See attached file.
PART a. A small mass m is attached to one end of a rod of negligible mass. The other end of the rod is fixed so that the mass can move in a circle of radius R. A force F is applied tangent to the circle, giving the mass angular acceleration 'alpha'.
SEE ATTACHMENT #1 for a diagram showing parameters.
Apply 'net torque= I alpha' to express the torque in terms of the moment of inertia and the angular velocity.
PART b. Example: A uniform thin ring, mass M, radius R, is rotating about an axis at its center with initial angular velocity. At some instant it breaks and rearranges into a straight bar rotating about its center with final angular velocity. Apply conservation of angular momentum to find the ratio of final angular velocity to initial angular velocity.
With diagrams and calculations, the solution presents complete answers to the problems.