A thin, massless string is wrapped around a 0.25m radius grindstone supported by

Question

A thin, massless string is wrapped around a 0.25m radius grindstone supported by bearings that produce negligible frictional torque.  A steady tension of 20 N in the string causes the grindstone to move from rest to a speed of 60 rad/s in 12s.  what's the moment of inertia of the grindstone? Please, show me.

A thin, massless string is wrapped around a 0.25m radius grindstone supported by bearings that produce negligible frictional torque. A steady tension of 20 N in the string causes the grindstone to move from rest to a speed of 60 rad/s in 12s. what's the moment of inertia of the grindstone?

Explanation / Answer

angular acceleration = 60/12 rad/s.s = 5 rad/s.s

Torque = 20 X 0.25 Nm = 5 Nm  

Torque = Moment of inertia X Angular acceleration  

This gives Moment of Inertia = 5/5 = 1 kg.m.m  

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