Finding the rate of change of angular momentum

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Homework Statement



I've uploaded a pic of the problem and my work at the link below:

http://i.imgur.com/K4ukj.jpg"

Homework Equations



I = mR^2 w



Hopefully everything thus far is correct, I'm stuck at finding the rate of change. From what I understood it's essentially the derivative of Angular Momentum with respect to time. Thank you in advance.
 
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The rate of change of angular momentum is torque, or the moment of inertia multiplied by angular acceleration.
 
Thank you Pi-Bond. Does my approach for getting the angular momentum appear to be correct?