Question

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.
two circles touching at one point. Larger circle has radius of 8 inches. Smaller circle has radius of 2 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

1.
The larger gear will have turned through an arc equivalent in length to the smaller circle's circumference. Thus:
2πr(small) = r(large)∅
2π(2) = 8∅
∅ = π/2 = 90°

2.
The distance covered by the larger gear will be:
C = 2πr
C = 2π(8)
C = 16π

Per revolution, the smaller wheel covers:
C = 2πr
C = 2π(2)
C = 4π

Number of revolutions of smaller wheel = 16π / 4π
Number of revolutions = 4