The rate of rotation of a solid disk with a radius of #4 m# and mass of #5 kg# constantly changes from #12 Hz# to #5 Hz#. If the change in rotational frequency occurs over #7 s#, what torque was applied to the disk?

1 Answer
Oct 11, 2017

Answer:

The torque was #=251.3Nm#

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 of the disc is #m=5kg#

The radius is #r=4m#

For the solid disc, #I=1/2mr^2#

So, #I=1/2*5*(4)^2=40kgm^2#

And the rate of change of angular velocity is

#(d omega)/dt=(Deltaomega)/t=(24pi-10pi)/7=2pirads^-2#

So,

The torque is

#tau=40*2pi=251.3Nm#