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.
In: 1
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.
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