AQA AS物理公式表指南 -- Insert Guide
一、Insert 2是什么？| What is Insert 2?
在AQA AS物理考试中，每位考生都会收到一份随卷发放的参考资料：Insert 2。这份文件是考试局官方提供的公式表与数据表，包含了Paper 1和Paper 2中可能用到的所有物理常数、公式和单位换算。与国内高考物理需要背诵大量公式不同，AQA考试并不要求学生默写公式：考核的重点是理解公式的物理意义、根据题目情景选择合适的公式并正确应用。因此，Insert 2既是你的"救命稻草"，也是你取得高分的关键工具。然而，许多学生在复习时完全忽略了对这份公式表的系统学习，到了考场上才匆忙翻阅，浪费了宝贵的答题时间。本文以2022年1月AS物理卷（7407/1和7407/2）附带的Insert 2为蓝本，逐节解析每一条公式的用法、适用条件和考试中的高频考点，帮助你彻底吃透这份公式表。
The AQA AS Physics exam provides every candidate with a reference booklet called Insert 2. This is the official formula sheet and data sheet issued by the exam board, containing all the physical constants, equations, and unit conversions you may need for both Paper 1 and Paper 2. Unlike some exam systems that require rote memorisation of dozens of equations, AQA focuses on whether you understand what each formula means, when to apply it, and how to interpret the result. The Insert is therefore both your safety net and your most powerful exam tool. Yet many students neglect to study it systematically, only flipping through it in the exam hall, wasting precious time. Using the January 2022 AS Physics Insert 2 (papers 7407/1 and 7407/2) as our reference, this guide walks you through every formula on the sheet, explaining its usage, conditions of application, and the most common exam scenarios where it appears.
二、基础常数：你需要记住的物理常量 | Fundamental Constants You Must Know
Insert 2的开头部分列出了AS物理涉及的八个基本常数。这些数值在考试中不需要背诵，但你必须知道每个常数的符号和数量级，才能在节省时间的同时避免低级错误。重点常数包括：真空介电常数（epsilon零，8.85乘以10的负12次方，单位是F/m）、基本电荷（e，1.60乘以10的负19次方C）、电子质量（me，9.11乘以10的负31次方kg）、普朗克常数（h，6.63乘以10的负34次方Js）、以及万有引力常数（G，6.67乘以10的负11次方，单位是N m^2/kg^2）。考试中最常出现的"陷阱"是单位换算：例如，当题目给出质量以克（g）为单位时，你需要先转换为千克（kg）再代入公式。另一个高频失分点是数量级错误：普朗克常数的负34次方和电子质量的负31次方容易混淆，建议考前专门默写一遍这些常数的数量级。
The opening section of Insert 2 lists the eight fundamental constants used in AS Physics. You do not need to memorise them for the exam, but you must know each symbol and its order of magnitude to save time and avoid careless mistakes. Key constants include: permittivity of free space (epsilon zero, 8.85e-12 F/m), elementary charge (e, 1.60e-19 C), electron rest mass (me, 9.11e-31 kg), Planck constant (h, 6.63e-34 Js), and gravitational constant (G, 6.67e-11 N m^2/kg^2). The most common exam trap is unit conversion: if a question gives mass in grams, you must convert to kilograms first. Another common error is mixing up orders of magnitude, particularly the minus 34 of Planck constant with the minus 31 of electron mass. Practise writing these from memory before the exam.
