A centripetal force is the force that keeps the object going in a circle, at a constant speed v (assuming a uniform motion - its not speeding up. It is accelerating due to a change in direction, but its speed is constant).
A centripetal force is made up of other forces. It might be gravity, normal forces or how have you, in this case it is tension.
Centripetal force = Tension force
mvv/r = T
But I'm assuming the circular path is parallel to the Earth. The diagram suggests otherwise, but it doesn't give an angle specifying the angle of the circular path to the Earth, from which to find the component of gravity contributing to the centripetal force.
For f, you know that w_0 = 0, w_f = r/v
You found v in part a. Find alpha (angular accel) using a = (change in v) / t
Torque = I*alpha
It says all the mass of the system is in the 'hammer'. This means I = mrr.
That assignment is just as hard as the Physics 1 assignment, and it looks like you don't get 3 goes :S If this is sort of the equivalent to our angular kinematics question, I'd rank this higher actually.
Sorry my explanation is a bit hurried and I don't know latex
