You are investigating using a flywheel (a heavy disk) to store energy to create

Question

You are investigating using a flywheel (a heavy disk) to store energy to create more energy efficient city buses (see video below).https://youtu.be/BOnjtEKArXk(Flywheel Bicycle Demo.mov. The idea is to store energy in the rotation of a flywheel when the bus slows down so that it can be used later to accelerate the bus. When the bus is going at its normal speed of 30 miles per hour, the flywheel rotates at 2 revolutions per second. However, when the bus slows to a complete stop, the flywheel will rotate at 20 revolutions per second. The materials used to build the flywheel have been tested to withstand an acceleration of up to 100g but you are worried that it might not be strong enough at the rim of the flywheel. To check, you consider the case in which the bus makes an emergency stop in 0.50 seconds (and the flywheel spins up to 20 revolutions per second in that time) and calculate the maximum radius that the flywheel can have while the acceleration of the rim stays within the 100 g limit. You assume that the flywheel has a constant angular acceleration.

Explanation / Answer

given
wi = 20 rev/s

= 20*2*pi rad/s

= 125.7 rad/s

wf = 0

t = 0.5 s

magnitude of angular acceleration, alfa = |(wf - wi)|/t

= 125.7/0.5

= 251.4 rad/s^2

now use, a_tan = r*alfa

a_tanmax = r_max*alfa

==> r_max = a_tanmax/alfa

= 100*g/alfa

= 100*9.8/251.4

= 3.90 m <<<<<<<------------------Answer

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