The flywheel has been used as a battery a bit in history. This is pretty old tech, check out the gyrobus.
https://en.wikipedia.org/wiki/Gyrobus
Quote:
Disadvantages
Weight: a bus which can carry 20 persons and has a range of 2 km (1.2 mi) requires a flywheel weighing about 3 tons.
The flywheel, which turns at 3000 revolutions per minute, requires special attachment and security—because the external speed of the disk is 900 km/h (560 mph).
Driving a gyrobus has the added complexity that the flywheel acts as a gyroscope that will resist changes in orientation, for example when a bus tilts while making a turn, assuming that the flywheel has a horizontal rotation axis. This effect can be counteracted by using two coaxial contra-rotating flywheels.
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It's interesting to hear a flywheel based energy storage was developed, the negatives are really bad for racing, resistance of changing direction, and added weight. I'm sure their efforts were focused on a small weight that spins at very high rpm. The one in the bus only spun at 3000 rpm, but it was around 3 tons too.
I was looking for a vid I saw before on these, and this one came up, seems to cover a little bit of everything. One I was thinking of was the power grid flywheel based energy storage where a guy tours the place and talks about the weight, rpm etc. Pretty crazy setup really. There's even a mention of the F1 system near the end, 6500 rpm seems quite low, but probably a lot safer than something half the weight spinning twice the speed.