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 # 14 Hz# to # 17 Hz# in #5 s#, what torque was applied to the object?

1 Answer
Oct 8, 2017

Answer:

The torque was #=554.2Nm#

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 of the object is #m=3kg#

The radius is #r=7m#

For the object, #I=mr^2#

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

And the rate of change of angular velocity is

#(d omega)/dt=(Deltaomega)/t=(34pi-28pi)/5=6/5pirads^-2#

So,

The torque is

#tau=147*6/5pi=554.2Nm#