📚 AS Physics Insert 1 (June 2022) Key Concepts Explained | AS物理2022年6月公式表核心概念解析
The AS Physics Insert 1 provided in the June 2022 examination contains the essential formulae, constants and relationships that are fundamental to the AS-level syllabus. Understanding these concepts not only helps in applying the formulas correctly but also deepens your grasp of physics principles. This article breaks down the key sections of the insert, explaining their meaning and typical applications in exam questions.
2022 年 6 月 AS 物理考试提供的公式表 1 包含了 AS 阶段的核心公式、常数和关系式。理解这些概念不仅有助于正确应用公式，还能加深对物理原理的把握。本文将逐一解析公式表中的关键部分，阐述它们的含义及在试题中的典型应用。
1. Physical Constants and Units | 物理常数与单位
The insert lists fundamental constants such as speed of light in vacuo c = 3.00 × 10⁸ m s⁻¹, Planck constant h = 6.63 × 10⁻³⁴ J s, elementary charge e = 1.60 × 10⁻¹⁹ C, electron mass mₑ = 9.11 × 10⁻³¹ kg and the gravitational acceleration g = 9.81 N kg⁻¹ (or m s⁻²). These constants are used across various topics, from quantum phenomena to mechanics. Always check the units and significant figures required in the question.
公式表列出了基本常数，如真空光速 c = 3.00 × 10⁸ m s⁻¹，普朗克常数 h = 6.63 × 10⁻³⁴ J s，基本电荷 e = 1.60 × 10⁻¹⁹ C，电子质量 mₑ = 9.11 × 10⁻³¹ kg，以及重力加速度 g = 9.81 N kg⁻¹（或 m s⁻²）。这些常数在从量子现象到力学的多个主题中都会用到，使用时务必注意题目要求的单位和有效数字。
2. Mechanics: Motion in a Straight Line | 力学：直线运动
The SUVAT equations relate displacement s, initial velocity u, final velocity v, acceleration a and time t for constant acceleration. They are: v = u + at; s = ½ (u + v)t; s = ut + ½ at²; v² = u² + 2as. These require constant acceleration and careful attention to vector directions. Remember to define positive direction before substituting values.
匀加速直线运动公式（SUVAT）关联了位移 s、初速度 u、末速度 v、加速度 a 和时间 t。公式有：v = u + at；s = ½ (u + v)t；s = ut + ½ at²；v² = u² + 2as。使用时要求加速度恒定，并需注意矢量的正方向定义，代入数值前先规定正方向。
3. Forces and Moments | 力与力矩
Newton’s second law F = ma, weight W = mg. Equilibrium requires net force and net moment to be zero. The principle of moments: sum of clockwise moments equals sum of anticlockwise moments about a pivot. For a couple, moment = force × perpendicular distance between forces. Friction f ≤ μR where μ is coefficient of friction and R is normal reaction.
牛顿第二定律 F = ma，重量 W = mg。平衡条件需要合外力为零且合力矩为零。力矩原理：绕支点的顺时针力矩之和等于逆时针力矩之和。对于力偶，力矩 = 力 × 两力间的垂直距离。摩擦力 f ≤ μR，μ 为摩擦系数，R 为法向反作用力。
4. Work, Energy and Power | 功、能和功率
Work done W = Fs cos θ, kinetic energy Eₖ = ½ mv², gravitational potential energy ΔEₚ = mgΔh. The principle of conservation of energy: total energy remains constant in a closed system. Power P = W/t or P = Fv for constant force and velocity. Efficiency = (useful output energy / total input energy) × 100%.
功 W = Fs cos θ，动能 Eₖ = ½ mv²，重力势能变化 ΔEₚ = mgΔh。能量守恒定律：封闭系统中总能量保持不变。功率 P = W/t，或当力与速度恒定时 P = Fv。效率 =（有用输出能量 / 总输入能量）× 100%。
5. Momentum | 动量
Momentum p = mv. Newton’s second law in terms of momentum: F = Δp / Δt. In a closed system, total momentum is conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for a two-body collision. Impulse = change in momentum = FΔt = area under a force-time graph. Elastic collisions conserve kinetic energy; inelastic collisions do not.
动量 p = mv。用动量表示的牛顿第二定律：F = Δp / Δt。在封闭系统中，总动量守恒：对于两体碰撞，m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。冲量等于动量变化 = FΔt = 力-时间图下的面积。弹性碰撞动能守恒，非弹性碰撞则不守恒。
6. Materials: Stress, Strain and Young Modulus | 材料：应力、应变和杨氏模量
Stress σ = F/A (unit Pascal), strain ε = ΔL / L (no unit), Young modulus E = σ/ε = FL / AΔL. The insert may list these relationships. Hooke’s law: F = kx, where k is spring constant. Elastic potential energy stored = ½ Fx = ½ kx². Stress-strain graphs show elastic limit, yield point, plastic flow and fracture.
