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.

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?

Please note that I need to find out how to START it off.

Answer 1

relate the circumferences

Answer 2

So I need to find the circumference?

Answer 3

circumference is linear, and so is radius

when we scale an object, the linears scale in proportion.

finding the circumferences is the basic method yes

Answer 4

Alright. So the first circle is \[C = 3.5\pi\] and the second is \[C = 1.5\pi \] ?

Answer 5

no, we are given radiuses not diameters :)

small = 6pi, large = 14pi

when the small one has turned once, the large one has turned in proportion: 6pi out of 14pi, or simply 3/7th of its rotation.

Answer 6

what is 3/7 of 360 degrees?

Answer 7

154.3 degrees?

Answer 8

yeah

Answer 9

Alright, so that explains the degrees for the first question, but what about the number of rotations for the smaller circumference?

Answer 10

Would I simply flip the fraction?

Answer 11

now for a complete rotation of 14pi, the smaller one moves what: 14pi out of 6pi

a ratio of 7/3 its made 7/3 turns

Answer 12

Thank you very much!

Answer 13

yep