# Angular and Linear Speed.

• May 8th 2013, 05:01 PM
FatimaA
Angular and Linear Speed.
My prof posted this problem as an example and, going over the steps, I haven't been able to work out how he got to the final answer.

A car has tires with 10 inch radius and is traveling at 60 miles per hour. Find the angular speed of the wheels in radians per second.

(60 miles/hr) = (60 miles/hr) * (5280 ft/1 mile) * (12 in/1 ft) * (2 pi rad/2 pi (10 in)) * (60 min/1 in) * (60 sec/1 min)

The angular speed $\displaystyle \omega$ is given as a function of the linear speed $\displaystyle v$ and radius $\displaystyle r$ as:
$\displaystyle \omega=\frac{v}{r}$
To find $\displaystyle \omega$ in radians per second, given that $\displaystyle r$ is in inches, we need to convert $\displaystyle v$ to inches per second:
$\displaystyle \omega=\frac{60\frac{\text{mi}}{\text{hr}}\cdot \frac{5280\text{ ft}}{1\text{ mi}}\cdot \frac{12\text{ in}}{1\text{ ft}}\cdot \frac{1\text{ hr}}{3600\text{ s}}}{10\text{ in}}=105.6\,\frac{\text{rad}}{\text{ s}}$