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A circular table rotates in the x - y plane. The table is the gray, solid...

A circular table rotates in the x - y plane. The table is the gray, solid cylinder. It has mass m and radius R. The axis of rotation is the z-axis. The direction of rotation is given by the arrow-heads. A hollow ring of mass to be specified and radius R/2 is held at rest, slightly above the table and dropped onto the rotating table. The center of the ring is exactly in-line with the table’s axis of rotation. There is double-sided, adhesive tape on the bottom of the ring so it immediately sticks to and rotates with the table.   Before the ring drops onto the table, the table rotates at a constant angular speed of ω0. Ignore friction. Determine the angular speed of the combined object just after the two join. Express your answer as a number multiplying the initial angular speed of the table. Enter the number in the format #.## where # is any digit from 0 to 9.

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Answer #1

In this system of solid cylinder and ring angular momentum is always conserved

so,

where I is the moment of inertia of solid cylinder about com which is

so

Now after the ring sticks to the table Final

Monent of inertia of ring of mass m and R/2

so equating both we get

so,

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We were unable to transcribe this image

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