A uniform disk of mass M and radius R is rotating freely about a vertical axis with initial angular velocity w0. Then sand is poured onto the disk in a thin stream so that it piles up on the disk at the radius r (< r).="" the="" sand="" is="" added="" at="" the="" constant="" rate="" mu="" (mass="" per="" unit="">

(a) At what rate are the angular velocity and the rotational kinetic energy varying with time at a given instant?

(b) After what length of time is the rotational kinetic energy reduced to half of its initial value? What has happened to this energy