# Homework Help: Finding a common angular velocity

1. Nov 15, 2008

### lmc489

1. The problem statement, all variables and given/known data
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:

2. Relevant equations
Conservation of Angular Momentum:
I1w1 = I2w2

3. 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?

2. Nov 15, 2008

### alphysicist

Hi lmc489,

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.

3. Nov 15, 2008

### lmc489

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

4. Nov 15, 2008

### alphysicist

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