17.2  (Rigid Body Work Energy Equation)

The rotor of an electric motor has an angular velocity of 3600 rpm (revolutions per minute) when the load and power are cut off.  The 50 kg rotor, which has a centroidal radius of gyration of 180 mm, then coasts to rest.  Knowing that the kinetic friction of the bearings onto the rotor produces a couple of magnitude 3.5 N-m, determine the number of revolutions that the rotor turns before coming to rest.

Comments/Hints:
1.  Calculate I_G = 1.62 kg-m².
2.  Use the work-energy equation:  T₁ + SU_1-2 = T₂
3.  Kinetic energy stored in a body in rotation is T = 1/2·I_G·w².
4.  The work of the couple is U_couple = Mq, with q in radians.
5.  You should get  q = 32.89E03 radians = 5235 revolutions.