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angular velocity of the disk after a ring of sand dropped

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A solid disk rotates in the horizontal plane at an angular velocity of 0.067 rad/s with respect to the axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.10 kg*m^2. 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 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

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The solution shows how to calculate the angular velocity of the disk after a ring of sand dropped onto it.

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