Answer:
1) their common angular speed = 3.038 rad/s
2) kinetic energy loss = 0.24J
Explanation:
1) This is a case of conservation of angular momentum.
The initial angular momentum must be equal to the final angular momentum
Initial angular momentum = I x w
Where I = moment of inertia, and
w = angular momentum.
Initial angular momentum = 0.0711 x 4.53 = 0.322 kg-m2-rad/s
After addition of ring, moment of inertia becomes,
0.0711 + 0.0353 = 0.106 kg-m2
Therefore, final angular momentum will be
0.106 x Wf
Where Wf = final common angular velocity
Equating the two angular momentum we have
0.322 = 0.106Wf
Wf = 0.322/0.106 = 3.038 rad/s
2) KE = 1/2 x I x w^2
Initial KE = 1/2 x 0.0711 x 4.53^2
= 0.729 J
Final KE = 1/2 x 0.106 x 3.038^2
= 0.489 J
Loss in KE = 0.729 - 0.489 = 0.24 J