应力 σ = F/A （单位帕斯卡），应变 ε = ΔL / L （无量纲），杨氏模量 E = σ/ε = FL / AΔL。公式表中会列出这些关系。胡克定律：F = kx，k 为劲度系数。储存的弹性势能 = ½ Fx = ½ kx²。应力-应变图显示了弹性极限、屈服点、塑性流动和断裂。
7. Electricity: Circuits and Resistivity | 电学：电路与电阻率
Current I = ΔQ / Δt, potential difference V = W/Q, resistance R = V/I. Ohm’s law gives V = IR for ohmic conductors. Resistivity ρ = RA / L. Power P = IV = I²R = V²/R. emf ε = E/Q = I(R+r), including internal resistance r. For series resistors: Rₜ = R₁ + R₂ + …; parallel: 1/Rₜ = 1/R₁ + 1/R₂ + …
电流 I = ΔQ / Δt，电势差 V = W/Q，电阻 R = V/I。欧姆定律适用于欧姆导体 V = IR。电阻率 ρ = RA / L。功率 P = IV = I²R = V²/R。电动势 ε = E/Q = I(R+r)，包含内阻 r。串联电阻：Rₜ = R₁ + R₂ + …；并联：1/Rₜ = 1/R₁ + 1/R₂ + …
8. Potential Divider and Sensors | 分压器与传感器
The potential divider formula V_out = V_in × (R₂ / (R₁ + R₂)) for two resistors in series. This is used in sensor circuits with thermistors and LDRs. As temperature rises, thermistor resistance falls (if NTC) and V_out can change. LDR resistance decreases with light intensity. Such circuits are common in AS practical and theory questions.
对于两个串联电阻，分压公式 V_out = V_in × (R₂ / (R₁ + R₂))。该电路常用于热敏电阻和光敏电阻的传感器。当温度升高，负温度系数热敏电阻（NTC）阻值下降，输出电压变化。光敏电阻随光照增强阻值减小。这类电路在 AS 实验和理论题中很常见。
9. Waves: Interference and Diffraction | 波：干涉与衍射
Wave speed v = fλ. For double-slit interference: fringe spacing w = λD / s, where s is slit separation, D is screen distance. Diffraction grating: d sin θ = nλ, with d = 1/N (N grooves per metre). Refractive index n = c / v, Snell’s law n₁ sin θ₁ = n₂ sin θ₂, critical angle sin θc = n₂ / n₁ (for n₁ > n₂). Understand coherence, path difference and superposition.
波速 v = fλ。双缝干涉：条纹间距 w = λD / s，其中 s 为缝间距，D 为屏幕距离。衍射光栅：d sin θ = nλ，d = 1/N（N 为每米刻线数）。折射率 n = c / v，斯涅尔定律 n₁ sin θ₁ = n₂ sin θ₂，临界角 sin θc = n₂ / n₁（n₁ > n₂）。需理解相干性、光程差和叠加原理。
10. Quantum Physics: Photoelectric Effect and Energy Levels | 量子物理：光电效应与能级
Photon energy E = hf = hc/λ. The photoelectric equation: hf = Φ + Eₖₘₐₓ, where Φ is work function and Eₖₘₐₓ is maximum kinetic energy of emitted electron, also expressible as Eₖₘₐₓ = eVs (Vs stopping potential). Threshold frequency f₀ = Φ/h. Electron beam wavelength: λ = h/p, where p is momentum. For atomic energy levels, photon emission/absorption relates to difference: ΔE = hf = E₂ – E₁. Excitation and ionisation energies are key.
光子能量 E = hf = hc/λ。光电效应方程：hf = Φ + Eₖₘₐₓ，其中 Φ 为逸出功，Eₖₘₐₓ 是逸出电子的最大动能，也可表示为 Eₖₘₐₓ = eVs（Vs 为遏止电势）。阈频率 f₀ = Φ/h。电子束波长 λ = h/p，p 为动量。对于原子能级，光子发射或吸收与能级差相关：ΔE = hf = E₂ – E₁。激发能和电离能是关键概念。
11. Projectile Motion | 抛体运动
For a projectile launched at an angle θ to horizontal with speed u, horizontal component uₓ = u cos θ (constant), vertical component uᵧ = u sin θ, subject to g = 9.81 m s⁻². Time of flight, range and maximum height can be derived using SUVAT independently for horizontal and vertical motions. Horizontal range = (u² sin 2θ)/g.
对于以速度 u 沿与水平面成 θ 角发射的抛体，水平分量 uₓ = u cos θ（恒定），竖直分量 uᵧ = u sin θ，受 g = 9.81 m s⁻² 作用。飞行时间、射程和最大高度可通过对水平和竖直方向分别应用 SUVAT 推导。水平射程 = (u² sin 2θ)/g。
12. Using the Insert Effectively in Exams | 考试中高效使用公式表
The insert is not just a reference list; it is a toolkit. Always know which formulas are provided and which you must recall (e.g., definitions may not be on the insert). Practice rearranging equations and substituting values with units. Check if a constant is given exactly or to 3 significant figures. Use the insert for quick verification during calculations and to avoid simple memorisation mistakes.
公式表不仅仅是一份参考清单，更是工具箱。要清楚哪些公式已提供、哪些需要自己记忆（如定义）。练习变换方程并代入带单位的数值。注意常数的数值是精确值还是取三位有效数字。在计算时用公式表做快速核查，避免因记忆偏差导致的错误。
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