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Math Help - Find the angular speed

  1. #1
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    Find the angular speed

    A car is traveling at 40 mph and has tires that are 94 meters in diameter. Find the angular speed of the wheel in revolution per minute.
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  2. #2
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    Hello, jcrodua!

    I'm sure there's typo . . . please check the wording.


    A car is traveling at 40 mph and has tires that are 94 meters in diameter.
    Find the angular speed of the wheel in revolution per minute.
    94 meters is over 300 feet ... the length of a football field!
    . .
    Now that is a monster truck!

    It's probably: . 94\text{ centimeters} \:\approx\:37\text{ inches.}

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, jcrodua!

    I'm sure there's typo . . . please check the wording.


    94 meters is over 300 feet ... the length of a football field!
    . .
    Now that is a monster truck!

    It's probably: . 94\text{ centimeters} \:\approx\:37\text{ inches.}

    Yah thats centimeters. its my mistake. so what would be the answer?
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  4. #4
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    Hello, jcrodua!

    You're expected to know how to change units.


    A car is traveling at 40 mph and has tires that are 94 cm in diameter.
    Find the angular speed of the wheel in revolution per minute.

    We know that: . \begin{array}{ccc}\text{1 hour} &=& \text{60 minutes} \\ \text{1 mile} &=& \text{1609.344 m} \end{array}


    \text{40 mph} \:=\:\frac{40\:{\color{blue}\rlap{/////}}\text{miles}}{1\:{\color{red}\rlap{////}}\text{hour}} \times \frac{1\:{\color{red}\rlap{////}}\text{hour}}{\text{60 minutes}} \times \frac{\text{1609.344 m}}{1\:{\color{blue}\rlap{////}}\text{mile}} \;=\;\frac{\text{1072.896 m}}{\text{1 minute}} .[1]

    The tire is moving down the road at 1072.896 meters per minute.


    The circumference of the tire is: . C \:=\:\pi d \:=\:94\pi\text{ cm} \:=\:0.94\pi\text{ m}

    . . That is: . \text{1 rev} \:=\:\text{0.94}\pi\text{ m}


    Convert [1]: . \frac{1072.896\:{\color{red}\rlap{/}}\text{m}}{\text{1 minute}} \times \frac{\text{1 rev}}{\text{0.94}\pi\:{\color{red}\rlap{/}}\text{m}} \;\approx\;363.3\text{ rev/min}

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