PhysicsLAB: 2005 C3

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?