A pair of long rods, each of length L and mass M are connected to a hoop of mass M and radius L/2 to form a 4-spoked wheel.
(a) Determine the moment of inertia of the wheel about an axis through the center of the wheel and perpendicular to its face in terms of the given quantiites.
(b) The wheel is now mounted to a frictionless axle and suspended vertically (like a pulley). Several turns of light cord are wrapped around the wheel, and a mass M is attached to the end of the cord and allowed to hang. The mass is released from rest. Determine the tension in the cord supporting the mass as it accelerates downwards in terms of the moment of inertia and the given quantities.
(c) Determine the angular acceleration of the wheel as the mass descends, assuming the cord does not slip.
(d) Determine the instantaneous velocity of the mass after the wheel has turned one revolution.
(e) Determine the instantaneous angular momentum of the mass-wheel system after the wheel has turned one revolution.