三、力学公式（上）：运动学与牛顿定律 | Mechanics Part 1: Kinematics and Newton's Laws
力学是AS物理中占比最大的模块，也是Insert 2上公式最密集的部分。运动学方面，你需要掌握四个基本公式（SUVAT方程组）：v = u + at，s = (u+v)t/2，s = ut + 1/2 at^2，以及v^2 = u^2 + 2as。这四个公式的适用前提是匀加速直线运动（constant acceleration），如果题目涉及变加速度（如简谐运动SHM），则不能直接套用。牛顿第二定律F = ma是所有力学计算的基础，但考试中更常见的考法是结合动量定理（F = delta p / delta t）：即力等于动量变化率。特别提醒：在Paper 1的选择题中，考试局经常将F = ma和F = mg放在同一题的两个选项里，考察你是否能区分数值相等但物理意义完全不同的两个力。
Mechanics carries the largest weighting in AS Physics, and the Insert contains the densest cluster of equations here. For kinematics, the four SUVAT equations form the backbone: v = u + at, s = (u+v)t/2, s = ut + 1/2 at^2, and v^2 = u^2 + 2as. These equations apply only when acceleration is constant; if a problem involves variable acceleration, such as simple harmonic motion, you cannot use SUVAT directly. Newton's second law, F = ma, underpins all mechanics calculations, but exam questions more frequently test the rate-of-change-of-momentum form, F = delta p over delta t. A common trap in Paper 1 multiple-choice questions pairs F = ma with F = mg as two options in the same question, testing whether you can distinguish between numerically equal forces with completely different physical meanings.
四、力学公式（下）：功、能与动量 | Mechanics Part 2: Work, Energy and Momentum
功和能部分的核心公式包括：功的定义（W = Fs cos theta，其中theta是力与位移的夹角）、动能公式（Ek = 1/2 mv^2）、重力势能（Ep = mgh）、以及功率公式（P = W/t 和 P = Fv）。特别要注意的是能量守恒原理：在无外力做功的情况下，动能损失等于势能增加，即1/2 mv^2 = mgh，这个等量关系在斜面问题和摆球问题中出现频率极高。动量部分的核心公式是p = mv，以及动量守恒定律：碰撞前后系统总动量不变。实验证明，弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒，但动量仍然守恒）的区分是考试中的高频考点。此外，冲量（impulse = F delta t = delta p）的概念经常与F-t图像的面积结合在一起考查。
The work and energy section centres on several key equations: work done, defined as W = Fs cos theta where theta is the angle between force and displacement; kinetic energy, Ek = 1/2 mv^2; gravitational potential energy, Ep = mgh; and power, expressed as P = W/t and P = Fv. Pay particular attention to conservation of energy: in the absence of external work, kinetic energy lost equals potential energy gained, giving the relationship 1/2 mv^2 = mgh, which appears frequently in inclined-plane and pendulum problems. For momentum, the central equation is p = mv, reinforced by the law of conservation of momentum: total momentum before and after a collision remains constant. Distinguishing between elastic collisions where kinetic energy is conserved and inelastic collisions where it is not, though momentum still is, is a high-frequency exam topic. Impulse, defined as F delta t equals delta p, is often tested alongside the area under a force-time graph.
五、材料物理：杨氏模量与应力应变 | Materials: Young Modulus, Stress and Strain
材料物理在AS大纲中是一个相对独立且计算量较轻的模块，但概念理解的准确性要求极高。Insert 2上这一部分的核心公式包括：应力（tensile stress = F/A，单位Pa或N/m^2）、应变（tensile strain = delta L / L，无量纲）、以及杨氏模量（Young modulus = stress/strain = FL / A delta L）。关键区分点：应力是单位面积上的力（类似于压强），而应变是长度的相对变化率，两者相乘得到杨氏模量：它是描述材料刚度的固有属性。实验题中，测量杨氏模量的标准方法是使用长金属丝加载荷，通过游标卡尺测量延伸量，画出应力-应变图。特别要注意弹性极限（elastic limit）和比例极限（limit of proportionality）的区别：超过弹性极限后材料发生永久形变，而比例极限是应力-应变曲线开始偏离直线的那一点。
Materials physics is a self-contained AS topic with lighter calculation but high demands for conceptual precision. The core equations on Insert 2 are: tensile stress (force per unit area, units Pa), tensile strain (fractional extension, dimensionless), and Young modulus (stress/strain = FL/A delta L). A crucial distinction: stress is force per unit area, while strain is a relative length change; Young modulus is an intrinsic property of material stiffness. In practical work, the standard method loads a long metal wire, measures extension with a vernier scale, and plots a stress-strain graph. Be clear on the difference between the elastic limit (permanent deformation) and the limit of proportionality (first deviation from linearity).
