An object with a mass of # 3 kg# is traveling in a circular path of a radius of #15 m#. If the object's angular velocity changes from # 25 Hz# to # 34 Hz# in #9 s#, what torque was applied to the object?

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Answer 1 · 2017-01-10T07:09:44

The torque is #=4241.2Nm#

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 mass is #I=mr^2#

#=3*15^2= 675 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(34-25)/9*2pi#

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

So the torque is #tau=675*(2pi) Nm=1350piNm=4241.2Nm#