Physics

A pendulum is made of two discs, one with mass M and radius R and the other with mass 2M and radius R, which are separated by a massless rod. The lighter disc is pivoted through its centre by a small pin. The discs lie on the same plane and their centres are a distance L apart. Find the period for small oscillations.

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  1. A uniform lamina consists of a disc with radius R with a disc of radius r cut off from its centre, with r < R. The total mass of the object is M. Find the moment of inertia when the lamina rotates about an axis perpendicular to the lamina, thought its centre.

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  2. An object consists of two thin rods, AB with mass M and length 2L, and CD, of mass 2M and length L, joined together at right angles at their midpoints to form a cross. Let E be the point where the two rods intersect. Find the moment of inertia of the object when it rotates about the following axes of rotation:
    (a) An axis along rod AB.
    (b) An axis along rod CD.
    (c) An axis through point E, perpendicular to the cross.
    (d) An axis through point A, perpendicular to the cross.

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  3. Find the moment of inertia of an A × A × A cube with mass M, for the following axes of rotation:

    (a) An axis through the midpoints of two opposing sides.
    (b) An axis along one of the edges of the cube.

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