What is the final angular velocity when two rotating disks are pushed together?

[duplaimp]

Homework Statement

Two disks are rotating about an axis common to both. The first disk has moment of inertia I and angular velocity ω. The second disk has moment of inertia 2I and angular velocity $\frac{ω}{2}$
Both rotate in same direction
If both disks are pushed into each other what is the angular velocity of the larger disk when both are rotating together?

The Attempt at a Solution

I don't know how to solve this.
I was thinking in $I+2I = \frac{ω}{2} + ω$ but that doesn't make sense.
Any idea in how to start solving this?

 

[rude man]

Homework Statement

Two disks are rotating about an axis common to both. The first disk has moment of inertia I and angular velocity ω. The second disk has moment of inertia 2I and angular velocity $\frac{ω}{2}$
Both rotate in same direction
If both disks are pushed into each other what is the angular velocity of the larger disk when both are rotating together?

The Attempt at a Solution

I don't know how to solve this.
I was thinking in $I+2I = \frac{ω}{2} + ω$ but that doesn't make sense.
Any idea in how to start solving this?

Conservation of angular momentum.

 

[siddharth23]

[1/2 Iω^2]1 + [1/2 Iω^2]2 = 1/2 (I1 + I2)ωc^2
Where ωc is the common angular velocity

 

[rude man]

[1/2 Iω^2]1 + [1/2 Iω^2]2 = 1/2 (I1 + I2)ωc^2
Where ωc is the common angular velocity

EDIT:
this is not conservation of angular momentum. It's an energy equation which is invalid since heat is dissipated when the two disks conjoin.

 

[siddharth23]

EDIT:
this is not conservation of angular momentum. It's an energy equation which is invalid since heat is dissipated when the two disks conjoin.

Oh my bad. That's a very specific case. Sorry.

I1ω1 + I2ω2 = (I1 + I2)ωc

 

[rude man]

Oh my bad. That's a very specific case. Sorry.

I1ω1 + I2ω2 = (I1 + I2)ωc

That is correct.