Common Physics Problem-Solving Methods | 常见物理解题方法归纳

📚 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? Replace every quantity with its base unit (kg, m, s, A, K, mol, cd). The units on both sides of an equation must match. For example, in v = u + at, velocity (m s⁻¹) = velocity (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 ∝ 1/T. If a question asks how the period T of a pendulum depends on length L and g, you can 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

Published by TutorHao | Physics Revision Series | aleveler.com

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