# © Boardworks Ltd 2006 1 of 36 These icons indicate that teacher’s notes or useful web addresses are available in the Notes Page. This icon indicates the.

## Presentation on theme: "© Boardworks Ltd 2006 1 of 36 These icons indicate that teacher’s notes or useful web addresses are available in the Notes Page. This icon indicates the."— Presentation transcript:

© Boardworks Ltd 2006 1 of 36 These icons indicate that teacher’s notes or useful web addresses are available in the Notes Page. This icon indicates the slide contains activities created in Flash. These activities are not editable. For more detailed instructions, see the Getting Started presentation. © Boardworks Ltd 2006 1 of 36 AS-Level Maths: Mechanics 2 for Edexcel M2.3 Centres of Mass

© Boardworks Ltd 2006 2 of 36 Contents © Boardworks Ltd 2006 2 of 36 Centres of mass Two dimensions Equilibrium Examination-style questions

© Boardworks Ltd 2006 3 of 36 Centres of mass The centre of mass of a body is the point at which the weight acts. This point can be located for one, two and three dimensional objects and composite bodies. The positions of the centres of mass of certain bodies are given as formulae, which can be applied without working. In general, we use moments to determine the position of the centre of mass. Sometimes the centre of mass of a uniform body can be found by symmetry.

© Boardworks Ltd 2006 4 of 36 Contents © Boardworks Ltd 2006 4 of 36 Two dimensions Centres of mass Two dimensions Equilibrium Examination-style questions

© Boardworks Ltd 2006 5 of 36 Symmetry If a uniform lamina has more than one axis of symmetry, then the centre of mass is located at the intersection of these axes. Rectangles, circles, and equilateral triangles are examples of this kind of lamina.

© Boardworks Ltd 2006 6 of 36 Contents © Boardworks Ltd 2006 6 of 36 Equilibrium Centres of mass Two dimensions Equilibrium Examination-style questions

© Boardworks Ltd 2006 7 of 36 Equilibrium A lamina suspended from a point is in equilibrium if its centre of mass is directly below the point from which it is suspended.

© Boardworks Ltd 2006 8 of 36 Equilibrium on an inclined plane A lamina resting on an inclined plane will be in equilibrium if the line of action of the weight lies within the side of the lamina in contact with the plane. The line of action of the weight is shown and is clearly within the side of the lamina that is in contact with the plane. The lamina is in equilibrium. The line of action of the weight is clearly beyond the side of the lamina that is in contact with the plane. The lamina will topple. If the line of action of the weight falls beyond the side of the lamina in contact with the plane, the lamina will topple.

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