AP Free - Response Question HELP iNCLUDES angular velocity and acceleration

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AP Free - Response Question HELP! iNCLUDES angular velocity and acceleration

http://www.fayar.net/east/Teacher.web/Math/young/APPC/APPC%201999/physics_c_m_99.pdf

Mechanics 3 is the problem I really need help on.
I tried to find the tension of the string by setting it equal to mg + Iwr, but I'm not sure if I'm doing it right! On part b, I set the angular acceleration equal to the initial angular velocity + moment of inertia, and I got through canceling some factors. On part c, I set the angular velocity equal to the linear velocity times the time.

I NEED HELP ON HOW TO DO IT RIGHT! I THINK I'M TOTALLY DOING IT WRONG BECAUSE MY ANSWERS SEEM TO BE WAY OFF!
 
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Its a string, so it can only support load in the axial direction.
 
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