An object with a mass of # 3 kg# is traveling in a circular path of a radius of #7 m#. If the object's angular velocity changes from # 6 Hz# to # 9 Hz# in # 8 s#, what torque was applied to the object?

1 Answer
Jun 4, 2018

Answer:

The torque is #=21.21Nm#

Explanation:

The torque is the rate of change of angular momentum

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

where #I# is the moment of inertia

For the object moving in a circular motion, #I=(mr^2)/2#

The mass is #m= 3kg#

The radius is #r=7m#

So, #I=3*(7)^2/2=73.5kgm^2#

The rate of change of angular velocity is

#alpha=(domega)/dt=(9-6)/8*2pi#

#=(3/4pi) rads^(-2)#

So the torque is #tau=9*(3/4pi) Nm=21.21Nm#