An object with a mass of # 8 kg# is traveling in a circular path of a radius of #12 m#. If the object's angular velocity changes from # 15 Hz# to # 6 Hz# in # 5 s#, what torque was applied to the object?

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Answer 1 · 2017-03-10T06:53:43

The torque was #=13028.8Nm#

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#

#=8*12^2= 1152 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(15-6)/5*2pi#

#=(18/5pi) rads^(-2)#

So the torque is #tau=1152*(18/5pi) Nm=piNm=13028.8Nm#