Dynamics | Part IA, 2002

Calculate the moment of inertia of a uniform rod of length 2l2 l and mass MM about an axis through its centre and perpendicular to its length. Assuming it moves in a plane, give an expression for the kinetic energy of the rod in terms of the speed of the centre and the angle that it makes with a fixed direction.

Two such rods are freely hinged together at one end and the other two ends slide on a perfectly smooth horizontal floor. The rods are initially at rest and lie in a vertical plane, each making an angle α\alpha to the horizontal. The rods subsequently move under gravity. Calculate the speed with which the hinge strikes the ground.

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