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if a smaller wheel on car causes the larger wheel to rotate at what degrees does the...

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r4rob92 | Valedictorian

Posted March 3, 2013 at 8:59 PM via web

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if a smaller wheel on car causes the larger wheel to rotate at what degrees does the larger tire rotate if the smaller has a radius of 5.4 cm and the largest tire radius is 6.2 cm?the smaller tire rotated 91 degrees.

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted March 4, 2013 at 11:47 AM (Answer #1)

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Since radius of smaller wheel is 5.4cm it follows that its circumference is 

`2cdot5.4 pi=10.8pi`cm.

Similarly circumference of larger wheel is 

`2cdot6.2 pi=12.4 pi`cm.

If a wheel with circumference length `c` rotates by 1° it has traveled `c/360` because full circle has 360°. So since our smaller wheel has rotated 91° it has traveled `(91cdot10.8pi)/360=2.73pi`cm. The larger wheel must travel the same as the smaller one, hence we have

`2.73pi=(d cdot 12.4pi)/360`

where `d` is how much degrees has the big wheel rotated.

`2.73=(12.4cdot d)/360`

`d=(2.73cdot360)/12.4`

`d approx 79.25806^o=79^o15'29''`  <-- Solution

 

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