If I hook up a big gear to a much smaller one to spin it incredibly fast could that be used to generate power? And if so could that idea be used to generate power on a much bigger scale? In my brain it makes perfect sense but there must be something wrong with this idea.
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There is no such thing as a free lunch with energy.
Have you ever ridden a bicycle in high gear? Notice how it becomes really hard to pedal from a stop when in high gear, but your overall top speed is higher? You have to work very hard to start out from a stop from high gear because there is low torque(rotational force) to the wheels in high gear. While there are applications for this, all this does on its face though is convert low speed/high torque into high speed/low torque. *There is no energy gained*.
An analogy would be like saying “What moves more material? Moving 10 1kg boxes, or moving 1 10kg box?”
If anything, energy is lost due to friction since gears touching increases friction.
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