An object with a mass of # 2 kg# is traveling in a circular path of a radius of #4 m#. If the object's angular velocity changes from # 3 Hz# to # 5 Hz# in # 1 s#, what torque was applied to the object?

1 Answer
Jun 26, 2017

Answer:

The torque was #=402.1Nm#

Explanation:

The torque is the rate of change of angular momentum

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

where #I# is the moment of inertia

For a the object, #I=mr^2#

So, #I=2*(4)^2=32kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(5-3)/1*2pi#

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

So the torque is #tau=32*(4pi) Nm=128piNm=402.1Nm#