A-Level Further Maths · Year 13 · Further Mechanics
Centres of Mass worksheets with answers
Free worksheets for the 6 lessons in A-Level Further Maths Centres of Mass, written by qualified teachers. Each lesson has a worksheet, full answers to the worksheet and a homework sheet, as PDFs to print or share. No sign-up needed.
6 lessonsAQA 7367 · Edexcel 9FM0
We don't publish answers to the homework, so teachers can set it as independent work.
Lesson 1 of 6
Centre of Mass of a System of Particles
Explains what the centre of mass is and why a body supported there balances. Students find the centre of mass of particles on a line and in a plane, and find an unknown mass or position from a given centre of mass.
- AQA 7367
- ME1
- Edexcel 9FM0
- FM2 Centres of mass of plane figures (particles)
Lesson 2 of 6
Rods, Wire Frameworks and Wires of Different Densities
Finds the centre of mass of uniform rods, wire frameworks and wires of different densities, including frameworks with particles attached. Students also use the standard result for a circular arc.
- AQA 7367
- ME1, ME2
- Edexcel 9FM0
- FM2 Centres of mass of plane figures (frameworks, circular arcs)
Lesson 3 of 6
Composite Laminas
Finds the centre of mass of composite laminas, including L-shapes and laminas with holes, using a table of areas and moments. Students use the standard results for triangles, semicircles and sectors, and handle folded laminas and laminas of different densities.
- AQA 7367
- ME2
- Edexcel 9FM0
- FM2 Centres of mass of plane figures (composite laminas, standard results)
Lesson 4 of 6
Freely Suspended Laminas and Frameworks
Explains why a freely suspended body hangs with its centre of mass directly below the point of suspension. Students find the angle at which a lamina or framework hangs, the mass that makes it hang at a given angle, and the force needed to hold a pivoted lamina.
- AQA 7367
- ME2 (bodies freely suspended)
- Edexcel 9FM0
- FM2 Centres of mass of plane figures (hanging)
Lesson 5 of 6
Uniform and Composite Solids
Finds the centre of mass of uniform and composite solids from their volumes, using symmetry and the standard results for cones, hemispheres and shells. Students also decide whether a toy resting on its curved surface returns upright, and find the angle at which a solid hangs.
- AQA 7367
- ME2 (uniform bodies, composite bodies, standard results)
- Edexcel 9FM0
- FM2 Further centres of mass (solids)
Mixed review · Lesson 6 of 6
Unit review: Centres of Mass
Mixed exam-style practice across the whole Centres of Mass unit: particles, rods and frameworks, laminas and solids, and bodies hanging freely. The focus is on choosing the right model and standard result before calculating.
- AQA 7367
- ME1, ME2
- Edexcel 9FM0
- FM2 Centres of mass of plane figures, Further centres of mass
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