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rotating cogs. a central angle question?
A bicycle has a chain that connects a chain ring of radius 6 in. with a cog of radius 2 in. If the chain ring rotates through an angle of 20 degrees, then through how many degrees does the cog rotate? I know the formula is s/r = a and we are solving for 'a' but I do not know how what to plug in to get the right answer.
I drew a picture out but yahoo wouldn't let me paste the link ... just add a 'JPG' at the end and you should be able to view it.
i51.tinypic.com/dcgc4m.
the final answer is a = 60 degrees
since the chain has fixed length and is taut, 's' in the chain ring is equal to 's' in the cog. thus, 6*20 = 2a, and a = 6*20/2 = 60 degrees.
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