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A flywheel works best with as high a speed as possible and with a large a diameter. Weight is not a critical factor in its energy storage potential.
If you can get it running in near vaccum conditions then you reduce friction. The other factor is to make the electro mechanical conversion as efficient as possible.
A flywheel for a given weight has probably got greater potential energy storage than a battery as you only need to be able to increase its speed but.....
Its disadvantages are primarily size, shape and energy loss to friction.
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