Question

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches. two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 3 inches.

Answer 1

Let r represent the radius of the smaller circle and R the radius of the larger
circle.

Apply ratios: the radius of the smaller circle to the radius of the larger circle.

r: R = 3 : 7.

I complete rotation = 360 degrees.

1st:

For one complete rotation of the smaller circle, the larger circle is rotated through (3/7)*(360) = 154.3 degrees

2nd:For one complete rotation of the larger circle, the larger circle is rotated through (7/3)*(360) = 840.0 degrees

This is equivalent to (840/360) = 2.3 rotations

Alternatively, use the ratios: The number of rotations = R/r = 7/3 = 2.3 rotations 

Hope this helped☺☺