Finding a common angular velocity

[lmc489]

Homework Statement

A disk is rotating freely at 1,000 revolutions per minute about a vertical axis through its center. A hoop with twice the mass of the disk and the same radius as the uniform disk is poised exactly above and is initially at rest. The hop is dropped gently upon the disk so that their rims coincide. The common angular velocity of the disk-hoop combination is:

Homework Equations

Conservation of Angular Momentum:
I1w1 = I2w2

The Attempt at a Solution

I1w1 = I2w2
1/2MR^2 x 1000 rpm = 2MR^2 w2

w2 = 1/2MR^2 x 1000 rpm/ 2MR^2
w2 = 250 rev/min

is this correct?

 

[alphysicist]

Hi lmc489,

Homework Statement

A disk is rotating freely at 1,000 revolutions per minute about a vertical axis through its center. A hoop with twice the mass of the disk and the same radius as the uniform disk is poised exactly above and is initially at rest. The hop is dropped gently upon the disk so that their rims coincide. The common angular velocity of the disk-hoop combination is:

Homework Equations

Conservation of Angular Momentum:
I1w1 = I2w2

The Attempt at a Solution

I1w1 = I2w2
1/2MR^2 x 1000 rpm = 2MR^2 w2

I don't believe this is correct. On the right hand side you only have the angular momentum of the hoop. You need the total angular momentum of the entire hoop-disk system.

 

[lmc489]

oh YES! i forgot. so instead the answer would be 200 right?

 

[alphysicist]

oh YES! i forgot. so instead the answer would be 200 right?

That looks right to me (if you want the answer in rpm).