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.

two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 4 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

@jim_thompson5910

Answer 2

let me think

Answer 3

we basically have this picture going on

Answer 4

what is the circumference of circle A?

Answer 5

25.12

Answer 6

let's leave it in terms of pi

Answer 7

you should get 8pi

Answer 8

ok

Answer 9

how about the larger circle?

Answer 10

14pi

Answer 11

if we divide 14pi by 8pi, we get

(14pi)/(8pi) = 14/8 = 7/4

Answer 12

convert 7/4 to a decimal to get 7/4 = 1.75

basically this number tells us that the smaller circle will do 1.75 full rotations as it rolls around the larger circle.

Basically the smaller circle does 1.75 rotations per 1 rotation of the larger circle

Answer 13

ok

Answer 14

take this ratio

1.75 rotations of A: 1 rotation of B

and divide both parts by 1.75 to get

(1.75/1.75) rotation of A: (1/1.75) rotation of B
1 rotation of A: 0.57142857 rotation of B

Answer 15

so 1 full revolution of circle A means circle B only does approx 0.57142857 of a full revolution

Answer 16

so how to answer part 1

Answer 17

well you simply multiply 0.57142857 by the number of degrees in a full rotation

Answer 18

oh ok

Answer 19

part 2 is pretty much answered when I said how many times A revolves as it rolls around B