Merry-go-round + sphere tied to rod

[Sw0rDz]

Homework Statement

A small 0.160 kg sphere is suspended by a light string from a vertical post mounted at the edge of a merry-go-round of radius R = 0.440 m.
The equilibrium position of the sphere is shown in the figure, with a = 0.430 m and b = 0.760 m. The axis of rotation is indicated by the dashed line. Calculate the angular velocity of the merry-go-round.

Image
http://img694.imageshack.us/img694/2586/physicshelp.jpg

The Attempt at a Solution

This is where I'm getting stuck. I can't figure out where to start. I have an idea that this problem deals with Newton's 2nd law, but I don't know how to apply it this situation.

Would using the torque equation help?: \tau = F * r * sin\theta

 

[Doc Al]

Follow standard procedure: Draw a free body diagram of the sphere, showing all the forces acting on it. (Hint: There are only two forces.) Key: What's the acceleration of the sphere? Then apply Newton's 2nd law.

(No need for torques.)