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?

Question

08-11-2016
Mathematics

contestada

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?

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alsteva alsteva · Answer 1 · 2016-11-12T11:28:29+01:00

R - radius of the larger circle
r - radius of the smaller circle

Circumference of the larger circle = [tex]2R\pi=2\times 8\pi=16\pi[/tex]
Circumference of the smaller circle = [tex]2r\pi=2\times 2\pi=4\pi[/tex]

Part 2: During one complete rotation of the larger gear both gears pass the same distance [tex]16\pi[/tex].
Therefore, the smaller gear makes [tex] \frac{16\pi}{4\pi}=4 [/tex] complete rotations.

Part 1: During one complete rotation of the smaller gear both gears pass the same distance [tex]4\pi[/tex].
Therefore, the larger gear makes [tex] \frac{4\pi}{16\pi}=\frac{1}{4} [/tex] of a complete rotation.
Since one complete rotation corresponds to 360 degrees, 1/4 of a complete rotation corresponds to 360/4=90 degrees.