high school geometry

gear a and gear b. gear a on the left has 18 teeth and gear b on the left has 8 teeth.

suppose gear b makes one complete rotation in the counterclockwise direction. give the angle of rotation and direction for the rotation of gear a.


Hi there.

Think of the ratios: gears fit tooth to tooth, so when gear b runs 8 teeth past the point where the two gears interact, then gear a also runs 8 teeth through that interaction zone.

Now if gear b goes around once, then it has moved 8 of its teeth through the interaction zone, so that means that gear a has also moved 8 of its own teeth through there. What fraction of a's teeth is that? What fraction of a complete rotation is that?

Hope this helps,
Stephen and Penny