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 # 2 Hz# in # 3 s#, what torque was applied to the object?

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Answer 1 · 2016-12-25T06:22:57

The torque is #=513.1 Nm#

The torque is the rate of change of angular momentum

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

The is #I=1/2mr^2#

#=1/2*2*7^2= 49 kgm^2#

The rate of change of angular velocity is

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

#=10/3pi rads^(-2)#

So the torque is #tau=49*10/3pi Nm=490/3piNm=513.1Nm#