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This whole chapter is A level only (not needed for AS Further Maths).
Contents
- Whole Topic Notes
- 3A Using Calculus to Find Centres of Mass*
- 3B Centre of Mass of a Uniform Body*
- 3C Non-Uniform Bodies*
- 3D Rigid Bodies in Equilibrium*
- 3E Toppling and Sliding*
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Mechanics 2 Further Centres of Mass Section
- Dr Frost Further Mechanics 2 Further Centres of Mass Slides
3A Using Calculus to Find Centres of Mass*
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 897a: Determine the centre of mass of a uniform lamina with polynomial equation.
- 897b: Determine the centre of mass of a uniform lamina with exponential equation.
- 897c: Determine the centre of mass of a lamina formed by the area between two polynomial lines.
- 897d: Use the area of a lamina with given equation to determine the centre of mass.
- 897: Exam Practice: Using calculus to find the centre of mass
3B Centre of Mass of a Uniform Body*
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Key Skills
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- 898a: Use calculus to determine the centre of mass of a uniform solid right circular cone.
- 898b: Use calculus to determine the centre of mass of a uniform solid hemisphere.
- 898c: Determine the centre of mass of a volume of revolution revolved around the x-axis.
- 898d: Determine the centre of mass of a volume of revolution revolved around the y-axis.
- 898e: Use calculus to determine the centre of mass of a uniform solid hemispherical shell.
- 898f: Determine the centre of mass of a uniform hollow right circular cone.
- 898g: Determine the centre of mass of a composite uniform solid consisting of cylinders, cones or hemispheres.
- 898: Exam Practice: Centre of mass of 3D solids or shells
3C Non-Uniform Bodies*
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Key Skills
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- 898g: Determine the centre of mass of a composite uniform solid consisting of cylinders, cones or hemispheres.
- 898h: Determine the mass or a non-uniform rod where the mass is a function of distance from the base.
- 898i: Determine the centre of mass of a non-uniform rod where the mass is a function of distance from the base.
- 898: Exam Practice: Centre of mass of 3D solids or shells
3D Rigid Bodies in Equilibrium*
Textbook resources
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Key Skills
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3E Toppling and Sliding*
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 899a: Determine the angle of a (sufficiently rough) inclined plane at which a cube would topple.
- 899b: Determine the range of angles of a (sufficiently rough) inclined plane at which a composite solid would remain in equilibrium.
- 899c: Determine the range of values for μ for which a solid would slide down a slope.
- 899d: Determine the angle of a (sufficiently rough) inclined plane at which a volume of revolution would topple.
- 899: Exam Practice: Toppling and sliding