a) Calculate its moment of inertia about the axis shown in the sketch below by direct integration. L/3 2L/3 Axis b) Check your answer with the parallel-axis theorem given that ICM = ML² /12. c) Assume that the rod has mass M = 2 kg, length L = 1 m and that it rotates around the axis in the above picture at 3 revolutions per second. What is its angular velocity, its angular momentum, and its rotational energy? d) Two small bodies of mass mį and m2 are attached to opposite ends of a thin rigid rod of length L and mass M. The rotational axis is oriented as before, see sketch below. What distance d from mị should the rotational axis be placed so that a minimum amount of work is required to set the rod rotating at a fixed angular velocity w? L-d- m1 m2

a) Calculate its moment of inertia about the axis shown in the sketch below by direct integration. L/3 2L/3 Axis b) Check your answer with the parallel-axis theorem given that ICM = ML² /12. c) Assume that the rod has mass M = 2 kg, length L = 1 m and that it rotates around the axis in the above picture at 3 revolutions per second. What is its angular velocity, its angular momentum, and its rotational energy? d) Two small bodies of mass mį and m2 are attached to opposite ends of a thin rigid rod of length L and mass M. The rotational axis is oriented as before, see sketch below. What distance d from mị should the rotational axis be placed so that a minimum amount of work is required to set the rod rotating at a fixed angular velocity w? L-d- m1 m2