What is the angular velocity of the two disks combined?

[mastamind518]

Homework Statement

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?
rad/s

m1 = 1.6 Kg
r1 = 0.63 m
w1 = 55 rad/s
m2 = 0.45 Kg
r2 = 0.38 m

Homework Equations

conservation of angular momentum

L=mvr

v=rw

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?)

I solved for v, and then divided by r1, since that's the radius of the whole system, and got an answer of 47.02rad/s. The answer key says the answer is 50 rad/s...

which concept did i get wrong?

 

[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

 

[mastamind518]

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

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...

 

[LowlyPion]

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...

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