A passenger bus in Zurich, Switzerland derived its motive power from the energy stored in a large flywheel. The wheel was brought up to speed periodically, when the bus stopped at a station, by an electric motor, which could then be attached to the electric power lines. The flywheel was a solid cylinder with a mass of 1090kg and a diameter of 1.90m ; its top angular speed was 2950rev/min .

Part A

At this angular speed, what is the kinetic energy of the flywheel?

Part B

If the average power required to operate the bus is 1.85

Explanation:

moment of inertia of flywheel

= 1/2 m R²

= .5 x 1090 x .95²

I = 491.8625 kgm²

angular speed ω = 2πn where n = revolution per second

= 2π x 2950 / 60

= 308.77 rad /s

Rotational kinetic energy

= 1/2 Iω²

= .5 x 491.8625 x 308.77²

= 23.446 x 10⁶ J

B )

power being used by bus = 1.85 x 10⁴ W .

energy provided by flywheel = 23.446 x 10⁶ J

energy used per second =  1.85 x 10⁴ J

Time duration of travel between two station

= 23.446 x 10⁶ / 1.85 x 10⁴

= 1267 s

21.11 minutes.

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