An object with a mass of # 3 kg# is traveling in a circular path of a radius of #3 m#. If the object's angular velocity changes from # 2 Hz# to # 7 Hz# in # 8 s#, what torque was applied to the object?

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Answer 1 · 2016-12-25T07:42:38

The torque is #=53.01Nm#

The torque is the rate of change of angular momentum

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

The moment of inertia is #I=1/2mr^2#

#=1/2*3*3^2= 27/2 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(7-2)/8*2pi#

#=5/4pi rads^(-2)#

So the torque is #tau=27/2*5/4pi Nm=135/8piNm=53.01Nm#