How fast does motion travel through a huge array of cogs?
Say i had 1 million cogs all in a straight line connected to each other and could turn the first cog how long would it take for the end cog to move it would be instant right? In an argument about this today
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answers:
Tom S say: I can't give a precise answer, but the concept of "instantaneous action" over any distance does not exist in "classical mechanics". Instantaneous action over a distance may exist in the "quantum realm". But then distance may not be a parameter in quantum, which would explain some things like Bell's theorem.
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Jeffrey K say: Nothing is instant. The movement is transmitted down the line of cogs at the speed of sound in the material the cogs are made of. Probably about 3000 or 4000 miles per hour.
The same is true if you push the end of a long stick. It will take time before the other end moves.
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Dixon say: They would never move because of the friction of a million cogs. But if you replace the cogs with a zero friction 1 to 1 motion translator, known as a stick, the impulse from one end to the other can never exceed the speed of light because the molecular binding is essentially electric charge. In practice the impulse can't achieve anything like the speed of light, it's more like the speed of sound.
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Whome say: Too many unknowns to give you a definitive answer, but in general, NO the motion would not be transmitted instantly even if all the slack between the gear teeth were initially removed.
The reason is that in all real materials, even the very stiff ones like steel, there is a bit of flex like a spring. In each of the million cogs, there would be two teeth that get loaded, the one being driven by the previous cog and the one driving the next cog. Even if each tooth only flexes by 0.001 mm, by the time you multiply that by 2 million teeth, the distance the first cog surface must move is about 2 m. That would be a lot of spinning for even a "large" cog.
All the above assumes zero friction. In a real setup, even a tiny amount of axle friction on each cog would prevent the whole system from moving any but the first few hundred cogs for a few moments before the whole setup would grind to a halt or fracture itself under excessive driving load.
I hope this helps.
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