六、波的公式：速度、频率与波长 | Wave Equations: Speed, Frequency and Wavelength
波是AS物理Paper 2的重点考察内容，涉及三个核心公式。第一个也是最基础的：c = f lambda，即波速等于频率乘以波长：这个公式适用于所有类型的波，从声波到电磁波。第二个：在杨氏双缝干涉实验中，条纹间距公式为w = lambda D / s，其中w是相邻亮（或暗）条纹的间距，D是双缝到屏幕的距离，s是双缝间距。这个公式经常与米级、毫米级和纳米级的单位换算结合考查：如果忘记将毫米转换为米，计算结果将偏差1000倍。第三个重要公式是光栅方程：d sin theta = n lambda，其中d是光栅常数（1除以每毫米线数），theta是衍射角，n是级数。考试中注意：当题目问"最大可见级数"时，令sin theta等于1，解出n的值。
Waves feature prominently in AS Physics Paper 2, centred on three core equations. First: c = f lambda, wave speed equals frequency times wavelength, applicable to all wave types. Second, for Young double-slit experiment: fringe spacing w = lambda D / s, where D is the slit-to-screen distance and s is the slit separation. This equation is often tested alongside unit conversions: forgetting to convert millimetres to metres can produce an answer off by a factor of one thousand. Third, the diffraction grating equation: d sin theta = n lambda, where d is the grating spacing and n is the order number. In questions asking for the maximum observable order, set sin theta equal to one and solve for n.
七、电学公式（上）：欧姆定律与电阻网络 | Electricity Part 1: Ohm's Law and Resistor Networks
电学在AS物理中占有近30%的权重，是除力学之外最重要的模块。电流定义式I = delta Q / delta t（电荷流动率）是理解一切电学现象的起点。欧姆定律V = IR虽然简单，但考试中重点考查的是其适用范围：仅适用于欧姆导体（ohmic conductor），即I-V特性曲线为直线的元件，如电阻丝。二极管、灯丝（白炽灯泡）等非欧姆元件不遵循V = IR的关系。电阻串并联公式是高频计算题核心：串联时R_total = R1 + R2 + R3（电阻相加），并联时1/R_total = 1/R1 + 1/R2 + 1/R3（倒数之和的倒数）。电阻率公式rho = RA/L连接了材料属性与几何尺寸，在实验题中频繁出现：标准实验是测量一根导线的电阻随长度的变化，画出R-L图，从斜率求出电阻率。
Electricity carries nearly 30% of the AS Physics weighting, second only to mechanics. The current definition, I = delta Q / delta t, is the foundation for all electrical phenomena. Ohm law, V = IR, holds only for ohmic conductors with straight-line I-V characteristics like fixed resistors; diodes and filament lamps do not obey this simple relationship. Resistor network formulas are at the heart of calculation questions: R total equals R1 + R2 + R3 in series; one over R total equals the sum of reciprocals in parallel. The resistivity formula, rho = RA / L, connecting material properties to geometry, appears frequently in practical contexts where resistance is measured as wire length varies to extract resistivity from the R-L gradient.
