An object with a mass of # 2 kg# is traveling in a circular path of a radius of #4 m#. If the object's angular velocity changes from # 1 Hz# to # 5 Hz# in # 3 s#, what torque was applied to the object?

1 Answer
Apr 7, 2017

Answer:

The torque is #=268.1Nm#

Explanation:

The torque is the rate of change of angular momentum

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

Where #I# is the moment of inertia

For the object, #I=mr^2#

So, #I=2*(4)^2=32kgm^2#

The rate of change of angular velocity is

#(Deltaomega)/(Deltat)=((5-1)*2pi)/(3)=8/3pirads^-2#

So,

The torque is

#tau=32*8/3pi=268.1Nm#