SOLUTION: 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 poi

Algebra ->  Trigonometry-basics -> SOLUTION: 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 poi      Log On


   

Question 870717: 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 by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
When the smaller gear makes one revolution, its outer edge has traveled the circumference,
S=2%2Api%2AR=2%2Api%2A2=4%2Api
Now find out the angular measure of the larger gear that travels 4%2Api
Set up a ratio.
%282pi%29%2F%282%2Api%2A8%29=theta%2F%284%2Api%29
1%2F4=theta%2F%284%2Api%29
1%2F8=theta%2F%284%2Api%29
theta=pi%2F2
So the larger circle made 1/4 revolution.
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We saw before when the small circle makes 1 revolution, the larger make 1/4 revolution.
So if the large one makes one revolution, the small one will make 4 times as many or 4 revolutions.