A flywheel in an energy-recovery system is designed to store 2.4×105J of mechanical energy when operating at its maximum safe angular speed. The flywheel can be modeled as a solid uniform disk of mass 65kg and radius 0.35m.
(a) Determine the rotational inertia of the flywheel about its central axis.
(b) Calculate the maximum safe angular speed of the flywheel in rad\,s−1.
(c) Express the angular speed found in part (b) in revolutions per minute (rpm). Show your unit conversion steps.
(d) In a short paragraph, interpret your numerical result by commenting on whether an inexpensive bicycle bearing (typically rated for 2000 rpm) could safely support the flywheel at its maximum speed.