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.