Yes. Although it can be done. I worked at an observatory where there was a massive flywheel generator combo to provide enough energy to stow all the telescopes to safe zenith position in the event of a mains failure.
The thing was a brute and had to be aligned so that it would not hit anything within 2 miles if it ever broke free of its bearings.
Today they tend to go for batteries and an inverter with diesel backup, but there was a period in the late 1960's when big fast flywheels were the method of choice for emergency power in remote observatories.
Swiss have had gyro powered buses for a long while.
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Edges of the gyro flywheels tend to be moving uncomfortably fast.
They have recently found favour for regenerative braking too.
That matches roughly what we had at the CERN Proton Synchrotron. There was this massive motor-generator set to smooth over the pulsing of the main bending magnets. These days, it's done with six or seven shipping container-sized boxes full of capacitors and a building full of power electronics.
I remember as a teenager reading about a "home-flywheel" concept in one of the local Electronics Magazines (must've been during the oil crisis of the 70s).
Several tonnes of mass in a sealed, evacuated enclosure with magnetic bearings. Required an excavation below the house the size of a basement (which are very rare in Australia). Needless to say none were ever marketed/built!.
Probably about a quarter of an hour. I don't ever recall seeing it do that. It saved us from brownouts a lot more often and kept the computer happy. A Marconi Myriad didn't like having its power removed suddenly.
The flywheel also provided regular supply conditioning as its much more common benefit. Most mains brownouts and glitches seldom lasted more than a couple of minutes before power came back on again.
The people with the biggest consuming kit in the 1960's were Prof Pippard's group studying Fermi surfaces with a 2MW magnet and a direct line to the national grid to warn them when they were about to switch it on (always late at night when electricity prices were cheaper)!
Superconducting magnets pretty much did away with that - out evolved.
I think it was mostly lead inside a tungsten sleeve overwound with high tensile steel a bit like a tyre would be. I never saw inside it. I was warned that if it ever made funny noises to leave the building immediately.
The maximum safe spin rate was used as an exam question not long after it was first brought into service (why waste a good calculation?).
Kinetic UPSes are still made for very short duration use, and are far more reliable than stacks of lead acid batteries. Long term, they're probably more efficient too as you can skip the double inversion step.
One use was for factory lighting. Losing a few cycles of power while switching feeds or to a generator can shut off discharge lighting, causing a 10 minute outage while the bulbs cool and restart. That's a no-go in a large warehouse or industrial setting.
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