Question

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches.

Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Answer 1

Any ideas? @robtobey

Answer 2

\[\frac{(8 \pi ) 360}{14 \pi }=205.7 {}^{\circ} \]

Answer 3

\[\frac{14 \pi }{8 \pi }=1+\frac{3}{4} \]

Answer 4

Not part of the problem statement.
"How many rotations of each wheel will leave the wheels in their same initial relative position?"

Answer 5

7/4?

Answer 6

From Mathematica's LCM, Lowest Common Multiple, function.\[\text{LCM}(8,14)=56 \]56 the smallest number that is divisable by 8 or 14.\[\left\{\frac{56}{14},\frac{56}{8}\right\}\to \{4,7\} \]For every 4 rotations of the large gear, the small gear will rotate 7 times.

Answer 7

that's the answer?

Answer 8

Yes.

Answer 9

wow that was more simple than I thought. THANK YOU ROBTOBY YOU ARE THE BEST

Answer 10

Thank you for the medals.