Question: A solid disk rotates in the horizontal plane at an angular velocity of 0.0661 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.136 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 of 0.390 m from the axis. The sand in the ring has a mass of 0.489 kg.
Part A: After all the sand is in place, what is the angular velocity of the disk?
Please show all work and explain your steps and methods to find the angular velocity of the disk.