Relate a rigid system’s rotational kinetic energy to rotational inertia and angular velocity, and compare rotational with translational energy.
(7 points, suggested time 13 minutes)
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 ⊗, as shown in Figure 1. The sphere is lightly tapped, and the rod-sphere system rotates clockwise with negligible friction about the axle due to the gravitational force.
A student takes a video of the rod rotating from the vertically upward position to the vertically downward position. Figure 2 shows five frames (still shots) that the student selected from the video.
Note: these frames are not equally spaced apart in time.
Figure 2
Use the frames of the video shown in Figure 2 to answer the following questions.
In which frame is the rotational kinetic energy of the rod-sphere system the greatest? Briefly justify your answer.
Figure 3