An object with a mass of # 8 kg# is traveling in a circular path of a radius of #12 m#. If the object's angular velocity changes from # 5 Hz# to # 7 Hz# in # 6 s#, what torque was applied to the object?

1 Answer
Nov 11, 2017

Answer:

The torque is #=2412.7Nm#

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=8kg#

The radius of the path is #r=12m#

For the object, #I=mr^2#

So, #I=8*(12)^2=1152kgm^2#

And the rate of change of angular velocity is

#(d omega)/dt=(Deltaomega)/t=(2pif_1-2pif_2)/t#

#=(14pi-10pi)/6=(2/3pi)rads^-2#

So,

The torque is

#tau=1152*2/3pi=2412.7Nm#