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 85.6 kg. The proposed radius of the disk is 1.22 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 29819.86 kg when it decelerates from a speed of 14.54 m/s down to a halt.

Write your answer (with no units) in the box below, showing at least one decimal place. You may assume that the moment of inertia of the flywheel is its mass times its radius squared.

Explanation / Answer

conserving energy of the system,

the energy of the bus is transferred to the flywheel

k.e of the bus is

1/2mv2

v=14.54m/s , m=29819.86 kg

hence K.Ebus = 3152132.157 J

rotational energy gained by the flywheel is change 1/2I2

the flywheel is at rest initially,

this gives, K.Ewheel=1/2(mflywheelr2)(2)

conserving total K.Ewheel=K.Ebus

r=1.22m

mflywheel=85.6 kg

=222.44 rad per sec

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