Finding Angular Acceleration of a spool.

[Mr. Sinister]

Homework Statement

A solid cylinder of 24 cm radius is postioned on a frictionless plane inclined at 30 degrees above horizontal. A force F is exerted by a string wrapped around the spool. When F has a certain critical value the center of mass of the spool does not move. When this is the case, what is the angular acceleration of the spool?

Homework Equations

Torque equals radius times Force times sin theta. Also angular acceleration times I.

The Attempt at a Solution

I don't have the force but I do have a radius and the angle.

 

[Mr. Sinister]

Does this have something to do with the center of mass?

 

[Mr. Sinister]

I mean like a number for the center of mass or something?