An object with a mass of # 3 kg# is traveling in a circular path of a radius of #5 m#. If the object's angular velocity changes from # 1 Hz# to # 8 Hz# in # 5 s#, what torque was applied to the object?

1 Answer
Feb 6, 2017

Answer:

The torque was #=329.9Nm#

Explanation:

The torque is the rate of change of angular momentum

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

The moment of inertia of the object is #I=mr^2#

#=3*5^2= 75 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(8-1)/5*2pi#

#=((7pi)/5) rads^(-2)#

So the torque is #tau=75*(7pi)/5 Nm=105piNm=329.9Nm#