Finding Angular Acceleration of a spool.

AI Thread Summary
To find the angular acceleration of a spool on a frictionless incline, the critical force exerted by the string must be analyzed in relation to the spool's radius and the angle of inclination. The torque equation, which relates torque to radius, force, and the sine of the angle, is essential for this calculation. The center of mass plays a crucial role in determining the spool's motion, particularly when the force is at a critical value where the center of mass remains stationary. Without the specific value of the force, the angular acceleration cannot be calculated directly. Understanding these relationships is key to solving the problem effectively.
Mr. Sinister
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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.
 
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Does this have something to do with the center of mass?
 
I mean like a number for the center of mass or something?
 
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