📚 Common Physics Problem-Solving Methods | 常见物理解题方法归纳
The OCR and WJEC A-level Physics specifications reward a systematic approach to problem-solving. This article condenses the essential techniques you need — from dimensional analysis to mark-scheme strategy — into a practical toolkit for both multiple-choice and extended-response questions. Master these methods, and you will not only earn full marks on routine calculations but also gain the confidence to tackle unfamiliar contexts.
OCR 与 WJEC 的 A-level 物理考纲一贯重视系统性解题思路。本文将这些核心技巧——从量纲分析到评分策略——浓缩为一套实用工具箱，帮你应对选择题和解答题。掌握这些方法，你不仅能在常规计算中拿满全分，更能自信应对陌生情境题。
1. Dimensional Analysis | 量纲分析
Dimensional analysis asks one question first: does the equation make physical sense? y (m s⁻¹) + acceleration (m s⁻²) × time (s) = m s⁻¹. √. It is the fastest check in an exam — and a reliable method when you cannot recall a formula.
量纲分析首先要问的问题只有一个：这个方程在物理上是否合理？将每个物理量替换为基本单位（kg、m、s、A、K、mol、cd），等式两侧的单位必须一致。例如在 v = u + at 中，速度（m s⁻¹）= 速度（m s⁻¹）+ 加速度（m s⁻²）× 时间（s）= m s⁻¹。✓。这是考试中最快的检查手段，也是当你忘记公式时最可靠的推断工具。
To derive an unknown relation, set up a general power law: area ∝ L², volume ∝ L³, frequency ∝ write T = kLᵃgᵇ and compare units: s = mᵃ × (m s⁻²)ᵇ. Balancing gives a = ½, b = −½, so T ∝ √L/g.
若要推导未知关系式，可设定一般幂律：面积 ∝ L²，体积 ∝ L³，频率 ∝ 1/T。若题目问单摆周期 T 如何依赖摆长 L 与重力加速度 g，可写 T = kLᵃgᵇ 并比较单位：s = mᵃ × (m s⁻²)ᵇ。平衡指数得 a = ½，b = −½，故 T ∝ √L/g。
T ∝ √L/g
Use this technique to spot typo-like errors in multiple-choice questions. If only one option has units of energy (kg m² s⁻²), you have effectively solved the problem without any calculation. In OCR paper 1 multiple-choice, this alone can save two minutes per question.
用这个技巧可以快速识别选择题中"打字错误"式的干扰项。若只有一项的单位是能量（kg m² s⁻²），你实际上不用计算就已解出此题。在 OCR 第一卷的选择题中，仅此一招每题可省两分钟。
2. Free-Body Diagrams & Force Resolution | 受力分析图与力的分解
Draw a clear diagram first. Show the object as a point mass, and draw every force acting on it as an arrow from that point: weight (mg), normal reaction (N), friction (F), tension (T), applied forces. Label each arrow with the name or its magnitude. Then choose two perpendicular axes — usually the direction of motion and the normal to it — and resolve forces along those axes.
先画一张清晰的示意图。把物体视为质点，从该点画出所有力的箭头：重力（mg）、支持力（N
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