Flywheels store rotational kinetic energy. You can store energy in or by increasing its speed and free energy from it by transferring or converting that energy – make something move, convert to electricity, etc.
How they’re implemented depends on their purpose. On a car with a manual transmission, they’re used to add rotational inertia to smooth the “impact” of releasing the clutch and putting a large load on the engine.
In power grids, they can be used to store over produced power, allowing that power to be drawn from at a later time.
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