A rod with a sphere attached to the end is connected to a horizontal mounted axle and carefully balanced so that it rests in a position vertically upward from the axle. The center of mass of the rod sphere system is indicated with a circle and an "X" through the center of the circle, as shown in Figure The sphere is lightly tapped, and the rod sphere systm rotates clockwise with negligible friction about the axle due to the gravitational force. sphere, 5 ~ Center of Mass *. Hod T Axde Figure | A student takes a video of the rod rotating from the vertically upward position to the vertically downward postion. Figure 2 shows five frames (still shots that the student selected from the video). MNote: these frames are not equally spaced apart in time. Frame A rame B Frame C Frame D Frame E Figure 2 The rod-sphere has mass M and length L, and the center of mass is located a distance 34 L from the axle, shown in Figure 3. Figure 3 i Derive an expression for the change in kinetic energy of the rod-sphere-Earth system from the moment shown in Frame A to the moment shown in Frame E. Express your answer in terms of M, L, and fundamental constants as appropriate. ii. Briefly explain why the rod and sphere gain kinetic energy, even if the Earth is not included in the system.|