The rate of rotation of a solid disk with a radius of #5 m# and mass of #5 kg# constantly changes from #11 Hz# to #24 Hz#. If the change in rotational frequency occurs over #1 s#, what torque was applied to the disk?

1 Answer
Jan 29, 2017

Answer:

The torque was #=5105.1Nm#

Explanation:

The torque is the rate of change of angular momentum

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

The moment of inertia of the solid disc is #I=1/2*mr^2#

#=1/2*5*5^2= 125/2 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(24-11)/1*2pi#

#=(26pi) rads^(-2)#

So the torque is #tau=125/2*(26pi) Nm=125*13piNm=5105.1Nm#