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sar_sar

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I have two gear wheels with an endless chain passing round them. The axles of the wheels are 100 chain_link_lengths apart, so we have 100 chain links along the top; 100 chain links along the bottom and, say, 20 links around the wheels, for a total of 220 links. I paint numbers 1 to 220 on the links.

If I set the chain moving at such a speed that the links are relatively contracted to 1/3 of their rest length, I will need 300 links along the top. But there are only 220 links in the chain.

How can I explain what is occurring? Note that this is not the usual "paradox" where a stationary and a moving observer see things differently - I stay stationary all the time and I apparently see more links appear.

If I take a photo of the assembly with the chain in motion, how many links do get in my photo? (ie for a given simultaneous time t in my stationary frame, how many links do I see?)

I came across the problem thinking of charges in a circuit. I know that charge conservation will not be violated, but I cannot explain why. When the charges are in motion, the space between them will contract and it appears that I will get an increased charge density. There is a wealth of material explaining what happens in an infinite conductor but none on what happens in a finite, complete circuit.

Any ideas or pointers will be GREATLY appreciated - I have googled extensively without luck.