You are working in a research group investigating more energy efficient city bus

Question

You are working in a research group investigating more energy efficient city busses. One option is to store energy in the rotation of a flywheel when the bus stops and then use it to accelerate the bus. The flywheel under consideration is a light-weight but extremely strong disk of carbon fibre composite, with a heavy iron rim of mass 51.6 kg. The proposed radius of the disk is 1.07 m.

Your boss is concerned that the ring may end up spinning so quickly that the bearings would overheat. To see if this is likely, you've been asked to work out how rapidly (in radians per second) the wheel would be spinning if it started from rest, and absorbed all the energy of motion of a bus of mass 26139.22 kg when it decelerates from a speed of 14.95 m/s down to a halt.

Explanation / Answer

he kinetic energy from the bus that needs to be stored as kinetic energy of the flywheel is

E = 1/2 M_bus (v_bus)^2

The kinetic energy of the flywheel when rotating with angular frequency w (in rad/s) is

E = 1/2 I w^2 ,

with I the moment of inertia. Here

I = M_wheel R_wheel^2

So

1/2 M_wheel R_wheel^2 w^2 = 1/2 M_bus v_bus^2

w = sqrt(M_bus/M_wheel) * v_bus / R_wheel

= sqrt(26139.22/51.6) * 14.95 m/s / 1.07m
= 314rad/s

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