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Answer :
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %.
How to compare rotations between two wheels of different diameter
The quantity of rotations (n), no unit, done by a wheel is equal by total traveled distance (s), in inches, divided by its circumference (p), in inches:
[tex]n = \frac{s}{p}[/tex]
[tex]n = \frac{s}{\pi\cdot D}[/tex] (1)
Where D is the diameter of the wheel, in inches.
If we know that n = 651 and D = 31 in, then the travelled distance is:
s = (651) · π · (31 in) (2)
s ≈ 63400.481 in
The travelled distance of the 31-in diameter wheel with 651 rotations is approximately 63400.481 inches.
By (2) we understand that the travelled distance is directly proportional to the diameter. Hence, if the diameter of the wheel is increased by 20 %, then we must multiply the diameter by 1.2 and divide the travelled distance by this result:
s ≈ 1.2 · π · (31 in)
s ≈ 116.867 in
[tex]n = \frac{63400.481\,in}{116.867\,in}[/tex]
[tex]n = 542.501[/tex]
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %. [tex]\blacksquare[/tex]
To learn more on circumferences, we kindly invite to check this verified question: https://brainly.com/question/4268218
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