A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm)by an electric motor.The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (I_cylinder = MR²/2).If the bus requires an average power of 10.0 kW,how long will the flywheel rotate? A)154 s B)308 s C)463 s D)617 s

Question

Quizplus · Accepted Answer

The kinetic energy stored in the flywheel can be given by:
KE = (1/2) I w^2
where I is the moment of inertia of the cylinder and w is the angular speed.
I = (1/2) MR^2  (moment of inertia of a solid cylinder about its axis of rotation)
KE = (1/4) MR^2 w^2

The average power required by the bus is given to be 10.0 kW. This power is supplied by the kinetic energy stored in the flywheel over a period of time t. We can write:
P = KE/t
t = KE/P

Substituting the values, we get:
t = (1/2) MR^2 w^2 / P
   = (1/2) * 500 kg * (0.5 m)^2 * (3000 rpm * 2*pi/60)^2 / 10 kW
   = 308.3 s
Rounding off to the nearest integer, we get:
t = 308 s

Therefore, the best choice is B) 308 s, as it is the closest to the calculated value.

A Bus Is Designed to Draw Its Power from a Rotating