八、电学公式（下）：功率、电动势与分压 | Electricity Part 2: Power, EMF and Potential Dividers
电功率的三个等价表达式（P = IV，P = I^2 R，P = V^2/R）是AS物理中最重要的公式组之一。考试中的关键考点是根据题目已知条件选择最合适的表达式：已知电流和电阻时用P = I^2 R，已知电压和电阻时用P = V^2/R。电动势（electromotive force, e.m.f.）和端电压（terminal potential difference）的区分是经典失分点：电动势是电池在断路时提供的总能量，端电压是实际接入电路后外部的可用电压，两者之差等于内阻（internal resistance, r）上的电压降（Ir）。分压器（potential divider）公式V_out = V_in × R2/(R1+R2)在传感器电路题中几乎每次考试都会出现：例如，用热敏电阻（thermistor）或光敏电阻（LDR）搭建温度或光照检测电路时，输出电压的变化反映了传感器电阻的变化。
The three equivalent power expressions, P = IV, P = I^2 R, and P = V^2/R, form one of the most important clusters in AS Physics. The key skill is selecting the right expression: use P = I^2 R when current and resistance are known, P = V^2/R when voltage and resistance are known. The distinction between e.m.f. and terminal p.d. is a classic confusion: e.m.f. is the total energy a cell supplies at zero current, while terminal p.d. is the usable voltage under load; the difference equals the voltage drop across internal resistance, Ir. The potential divider formula, V out = V in times R2 over (R1 + R2), appears in nearly every sensor-circuit question with thermistors or LDRs.
九、量子物理：光子与光电效应 | Quantum Physics: Photons and the Photoelectric Effect
量子物理在AS阶段的核心是光量子理论。光子能量公式E = hf（等于hc/lambda）是连接波模型和粒子模型的桥梁：频率越高的光，单个光子的能量越大。光电效应方程hf = phi + Ek_max是Paper 2中最常出现的推导题和解释题来源：入射光子的能量hf，一部分用于克服金属表面的逸出功（work function, phi），剩余部分转化为逸出电子的最大动能Ek_max。考试中的关键概念区分包括：光电效应的瞬时性（光子能量一次性传递给电子，无需积累时间）、阈值频率（threshold frequency，即hf0 = phi，低于此频率的光无论强度多大都不能产生光电子）、以及光强度只影响光电子数量而不影响其最大动能。实验题通常要求画出不同频率下的I-V特性曲线并解释停止电压（stopping potential）。
Quantum physics at AS level centres on photon theory. The photon energy formula, E = hf, equivalently expressed as hc over lambda, is the bridge between wave and particle models: the higher the frequency, the greater the energy of each individual photon. The photoelectric equation, hf = phi plus Ek max, is the most common source of derivation and explanation questions in Paper 2: the energy of an incident photon, hf, is partly used to overcome the work function phi of the metal surface, with the remainder becoming the maximum kinetic energy of the emitted electron. Key conceptual distinctions include the instantaneous nature of photoemission, where photon energy is transferred to a single electron in one interaction with no accumulation time; the threshold frequency, given by hf0 = phi, below which no amount of intensity can liberate electrons; and the fact that light intensity affects only the number of photoelectrons, not their maximum kinetic energy. Practical questions typically ask you to sketch I-V characteristics at different frequencies and explain the stopping potential.
十、粒子物理：核反应与能量守恒 | Particle Physics: Nuclear Reactions and Energy Conservation
粒子物理部分在Insert 2上虽然没有独立的公式部分，但涉及核反应的能量计算时，需要用到爱因斯坦的质能方程E = mc^2。AS阶段主要考查alpha衰变、beta负衰变和beta正衰变（positron emission）的核反应方程式书写，以及质量-能量守恒。关键考点包括：alpha衰变后，原子序数减少2，质量数减少4；beta负衰变（neutron→proton + electron + antineutrino）时，原子序数增加1，质量数不变；伽马衰变（gamma emission）仅释放能量，不改变原子核的组成。在计算释放能量时，需要先求出反应前后的质量亏损（mass defect），再将质量差乘以c^2得到以焦耳为单位的能量：通常题目会要求你进一步转换为电子伏特（eV）或兆电子伏特（MeV），牢记1 eV = 1.60乘以10的负19次方J。
While particle physics does not have a dedicated formula section on Insert 2, nuclear reaction energy calculations require Einstein's mass-energy equivalence, E = mc^2. At AS level, the main focus is writing balanced nuclear equations for alpha decay, beta-minus decay, and positron emission, alongside mass-energy conservation. Key points: after alpha decay, the atomic number decreases by 2 and the mass number decreases by 4. In beta-minus decay, where a neutron converts to a proton, an electron, and an antineutrino, the atomic number increases by 1 while the mass number stays unchanged. Gamma emission only releases energy without altering the nuclear composition. When calculating released energy, first determine the mass defect before and after the reaction, then multiply the mass difference by c^2 to obtain energy in joules. Questions often require further conversion to electronvolts or megaelectronvolts: remember that 1 eV = 1.60 times 10 to the minus 19 J.
