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 # 4 Hz# to # 6 Hz# in # 6 s#, what torque was applied to the object?

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Answer 1 · 2017-02-28T16:28:33

The torque was #=2412.7Nm#

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=(6-4)/6*2pi#

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

So the torque is #tau=1152*(2/3pi) Nm=2412.7Nm#