An object with a mass of # 6 kg# is traveling in a circular path of a radius of # 1m#. If the object's angular velocity changes from # 6 Hz# to # 14 Hz# in #3 s#, what torque was applied to the object?

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Answer 1 · 2017-01-12T08:37:47

The torque is #=100.5Nm#

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#

#=6*1^2= 6 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(14-6)/3*2pi#

#=((16pi)/3) rads^(-2)#

So the torque is #tau=6*(16pi)/3 Nm=96/3piNm=100.5Nm#