An object with a mass of # 2 kg# is traveling in a circular path of a radius of #7 m#. If the object's angular velocity changes from # 7 Hz# to # 9 Hz# in # 5 s#, what torque was applied to the object?

1 Answer
Jun 2, 2017

Answer:

The torque was #=246.3Nm#

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

The mass is #m=2kg#

The radius is #r=7m#

For the object, #I=mr^2#

#I=2*7^2=98kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(9-7)/5*2pi#

#=(4/5pi) rads^(-2)#

So the torque is #tau=98*(4/5pi) Nm=246.3Nm#