A solid disk of mass M and radius R is pivoted so that it can rotate about its center. The disk is initially at rest. A ball of mass m and speed v travels along a path tangential to the rim of the disk. The ball sticks to the disk and the assembly starts to rotate. (Consider the ball a point particle.)
i) What is the initial angular momentum of the ball about the pivot through the center of the disk just before it hits the disk? (Magnitude and direction).
ii) What is the moment of inertia of the disk about the pivot through its center?
iii) What is the final moment of inertia of the system about the center of the disk?
iv) What is the final angular velocity of the system?