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flywheels have fantastic power density, but horrible energy density. Something like 10-11 wh/kg tops at great expense. Using them to power a car is not really feasible.
Flywheels, its about size. For a car its not practical in the sense of storing energy required for actually making it move. Scale things up, store energy from a windmill for instance!
Try to build a flywheel with the size of a stadium. I think its possible to change earths orbit by the amount of energy it required to spin it up!
 

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gyroscopic effects a 1000lb flywheel spinning at 50k rpm would do to the handling of a car.
or the scatter shield required if it blew!

The handling would be VERY interesting though. I have a hard time imagining what would happen if you tried any maneuver other than in a perfect plane about the axis?
 
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