An object with a mass of # 7 kg# is traveling in a circular path of a radius of #9 m#. If the object's angular velocity changes from # 2 Hz# to # 23 Hz# in # 8 s#, what torque was applied to the object?

1 Answer
Jul 7, 2017

Answer:

The torque was #=9352Nm#

Explanation:

The torque is the rate of change of angular momentum

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

where #I# is the moment of inertia

For the object, #I=mr^2#

So, #I=7*(9)^2=567kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(23-2)/8*2pi#

#=(21/4pi) rads^(-2)#

So the torque is #tau=567*(21/4pi) Nm=9352Nm#