Rotational Dynamics
A system consists of a ball of mass and a uniform rod of mass and length . The rod is attached to a horizontal frictionless table by a pivot at point and initially rotates at an angular speed , pictured below on the left. The rotational inertia of the rod about point is . The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves in the direction shown on the right. Express all answers in terms of , , , , and fundamental constants.
D. A new ball with the same mass as the rod is now placed a distance from the pivot, as shown above. Again assuming the collision is elastic, for what value will the rod stop moving after hitting the ball?
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