An almost empty bobbin is pulled along a flat surface by a

thread which is wrapped around...
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thread which is wrapped around the central part/inner reel. The diameter of the inner reel is 5 cm and that of the outer wheel is 10 cm. Assuming no slipping or sliding how far has the bobbin moved when the end of the thread has moved 12 cm

Hi, Thank you for using the site. I'll be happy to help you with this problem. I'll have the solution posted for you in a few minutes, as soon as I finish typing it up. Thanks, Ryan

Hi again, I'm sorry for the unexpected delay. I had to restart my computer. Here is the solution: Distance Please feel free to ask if you have any questions about this solution. Thanks, Ryan

Customer replyreplied 2 years ago.

Thanks - this distance seems quite far? I had wondered whether it would be a ratio of the circumferences??

Hi, Yes, in this case, the distances are exactly related by the ratio of the circumferences. I wrote out a solution "the long way" in order to be thorough, and potentially less confusing. You could also write out a proportion using the ratio of the diameters (you don't really need the actual circumferences, since the ratio of the diameters and the ratio of the circumferences is the same). One key to this problem is that the inner reel is "almost empty". This is interpreted to mean that the thread which is wound around the inner reel is peeling off of a constant diameter. If the bobbin had more thread in it, such that there was thread wrapped over thread, then the inner diameter would be changing as the thread was unwound, which would complicate the problem. Ryan