Question

GEARS
Example 1.1
Two connected gears are rotating. The smaller gear has a radius of 0.4 m and
the larger gear's radius is 0.7 m. What is the angle through which the larger
gear has rotated when the smaller gear has made one complete rotation2​

Answer 1

Step-by-step explanation:

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.

two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 3 inches.

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Larger circumference: 2pi*r = 14pi inches

Smaller circumference: 2pi*r = 6pi inches

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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?

Ans: (6pi/14pi)(360) = (3/7)360 = 0.4286(360) = 154.29 degrees

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Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Ans: # of rotations = 14pi/6pi = 7/3 = 2 1/3 rotations

Answer 2

Let C4 = 2pi(.4)

Let C7 = 2pi(.7)

Let F = Fraction of rotation

Let Angle = F * 360º

F = C4 / C7

= 2pi(.4) / 2pi(.7)

= 4 / 7

Angle = 4/7 * 360º

Angle = 205.7º

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