PhysicsLAB AP Free Response Question
2005 C3

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A system consists of a ball of mass M2 and a uniform rod of mass M1 and length d. The rod is attached to a horizontal frictionless table by a pivot at point P and initially rotates at an angular speed , as shown above left. The rotational inertia of the rod about point P 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 above right.
Express all answers in terms of M1 , M2 , , d, and fundamental constants.
 (a) Derive an expression for the angular momentum of the rod about point P before the collision.

 (b) Derive an expression for the speed v of the ball after the collision.

 (c) Assuming that this collision is elastic, calculate the numerical value of the ratio .

A new ball with the same mass M1 as the rod is now placed a distance x from the pivot, as shown below.
 (d) Again assuming the collision is elastic, for what value of x will the rod stop moving after hitting the ball?

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