十一、不确定度与实验误差分析 | Uncertainties and Experimental Error Analysis
测量与误差分析是AS物理Paper 3（实验技能）和Paper 2中实验设计题的核心。Insert 2虽然不直接给出误差公式，但实验题中频繁涉及绝对不确定度（absolute uncertainty）、相对不确定度（percentage uncertainty）和组合不确定度的计算。关键规则包括：当两个测量值相加或相减时，绝对不确定度相加（delta Q = delta A + delta B）；当两个测量值相乘或相除时，百分比不确定度相加（% Uncertainty in Q = % Uncertainty in A + % Uncertainty in B）；当一个测量值乘以常数时，百分比不确定度不变，绝对不确定度乘以该常数。在实验评估题中，你需要指出误差的主要来源（通常是测量长度时的视差误差或时间测量时的反应时间）并提出改进方案（如使用游标卡尺替代米尺、使用光门替代手动秒表）。
Measurement and error analysis are central to AS Physics Paper 3, the practical skills paper, and to experimental design questions in Paper 2. While Insert 2 does not explicitly list error formulas, exam questions frequently involve calculating absolute uncertainty, percentage uncertainty, and combined uncertainties. The key rules: when two measured values are added or subtracted, absolute uncertainties add; when two measured values are multiplied or divided, percentage uncertainties add; when a measured value is multiplied by a constant, the percentage uncertainty stays the same while the absolute uncertainty is multiplied by that constant. In experimental evaluation questions, you need to identify the main sources of error, typically parallax error when measuring lengths or reaction time when measuring time intervals, and propose improvements such as using a vernier calliper instead of a metre rule or a light gate instead of a manual stopwatch.
十二、考场上高效使用Insert的实战策略 | Practical Strategies for Using the Insert in the Exam
掌握了Insert 2上的所有公式之后，更重要的是学会如何在考试中高效使用它。以下是经过实际考试验证的五条策略。第一，拿到试卷后，用30秒快速浏览Insert上的公式分布：知道每个模块的公式在哪个位置，而不是遇到题目才乱翻。第二，标记你最不熟悉的公式：考前用荧光笔（如果是打印版）或心理标记出那些容易遗忘的公式，如电阻率公式rho = RA/L和杨氏模量公式，这样在考场上能快速定位。第三，单位检查法：每代入一个公式后，立即用两秒钟检查单位是否自洽：如果公式左边是牛顿（N），右边算出来是kg·m^2/s^2，那一定是哪里写错了（正确的应该是kg·m/s^2等于N）。第四，先写公式再代数字：这是获取"方法分"（method marks）的关键策略：即使你最后算错了答案，只要在答题纸上正确写下了公式，就能拿到至少1分的方法分。第五，发现公式记反了不要慌：如果忘记了某个变形公式（例如从F = BIL求B），直接利用Insert上的原公式做代数变换，而不是凭模糊的记忆拼凑。
Mastering the formulas on Insert 2 is essential, but efficient exam use is equally important. Here are five strategies. First, spend 30 seconds scanning the formula layout when you receive the paper: know where each topic sits so you can find equations instantly. Second, mentally mark your weakest formulas like resistivity and Young modulus before the exam. Third, practise the unit-check habit: after substituting into any formula, verify units are consistent; if the left side expects newtons but the right gives kg m^2/s^2, something is wrong since a newton is kg m/s^2. Fourth, always write the formula before plugging in numbers to secure method marks even if your final answer is wrong. Fifth, derive rearranged forms algebraically from the Insert rather than relying on memory.
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