Question

A solid disk rotates in the horizontal plane at an angular velocity of 0.040 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.13 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance 0.41 m from the axis. The sand in the ring has a mass of 0.33 kg. After all the sand is in place, what is the angular velocity of the disk?