A solid disk of mass m1 = 9 kg and radius R = 0.21 m is rotating with a constant

Question

A solid disk of mass m1 = 9 kg and radius R = 0.21 m is rotating with a constant angular velocity of ? = 31 rad/s. A thin rectangular rod with mass m2 = 3.4 kg and length L = 2R = 0.42 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk.
1)What is the initial rotational energy of the rod and disk system?
2)What is the final angular velocity of the disk?
3)What is the final angular momentum of the rod and disk system?
4)What is the final rotational energy of the rod and disk system?

Explanation / Answer

initial rotional energy = .5*9*.21^2/2 *31^2 = 95.4J  <------answer(1)

 

conserving angular momentum,
9*.21^2/2 *31 = (9*.21^2/2 + 3.4*.42^2/12)*

so, = 24.8 rad/s    <-----answer(2)

 

final angular momentum = initial = 9*.21^2/2 *31 = 6.15 kg.m2.rad/s    <----answer(3)

 

final rotational energy = .5*(9*.21^2/2 + 3.4*.42^2/12)*24.8^2 = 76.4 J

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