# Homework Help: What is the angular velocity of the two disks combined?

1. Jun 7, 2009

### mastamind518

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

A 1.6 kg disk with radius 0.63 m is rotating freely at 55 rad/s around an axis perpendicular to its center. A second disk that is not rotating is dropped onto the first disk so that their centers align, and they stick together. The mass of the second disk is 0.45 kg and its radius is 0.38 m. What is the angular velocity of the two disks combined?

m1 = 1.6 Kg
r1 = 0.63 m
m2 = 0.45 Kg
r2 = 0.38 m

2. Relevant equations

conservation of angular momentum

L=mvr

v=rw

3. The attempt at a solution

i set up the equation as.... (m1)(v1)(r1)=(m1r1 + m2r2)(v)

where v1 = r1w1 and v is equal to the linear velocity(which should be same for both?)

which concept did i get wrong?

2. Jun 7, 2009

### LowlyPion

Welcome to PF.

For rotational momentum don't you want to consider the Moment of Inertia of the disks and not just the mass?

For a solid disk I = 1/2*m*r2

3. Jun 7, 2009

### mastamind518

Thanks a lot for that tip...

So by using moment, i would have...

(Iinitial)(winitial) = (Ifinal)(wfinal)

(1/2)(m1)(r1)^2(w1) = (1/2)(m1(r1)^2+m2(r2)^2)(w2) where w2 is the final angular velocity

I get 49.89rad/s for w2....just wanted to confirm i was doing it right...

Last edited: Jun 7, 2009
4. Jun 7, 2009

### LowlyPion

Without calculating it out, that looks like the right approach.