Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Centres of mass: position, applications to uniform bodies and composite bodies
Learning Objective/s:
  • Describe the definition of centre of mass for discrete and continuous bodies.
  • Apply symmetry and integration to locate the COM of uniform rods, rectangles, semicircles and other simple shapes.
  • Compute the COM of composite bodies by treating components as point masses.
  • Solve typical A‑Level mechanics problems involving COM and interpret the results.
Materials Needed:
  • Projector or interactive whiteboard for displaying formulas and diagrams.
  • Printed worksheet with worked examples and practice questions.
  • Rulers, graph paper, and calculators for student calculations.
  • Set of uniform rods and rectangular plates for a quick classroom demonstration (optional).
 Introduction:
Begin with a quick visual of a balanced seesaw to spark curiosity about how objects balance. Recall the previous lesson on vectors and moments, linking them to the idea of a single point representing total mass. Explain that today’s success criteria are to define centre of mass, locate it for uniform shapes using symmetry or integration, and combine sub‑bodies to find an overall COM.
Lesson Structure:
  1. Do‑now (5'): Students answer a short question on the definition of centre of mass from the previous lesson. (Check understanding)
  2. Mini‑lecture (10'): Derive the COM formula for discrete particles and continuous bodies; illustrate with the uniform rod example. (Guided notes)
  3. Interactive demonstration (8'): Use a physical rod and a rectangular plate to show symmetry points; students predict COM positions. (Peer discussion)
  4. Worked example walkthrough (12'): Solve Example 2 (L‑shaped composite body) step‑by‑step on the board, emphasizing the composite formula. (Teacher modelling)
  5. Guided practice (15'): Students work in pairs on the three practice questions, using calculators and sketching diagrams. (Teacher circulates)
  6. Quick check (5'): Collect exit tickets where each student writes the COM of a given uniform shape. (Formative assessment)
Conclusion:
Summarise that the centre of mass can be found by symmetry for uniform bodies or by weighted averaging for composites. Highlight common pitfalls such as inconsistent origins and non‑uniform density. For the exit ticket, ask students to state one strategy they will use next time. Assign homework: complete the worksheet’s additional problems on COM of irregular shapes.