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

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Answer 1 · 2017-04-29T07:24:03

The torque is #=205.3Nm#

The torque is the rate of change of angular momentum

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

The moment of inertiai is #=I#

For the object, #I=(mr^2)#

So, #I=2*(7)^2=98kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(8-7)/3*2pi#

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

So the torque is #tau=98*(2/3pi) Nm=205.3Nm#