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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- Aug 29th 2008, 02:10 AMjcroduaFind 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.

- Aug 29th 2008, 07:38 AMSoroban
Hello, jcrodua!

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

Quote:

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: .$\displaystyle 94\text{ centimeters} \:\approx\:37\text{ inches.}$

- Aug 29th 2008, 08:41 AMjcrodua
- Aug 29th 2008, 12:41 PMSoroban
Hello, jcrodua!

You're expected to know how to change units.

Quote:

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