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.
Hello, jcrodua!
I'm sure there's typo . . . please check the wording.
94 meters is over 300 feet ... the length of a football field!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.
. . Now that is a monster truck!
It's probably: .$\displaystyle 94\text{ centimeters} \:\approx\:37\text{ inches.}$
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: .$\displaystyle \begin{array}{ccc}\text{1 hour} &=& \text{60 minutes} \\ \text{1 mile} &=& \text{1609.344 m} \end{array}$
$\displaystyle \text{40 mph} \:=\:\frac{40\:{\color{blue}\rlap{/////}}\text{miles}}{1\:{\color{red}\rlap{////}}\text{hour}} \times \frac{1\:{\color{red}\rlap{////}}\text{hour}}{\text{60 minutes}} \times \frac{\text{1609.344 m}}{1\:{\color{blue}\rlap{////}}\text{mile}} \;=\;\frac{\text{1072.896 m}}{\text{1 minute}}$ .[1]
The tire is moving down the road at 1072.896 meters per minute.
The circumference of the tire is: .$\displaystyle C \:=\:\pi d \:=\:94\pi\text{ cm} \:=\:0.94\pi\text{ m}$
. . That is: .$\displaystyle \text{1 rev} \:=\:\text{0.94}\pi\text{ m} $
Convert [1]: .$\displaystyle \frac{1072.896\:{\color{red}\rlap{/}}\text{m}}{\text{1 minute}} \times \frac{\text{1 rev}}{\text{0.94}\pi\:{\color{red}\rlap{/}}\text{m}} \;\approx\;363.3\text{ rev/min}$