重要形式：F = ma 和 F = Δp/Δt。第二种形式更普遍，因为它也能描述质量变化的系统，例如喷出燃料的火箭。

Work done by a force is W = F s cos θ, where θ is the angle between the force and displacement. Kinetic energy is Eₖ = ½mv² and gravitational potential energy near Earth’s surface is Eₚ = mgh.

力所做的功为 W = F s cos θ，其中 θ 是力与位移之间的夹角。动能为 Eₖ = ½mv²，地球表面附近的引力势能为 Eₚ = mgh。

Power is the rate of energy transfer, P = W/t. When a constant force moves an object at speed v, power is also P = Fv.

功率是能量传递的速率，P = W/t。当恒力以速度 v 移动物体时，功率也可写成 P = Fv。

5. Circular Motion and Gravitational Fields | 圆周运动与引力场

For uniform circular motion, angular velocity ω is related to frequency and period by ω = 2πf = 2π/T. The linear speed is v = ωr, and the centripetal acceleration is a = v²/r = ω²r.

对于匀速圆周运动，角速度 ω 与频率和周期的关系为 ω = 2πf = 2π/T。线速度为 v = ωr，向心加速度为 a = v²/r = ω²r。

Centripetal force is therefore F = mv²/r = mω²r. Remember that centripetal force is not a separate force; it must be provided by tension, friction, gravity or another real force acting towards the centre.

因此向心力为 F = mv²/r = mω²r。记住向心力不是一种独立的力，它必须由张力、摩擦力、重力或其他指向圆心的真实力提供。

Newton’s law of gravitation is F = Gm₁m₂/r². The gravitational field strength at a distance r from a point or spherical mass is g = GM/r², and gravitational potential is φ = -GM/r.

牛顿万有引力定律为 F = Gm₁m₂/r²。距离点质量或球对称质量 r 处的引力场强度为 g = GM/r²，引力势为 φ = -GM/r。

Kepler’s third law follows from equating gravitational force and centripetal force, giving T² = 4π²r³/(GM). This relationship is particularly useful for satellite and planet orbit calculations.

开普勒第三定律可由引力等于向心力推导出来，得到 T² = 4π²r³/(GM)。这个关系在卫星和行星轨道计算中特别有用。

6. Oscillations, Waves and Optics | 振动、波动与光学

Simple harmonic motion is defined by acceleration being proportional to displacement and directed towards equilibrium: a = -ω²x. The displacement can be written as x = A sin ωt or x = A cos ωt depending on the starting point.

简谐运动的定义是加速度与位移成正比并指向平衡位置：a = -ω²x。根据起点不同，位移可写作 x = A sin ωt 或 x = A cos ωt。

The speed of an oscillator is v = ±ω√(A² – x²), and the maximum speed is v_max = ωA. The period of a mass-spring system is T = 2π√(m/k), while a simple pendulum has T = 2π√(L/g).

振子的速度为 v = ±ω√(A² – x²)，最大速度为 v_max = ωA。质量-弹簧系统的周期为 T = 2π√(m/k)，而单摆的周期为 T = 2π√(L/g)。

All waves obey v = fλ. For sound waves and light waves, intensity is proportional to amplitude squared, so doubling amplitude multiplies intensity by four.

所有波都遵循 v = fλ。对于声波和光波，强度与振幅的平方成正比，因此振幅加倍会使强度变为原来的四倍。

In Young’s double-slit experiment, λ = ax/D, where a is slit separation, x is fringe spacing and D is the distance from slits to screen. For a diffraction grating, d sin θ = nλ, where d = 1/N and N is the number of lines per metre.

在杨氏双缝实验中，λ = ax/D，其中 a 是缝间距，x 是条纹间距，D 是双缝到屏幕的距离。对于衍射光栅，d sin θ = nλ，其中 d = 1/N，N 是每米刻线数。

Refraction is described by n = c/v and Snell’s law, n₁ sin θ₁ = n₂ sin θ₂. Total internal reflection occurs when sin θ_c = 1/n for light leaving a medium of refractive index n into air.

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