A horizontal solid disk of mass M and radius R rotates at an angular velocity of w with respect to an axis perpendicular to the disk at its center. Assume that the axis is perfectly frictionless, so that the disk rotates freely.

a. The moment of inertia for a solid disk is .5MR^2. What is the angular momentum of the disk?

From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of R/2 from the axis. The total mass of the sand deposited is M/2.

b. After all the sand is in place, wha is the final angular velocity of the disk? Express your answer in terms of the initial angular velocity w.

c. Calculate the initial and final values of the kinetic energy in the system. Is kinetic energy conserved in this situation? Explain why or why not.

Please help me get started on each step of this problem. I'm not even sure where to begin. Thank you!