Energy stored in a flywheel

Question

Ive read about the potential to use a flywheel in the KERS system in Formula 1 ( other battery related stuff) and about buses using flywheels to to power them and then dock with an electrical cable overhead to restore this energy. The flywheels I know are the ones in between the engine & gearbox in your car, is it the rotational inertia alone that can store all this energy ?

Answer 1

One can think of a flywheel  as battery fro storing mechanical energy. The kinetic energy Ke stored in the flywheel is proportional to its moment of inertia I and the square of its angular velocity

Ke=0.5 I w^2

For a solid disk I= 0.5 m R^2

For example if we have a flywheel of 250kg that is rotating a 500 rpm and has a radius of 1.0 m has a kinetic energy

Ke= 0.25 m R^2 (2 pi  w / 60)^2

Ke= 0.25 x 250 x (1)^2 x ( 2 x pi x 500/60)^2=

Ke= 171,000 J

Since for a moving body Ke = 0.5 mV^2

If this energy is transferred to a vehicle weighing 1000 kg is would achieve a velocity

V= sqrt( 2 Ke /m)

V= 18.5 m/s or  66.6 km/h (this is an ideal situation )