Answer:
1.
2.
3.
4.
5.
6.
Explanation:
Given:
mass of the person,
radius of the disk,
mass of the disk,
initial angular speed of the disk,
distance of the person from the center of the disk,
1.
<u>Initial moment of inertia of the system when the man stands at the rim of disk:</u>
<em>Moment of inertia of the disc:</em>
<em>Now for the person, we treat the mass to be a point revolving around R:</em>
∴We have the moment of inertia of the system in this case as:
2.
<u>Moment of inertia when the person stands at 0.53 m from the center of the disk:</u>
<em>Moment of inertia of the disk will be constant:</em>
<em>For the person, we treat the mass to be a point revolving around radius 0.53 m:</em>
∴We have the moment of inertia of the system
3.
<u>The final angular velocity of the disk:</u>
<em>Using the conservation of angular momentum:</em>
4.
<u>Change in Kinetic Energy:</u>
∵
∴
5.
<u>Centripetal acceleration of the person when she is at R/3:</u>
Centripetal acceleration is given as:
we have ω=3.3158 radian per second at R=0.53 m
6.
<u>If the person now walks back to the rim of the disk:</u>
Then by the law of conservation of angular momentum the initial angular speed of will be restored.