Some basic physics: Objects have mass, and when they are pivoting on their axis, they store energy. To speed them up, or to slow them down, somehow more energy needs to be applied.
A flywheel is a rotating device that is primarily intended to store and release energy. Whether that happens efficiently or inefficiently depends entirely on the application.
A potter, kicking the flywheel that drives his pot as he molds it with his hands? Economically? Muscle power driving a simple machine? It might be wasting a fair % of the energy, but economically? It’s been done for 100s of years in poor and rich countries, so obviously it’s very effective in some sense!
In situations where huge flywheels are storing energy, say from a dam during non-peak hours, the mechanical efficiency is very high. And will be even higher as technology advances. But that situation is directly competitive with others. The question is whether the flywheel at such-and-such a dam is more efficient than, for example just holding the water. It’s not just a question of whether flywheels are always better!
Also note that there are devices where we rely on the “flywheel effect” indirectly, even though we do not call them flywheels. A bicycle is very unstable until its two flywheels get up to a moderate speed. The momentum in the four car tires help to keep the ride smooth from mini-accelerations and declerations. Even the spinning of the disk on a laptop helps to keep it stable, in a small way.
So the answer is that flywheels have their place, just as batteries, capacitors, and the water behind a dam all do.
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