Revolutions of a tire and angle in radians thru warranty

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Homework Help Overview

The problem involves calculating the angle in radians that a tire will rotate through during its warranty period, given the tire's radius and the total distance covered. The subject area relates to rotational motion and geometry.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the tire's circumference and the total number of revolutions based on the warranty distance. There are questions about the correctness of the calculations and the method to find the angle in radians from the number of revolutions.

Discussion Status

Some participants have pointed out potential errors in the calculations regarding the number of revolutions. There is an ongoing exploration of how to derive the angle in radians from the number of revolutions, with some confirming that multiplication by 2π is necessary.

Contextual Notes

Participants are working with a specific warranty distance and tire radius, and there are indications of confusion regarding unit conversions and the application of formulas.

chaotiiic
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Homework Statement


The tires on a new car have a radius of .275 meters and are warranted for 75,000km

a)what is the angle in radians that one of these tires will rotate thru in the warranty period?
b) how many revolutions does this make?

Homework Equations


1rev = 2pi radians
circumference = 2pi*r

The Attempt at a Solution


circumference = (2pi)(.275m) = 1.727m
b) 75m/.001727= 43427.9
a) 43427 *2pi = 272865
 
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Your calculation for b) is wrong. You should find the number of revolutions as {{75,000,000m}\over{1.727 {{m}\over{turn}}}}
 
Pengwuino said:
Your calculation for b) is wrong. You should find the number of revolutions as {{75,000,000m}\over{1.727 {{m}\over{turn}}}}
43,427,909.66 revolutions.
to find the angle do i multiply this by 2pi?
 
chaotiiic said:
43,427,909.66 revolutions.
to find the angle do i multiply this by 2pi?

Yes.
 

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