An object with a mass of # 8 kg# is traveling in a circular path of a radius of #12 m#. If the object's angular velocity changes from # 2 Hz# to # 12 Hz# in # 6 s#, what torque was applied to the object?

1 Answer
Apr 19, 2017

Answer:

The torque was #=12063.7Nm#

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#

For the object, #I=mr^2#

So, #I=8*(12)^2=1152kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(12-2)/6*2pi#

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

So the torque is #tau=1152*(10/3pi) Nm=12063.7Nm#