a) L=Iw
L=(1/3 md^2)w
b) L1=L2
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A system consist of a ball of M2 and a uniform rod of M1 and length d. The rod is attached to a horizontal frictionless rotates at an angular speed w, as shown in the figure. The rotational inertia of the rod about point P is ? M1 d^2. 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. Express all answers in terms of M1, M2, w, d, and fundamental constants.
A. Derive an expression from 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 M1/M2
D. A new ball with the same mass M1 as the rod is now placed a distance x from the pivot as shown. Again assuming the collision is elastic, for what value x will the rod stop moving after hitting the ball?
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