Name: Partner: Section PHY 124 Workshop Week FEB 6 2017 Chap 11, 13 & Review Par

Question

Name: Partner: Section PHY 124 Workshop Week FEB 6 2017 Chap 11, 13 & Review Part III. Conservation of angular momentum Two discs with moments of inertia l rotate freely about the same vertical axis without friction. Initially one disc has angular speed cu1 and the other w2. The discs come into contact and due to friction rotate together at the same angular velocity wr 1. What is the initial angular momentum? 2. What is the final angular momentum? 3. What is the final angular speed in terms of co1 and w2? 4. What is the initial kinetic energy of the system of both discs? 5. Write an expression for the ratio of the final kinetic energy to the initial kinetic energy. Your answer should be in terms of w w2, and I

Explanation / Answer

1)
angular momentum is product of moment of inertia and angular speed

initial angular momentum = I*w1 + I*w2 = I*(w1+w2)

2)
final angular momentum = I*wf + I*wf = 2*I*wf

3)
use conservation of angular momentum,
initial angular momentum = final angular momentum
I*(w1+w2) = 2*I*wf
wf = (w1+w2)/2

4)
initial kinetic energy = 0.5*I*w1^2 + 0.5*I*w2^2
= 0.5*I*(w1^2 + w2^2)

5)
final kinetic energy = 0.5*I*wf^2+ 0.5*I*wf^2
= I*wf^2

we have, wf = (w1+w2)/2

put this value in above expression,
final kinetic energy = I*wf^2
= I* (w1+w2)^2/2^2
= 0.25*I*(w1+w2)^2

KE final / KE initial = {0.25*I*(w1+w2)^2}/0.5*I*(w1^2 + w2^2)
= 0.5*(w1+w2)^2 / (w1^2 + w2^2)

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