A solid disk rotates in the horizontal plane at an angular velocityof 0.067 rad/s with respect to an axis perpendicular to the disk atits center. The moment of inertia of the disk is 0.10 kgImage for A solid disk rotates in the horizontal plane at an angular velocityof 0.067 rad/s with respect to an axis perp m2. From above, sand is dropped straight down onto the rotating disk, so that athin uniform ring of sand is formed at a distance of 0.40 m fromthe 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 thedisk?

The angular velocity of the disk is .

Explanation:

Given:

The angular velocity of the solid disk,

Moment of inertia of the disk,

The radius of the sand ring,

Mass of the sand disk, .

From the conservation of angular momentum

Here, is the moment of inertia of the disk after the sand ring is formed and is the new angular velocity.

The new moment of inertia of the disk and sand ring is given by

Comparing equations (1) and (2), we have

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