Pulley System: Solving for Acceleration (a3)

[asi123]

Homework Statement

Hey guys.
Look at this pulley system, I wrote down all the equations.
The pulley on the left is massless, the one on the right has the mass of m3 and radius R.
I also wrote the the torque equation of the pulley and the thing I don't understand is the what is the acceleration of the pulley (a3), is it equal to a2 or to a1?
Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Aren't m2 and m3 (the pulley) attached?

 

[asi123]

Aren't m2 and m3 (the pulley) attached?

Oh, you right...
Thanks.