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 # 9 Hz# to # 6 Hz# in # 6 s#, what torque was applied to the object?

1 Answer
Mar 14, 2018

Answer:

The torque is #=3619.1Nm#

Explanation:

The torque is the rate of change of angular momentum

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

where #I# is the moment of inertia

For the object, #I=mr^2#

The mass is #m=8 kg#

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

So the moment of inertia is

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

The angular acceleration is

#alpha=(2pif_1-2pif_0)/t=(18-12)pi/6=pirads^-2#

So,

The torque is

#tau=Ialpha=1152*pi=3619.1Nm#