# Dimensional Analysis Problem?

Ms. McDonald likes to cut her grass with her fast lawn mower that travels at 122 rpm when she’s moving at 3.2 mph. Find the radius of the mower’s wheel in inches?

### 4 Answers

- Anonymous8 months agoFavourite answer
(1) Circumference of a circle:

C = 2 π r | |

r | radius

C | circumference

therefore,

r = C / (2 π)

(2) Linear speed vs revolutions:

v = C * f | |

v | speed

C | circumference

f | revolution frequency

Therefore,

C = v / f

Therefore from the two equations for circumference, we get:

v / f = 2 π r

Rearrange to find radius:

r = v / ( 2 π f)

= 3.2 mph / (2 π (122/min))

= 3.2 mph / (2 π {7320/hour))

= 6.96×10^-5 miles

= 4.41 inches

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- RealProLv 78 months ago
Did you copy the problem incorrectly?

Assuming the wheels spin at 122 rpm

Assuming you can convert miles to inches

(x mi) * (5280 ft/mi) * (12 in/ft) = 12*5280x in

And that you can convert h to min

(x h) * (60 min/h) = 60x min

Then converting mi/h to in/min is not a problem

(3.2 mi/h) * (5280 ft/mi) * (12 in/ft) * (1/60 h/min) = 3380 in/min

Then dividing with 122/min gives you the single circumference of a wheel in inches, and dividing with 2pi gives you its radius.

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- AmyLv 78 months ago
Dimensional analysis is seeing that to get a final answer in inches, you'll have to divide mph by rpm.

Dimensional analysis is converting the 3.2 mph to inches per minute.

Dimensional analysis does NOT tell you how to get from revolutions to radius. That's geometry.

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- 8 months ago
Can’t be bothered

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- Lv 78 months agoReport
Then why bother answering anything at all? Is it to get the automatic 2 points?

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