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.

The rotational energy of a flywheel is 0.5 times its moment of inertia times the rotation speed (in radians per second) squared. The moment of inertia of the flywheel is its mass times its radius squared.

Explanation / Answer

Given:

mass of flywheel m1 = 51.6Kg

radius of flywheel r1 = 1.07m

Mass of bus m2 = 26139.22Kg

speed of bus v2 = 14.95m/s

Formula used:

Kinetic energy of bus KE = 1/2 m2 x v2^2

Rotational energy = 1/2(Iw^2)

where I is the moment of inertia

w is the rotational speed

I = m1 x r1^2

Solution:

Energy of the bus = 1/2 m2 x v2^2

KE = 1/2 (26139.22) (14.95)^2 ................1

rotational energy of flywheel = 1/2 (I x w^2)

we know I = m1 x r1^2

rotational energy = 1/2 x m1 x r1^2 x w^2 .....................2

The energy of bus is to be transferred to energy in flywheel, so equating 1 and 2 we get:

1/2 m2 x v2^2 = 1/2 x m1 x r1^2 x w^2

simplify and find w from this equation;

w^2 = (m2 x v2^2)/(m1 x r1^2)

w^2 = (26139.22 x 14.95^2 )/ (51.6 x 1.07^2)

w = 314.467rad/sec

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