A solid disk rotates in the horizontal plane at an angular velocityof 0.042 rad/s with respect to an axisperpendicular to the disk at its center. The moment of inertia ofthe disk is 0.12 kg ·m2. From above, sand is dropped straight down onto thisrotating disk, so that a thin uniform ring of sand is formed at adistance of 0.40 m from the axis. The sand in the ring has a massof 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?