Rotational Dynamics and tangential velocity

[flash]

Homework Statement

Find the rotational acceleration, final tangential velocity and centripetal acceleration of a 50.0 g rubber bung, starting from rest, swung in a horizontal circular path on a very light string of length 90.0 cm. The tension in the string is provided by a mass of 250.0 g. Find the angular momentum of the rubber bung.

I have attached the diagram we were given. This is all the information available.

Homework Equations

The Attempt at a Solution

More looking at a clarification of the question at this stage - as far as I can tell the rubber bung would not accelerate in a circle at all.

 

[HallsofIvy]

What is the centripetal force?

You are, of course, correct that if the object started from rest and the only force on it was the centripetal force, it would not move in a circle, it would move directly toward the center of the circle. However, I note that you quote the problem as saying "swung in a horizontal circular path on a very light string of length 90.0 cm", so it clearly is moving in a circle. At what distance and angular velocity will the force necessary to cause it to move in a circle be the same as the centripetal force?

 

[flash]

The centripetal force is 0.25g which must equal mrw^2 right? So if I let m=0.05, r=0.9 and Fc=0.25*9.8 I can solve for omega (23.3). As the string gets shorter (r decreases), the angular velocity necessary for circular motion increases because Fc is constant.
I'm still confused about the angular acceleration. Why would the bung accelerate?