How Does Radius Change Over Time Relate to Torque and Newton's Second Law?

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gogeta234
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i was wondering what a rate-change radius equation in terms of time (r(t)) relates to torque/Newtons second law\
 
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This question doesn't make much sense to me. Can you rephrase and expand?
 
Are you asking for an equation that calculates the angular velocity due to a certain torque (without friction) with respect to time using Newton's second?