Paper 4, Section II, A

Obtain the moment of inertia of a uniform disc of radius $a$ and mass $M$ about its axis of rotational symmetry. A uniform rigid body of mass $3 M / 4$ takes the form of a disc of radius $a$ with a concentric circular hole of radius $a / 2$ cut out. Calculate the body's moment of inertia about its axis of rotational symmetry.

The body rolls without slipping, with its axis of symmetry horizontal, down a plane inclined at angle $\alpha$ to the horizontal. Determine its acceleration and the frictional and normal-reaction forces resulting from contact with the plane.

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