Another question for all you physics guru's?

Question

A disc rotates about an axis which is perpendicular to it and passes through its centre with initial angular velocity w1. A second disc, identical to the first and at rest, is dropped on top of the first one and sticks to it. The discs then rotate together with angular velocity wf. What is the relation between w1 and wf?

Answers

a) wf^2 = 0.5 w1^2

b) wf = 0.5 w1

c) wf = 0.7 w1

d) wf^2 = 1.4 w1^2

e) wf = 1.4 w1

f) wf = 2.0 w1

Answer 1

Use conservation of angular momentum.  The angular momentum of the rotating disc is I1*w1 where I1 is the moment of inertia of the first disc The angular momentum of the dropped disc is 0.  After they rotate together, the system's angular momentum is (I1 + I2)*wf.  Since the discs are identical, I1 = I2 and I1 + I2 =  2*I1.

I1*w1 = 2*I1*wf

wf = 0.5*w1

Answer 2

b)wf = 0.5 w1

This is by law of conservation of momentum. Consider the two disks together as system. There is no external torque on the system. Therefore, angular momentum should be conserved.

Angular momentum = moment of inertia * angular velocity

Earlier only one disk was rotating. When both disks stick, then moment of inertia doubles. Therefore, angular velocity should become half so that angular momentum remains the same.