An m=0.490 kg object moves on a frictionless horizontal table in a circular path

Question

An m=0.490 kg object moves on a frictionless horizontal table in a circular path of initial radius r0=2.80m.  The initial angular speed is w0=3.37 rad/s,  in regards to the larger circle. The object is attached to a string of negligible mass that passes through a small hole in the table at the centre of the circle.  Sometime under the table begins to pull the string downward to make the circle smaller.  If the string will tolerate a tension of no more than Tmax=160N in magnitude, what is the radius of the smallest possible circle, rf, on which the object can move, in regards to the smaller circle?

Explanation / Answer

Final centripetal acceleration = 160 /0.49 and
Initial centripetal acceleration = 2.8*3.37

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