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?

Show all work.

Answer 1

well lets see here

Part 1: 

the full rotation will have a perimeter of 1

so we can then determine the distance from the big gear how much the smaller gear will move

smaller gear=the disance of: 1* (22/7)*2*2

If the distance converted into degrees, then: 

gear A rotation= gear A distance/ gear A perimeter * 360°

gear A rotation=  (22/7) * 2 *2/ {(22/7) * 8 *8}   * 360°

gear A rotation= (1/16) * 360°= 22.5 degrees

Part 2: 

The problem is similar to part 1 but the number is reversed.

bigger gear= 1 * (22/7) * 8 *8

bigger gear=  (22/7) * 8 *8/ {(22/7) * 2 *2} = 16 rotation

hope i could help u