Subject: Re: Train Wheels Quandary
Date: Thu, 25 Jun 1998 22:57:35 -0400
From: Alex Bogomolny
This is because both circles can't rotate without slipping. If the big one is assumed to move so that AA is the length of its circumference, the small circle is bound to do some slipping.
Think of gears on the circles and small triangles on lines AA and BB. Let this triangles be of equal size on both lines. To match the size of the triangles, you'll have to place more cogs on the big circle than on the small one. If you actually do that, the circles will never rotate. But if on one there are real cogs whereas on the other you place only cog marks, you will notice that the latter simply slips while in motion.