>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.

If you feed 10J of electric energy into a 90% efficient electric motor to generate 9J of mechanical work and then convert those 9J of mechanical work into electrical energy via a 90%efficient generator you end up with 8.1J of electric energy. If you repeat that often enough you’ll end up with 0J of electric energy. Congratulations, you invented a machine that turns electric energy into heat! Gear ratios don’t change anything about it.

In short, no. Using gear ratios the power of the gears is constant (minus some losses). In order to increase the speed of the gear the torque of the gear is lowered. if you mean in the sense to generate electricity the losses of the system will pile up, energy lost to heat, friction. You’d essentially be plugging an extension chord into itself to try to get infinite power.

That’s not how it works.

Power is torque (force) x speed.

For the same power you can either go faster with less force or slower with more force. Think of a bike: low gears for uphill gives more force but slower, whereas higher gears for flat gives more speed but less force. The actual power you’re putting out can remain constant throughout.

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.

The misconception is that you don’t have a clear idea of what power is. Power is a rate, energy per second (or any time unit). Specifically, your question refers to mechanical field.

In this field: You can translate the term power as: things you do per second. Ok what is qualified “thing you do” then. Anything that is a force and a distance.

Power is how much force for how much distance you exert per second.

Leaving math alone. Your arm can lift a basket of apples by one meter, in one second. An arm with twice your power, will lift that basket in half that time. This is power in linear motion.

In rotation, we replace speed with revolutions multiplied by the diameter. The bigger the diameter, the higher the speed for the same revolutions per second.

Now, in your gear set, what happens is that shaft one rotates a big gear slowly. Let’s say, the gear is 10 big. The speed of its tooth is 1 rotation multiplied by 10 diameter. So the speed of the tooth is 10. It drives a smaller gear. The small gear is 1 big. The speed of the tooth of the small gear is 10 again, but the diameter is only 1 big. Therefore, the small gear has to rotate 10 times faster to stay engaged with the big wheel.

The torque needed to rotate the big gear is the tooth force multiplied by diameter. So the power is 10 big, times one force. That’s the torque at the shaft. Shaft of big gear has let’s say, 10 of power, coming from a 10 torque to push the tooth with a force of 1 at a diameter of 10.

The driven shaft gets its tooth pushed with force one, times a diameter 1 big. The result is 1 torque. but it is rotating 10 times faster, as we previously say.

The result, is that both driving and driven shaft have a power of 10. One has its power coming fro high torque and low speed. The driven gear has its power coming from small torque but big speed. Power is always 10.

The the big gear is a slow arm lifting 10 apple baskets by one meter in one second, the driven gear is a fast arm that lifts one apple basket by 10 meter in a second.

The fact that there is rotation, speed and torque involved does lead to get some misconceptions. But the principle is the same as linear motion. Your power is how much you do per second. You can do a 10 force at speed 1, or do a 1 force at speed 10. In both cases your power is 10.

Thats why Power is a very important metric in mechanics. Because it’s the only constant thing when you link multiple linkages, gears, levers, pulleys. What stays the same is the power. Power in = power out. While everything else may change. Speed, distance, force torque… those are all variables you can play with and trade off one with the other.

A generator experiences resistance based on the load it’s carrying/supporting; think of pushing two magnets together, with the same poles pointing at each other. Spinning a magnet at high speed, low torque means that it can move fast, but will not be able to support higher loads. There’s no free lunch; gearing can convert speed to torque or vice versa but not generate free power.

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