How do I calculate torque on a pulley with hanging weights?

[Hockeystar]

Homework Statement

Lets say I have a the generic pulley setup with no friction

http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0014/tablewpulleyFBD.gif

How would I calculate the Torque on the pulley?

Homework Equations

Torque = Force times Radius

The Attempt at a Solution

Would the torque simply be the torque caused by gravity of the free hanging weight or do I have to take the force of tension into account?

 

[zachzach]

Use the free body diagrams and Newton's 2nd law to find the acceleration of the system. Then you can find the torque.

 

[Hockeystar]

Thank You.