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 # 8 Hz# in # 8 s#, what torque was applied to the object?

1 Answer
Jun 7, 2017

Answer:

The torque was #=230.9Nm#

Explanation:

The torque is the rate of change of angular momentum

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

Where the moment of inertia is #=I#

and #omega# is the angular velocity

The mass is #m=3kg#

The radius is #r=7m#

For the object, #I=(mr^2)#

So, #I=3*(7)^2=147kgm^2#

The rate of change of angular velocity is

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

#=(1/2pi) rads^(-2)#

So the torque is #tau=147*(1/2pi) Nm=147/2piNm=230.9Nm#