An object with a mass of # 2 kg# is traveling in a circular path of a radius of #4 m#. If the object's angular velocity changes from # 1 Hz# to # 19 Hz# in # 3 s#, what torque was applied to the object?

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Answer 1 · 2017-01-15T09:12:40

The torque is #=1206.4Nm#

The torque is the rate of change of angular momentum

#tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt#

The moment of inertia of the object is #I=mr^2#

#=2*4^2= 32 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(19-1)/3*2pi#

#=(12pi) rads^(-2)#

So the torque is #tau=32*12pi Nm=384piNm=1206.4Nm#