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 # 7 Hz# in #3 s#, what torque was applied to the object?

1 Answer
Apr 25, 2017

Answer:

The torque was #=307.9Nm#

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=(3*(7)^2)=147kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(7-6)/3*2pi#

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

So the torque is #tau=147*(2/3pi) Nm=307.9Nm#