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Contents
- Whole Topic Notes
- 2A Centre of Mass of a Set of Particles on a Straight Line
- 2B Centre of Mass of a Set of Particles Arranged in a Plane
- 2C Centres of Mass of Standard Uniform Plane Laminas
- 2D Centre of Mass of a Composite Lamina
- 2E Centre of Mass of a Framework
- 2F Lamina in Equilibrium
- 2G Frameworks in Equilibrium
- 2H Non-uniform Composite Laminas and Frameworks
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Mechanics 2 Centres of Mass of Plane Figures Section
- Dr Frost Further Mechanics 2 Centres of Mass of Plane Figures Slides
2A Centre of Mass of a Set of Particles on a Straight Line
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Key Skills
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2B Centre of Mass of a Set of Particles Arranged in a Plane
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Key Skills
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- 893b: Determine the coordinates of the centre of mass of a system where masses are placed on a plane at given coordinates.
- 893c: Determine the coordinates of the centre of mass of a light loaded plate given placement of particles at its vertices.
- 893d: Determine the coordinates of the placement of a particle on a plane given the coordinates of the centre of mass.
- 893e: Determine the mass of a particle on a plane given the coordinates of the centre of mass.
- 893: Exam Practice: Centre of mass of particles on a line or plane
2C Centres of Mass of Standard Uniform Plane Laminas
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Key Skills
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- 894a: Determine the coordinates of the centre of mass of a uniform triangular lamina with vertices at given coordinates.
- 894b: Determine the coordinates of the centre of mass of a uniform right-angled triangular lamina with given lengths.
- 894c: Derive the formula for the centre of mass of a uniform sector of a circle lamina along its axis of symmetry.
- 894d: Determine the centre of mass of a uniform semicircular lamina.
- 894e: Determine the centre of mass of a uniform general sector of a circle lamina.
- 894: Exam Practice: Centre of mass of a lamina
2D Centre of Mass of a Composite Lamina
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Key Skills
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- 894f: Determine the coordinates of the centre of mass of a composite uniform lamina consisting of a rectangle and triangle.
- 894g: Determine the coordinates of the centre of mass of a composite uniform lamina consisting of multiple triangles.
- 894h: Determine the coordinates of the centre of mass of a composite uniform lamina consisting of a rectangle and semicircle.
- 894i: Determine the coordinates of the centre of mass of a composite uniform rectilinear lamina.
- 894j: Determine the coordinates of the centre of mass of a uniform rectangular lamina with a rectangle removed.
- 894k: Determine the coordinates of the centre of mass of a uniform lamina removed from another involving triangles and rectangles.
- 894l: Determine the coordinates of the centre of mass of a uniform rectangular lamina with a circle removed.
- 894m: Determine the coordinates of the centre of mass of a uniform circular lamina with a circle removed.
- 894n: Determine the coordinates of the centre of mass of a uniform lamina removed from another where one shape is semicircular or a sector of a circle.
- 894: Exam Practice: Centre of mass of a lamina
2E Centre of Mass of a Framework
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Key Skills
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- 895a: Determine the coordinates of the centre of a mass of a framework of a general polygon.
- 895b: Determine the coordinates of the centre of a mass of a framework of a semicircle.
- 895c: Determine the coordinates of the centre of mass of a framework consisting of a rectangle and a semicircle.
- 895d: Determine the coordinates of the centre of mass of a framework in the shape of a sector of a circle.
- 895e: Determine the coordinate of the centre of mass of a framework where additional weights are loaded onto it.
- 895: Exam Practice: Centre of mass of a framework
2F Lamina in Equilibrium
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Key Skills
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- 896a: Determine the angle at which a uniform rectilinear lamina would hang when freely suspended from a given point.
- 896b: Determine the angle at which a uniform general polygonal lamina would hang when freely suspended from a given point.
- 896c: Determine the angle at which a uniform semicircular or general sector lamina would hang when freely suspended from a given point.
- 896d: Determine the angle at which a uniform composite lamina, involving circular or semicircular areas, would hang when freely suspended from a given point.
- 896i: Determine the mass of a particle attached to a uniform lamina that would result in a given angle of suspension.
- 896: Exam Practice: Lamina and frameworks in equilibrium
2G Frameworks in Equilibrium
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Key Skills
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- 896e: Determine the angle at which a uniform rectilinear framework would hang when freely suspended from a given point.
- 896f: Determine the angle at which a uniform general polygonal framework would hang when freely suspended from a given point.
- 896g: Determine the angle at which a uniform semicircular or general sector framework would hang when freely suspended from a given point.
- 896h: Determine the angle at which a uniform framework, with an additional particle attached, would hang when freely suspended from a given point.
- 896j: Determine the mass of a particle attached to a uniform framework that would result in a given angle of suspension.
- 896: Exam Practice: Lamina and frameworks in equilibrium
2H Non-uniform Composite Laminas and Frameworks
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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
- 894o: Determine the coordinate of the centre of a mass of a non-uniform lamina created by folding.
- 895f: Determine the coordinate of the centre of a mass of a non-uniform framework where its edges are of stated masses.
- 896k: Determine the angle at which a non-uniform lamina, created by folding, would hang when freely suspended from a given point.
- 894: Exam Practice: Centre of mass of a lamina
- 895: Exam Practice: Centre of mass of a framework
Whole Topic Summary Resources (Including Past Paper Questions)
External whole topic past paper style questions
- WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)