Two gears are adjusted so that the smaller gear drives the larger one. The radius of the smaller gear is 5.23cm and the radius of the larger gear is 8.16 cm. How many degrees will the larger gear rotate if the smaller one rotates 60°?
Two gears are adjusted so that the smaller gear drives the larger one. The radius of the smaller gear is 5.23cm and the radius of the larger gear is 8.16 cm. How many degrees will the larger gear rotate if the smaller one rotates 60°?
Since they're gears, the length of the arc on the smaller gear will be equal to the length of the arc on the larger gear. The arc length for the smaller gear is $\displaystyle \frac{60}{360}2\pi(5.23cm)$. Let x be the number of degrees the larger gear rotates and make a similar expression. If you set them equal, you'll cancel a whole bunch and the answer should come pretty easy. You should get something less than 60 degrees.
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