Two disks are located on an axle as shown in the figure below. The lower disk is

Question

Two disks are located on an axle as shown in the figure below. The lower disk is initially spinning at 49 rad/s, and the upper one is not spinning. The upper disk then falls onto the lower disk, and they stick together.

(a) Is there a torque on the lower disk?

Yes or No    

On the upper disk?

Yes or No    

(b) Identify a system for which the external torque is zero so that the angular momentum is conserved.

The external torque is zero for a system comprised of:

1) just the bottom disk

2) the top disk and the Earth

3) the bottom disk and the Earth

4) both disks

(c) What is the initial angular momentum of your system?
(kg · m2/s)

(d) What is the final angular momentum of your system? Express your answer in terms of f, the final angular velocity of the two disks. (Recall that f has units of rad/s and angular momentum will have units of kg · m2.) (f)

(e) Find f. (rad/s)

Explanation / Answer

a) There is NO torque on the lower disk and upper disk as gravity and normal forces are present and act at a distance zero, so produces no torque.

b) The external torque is zero for a system comprised of both disks

c) Initial angular momentum of your system, Li= wi*Ii= wi*1/2*m1*R1^2= 49*0.5*20*2^2= 1960 kg m2/s

d) final angular momentum of your system, Lf= wf*If=wf* (I1+I2)= wf* {(1/2*m1*R1^2) + (1/2* m2*R2^2)}

e) As angular momentum is conserved----> Li=Lf= wf* {(1/2*m1*R1^2) + (1/2* m2*R2^2)}

1960= wf* {(1/2*20*2^2) + (1/2* 7*1^2)}

1960= wf* 43.5

wf= 1960/43.5= 45.06 rad/s

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