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 # 12 Hz# to # 7 Hz# in # 8 s#, what torque was applied to the object?

1 Answer
Dec 31, 2016

The torque is #=67.9 Nm#

Explanation:

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=mr^2#

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

The rate of change of angular velocity is

#(domega)/dt=(12-7)/8*2pi#

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

So the torque is #tau=27*(4pi)/5 Nm=108/5piNm=67.9Nm#