An automobile tire is 30 inches in diameter. How fast in rpm does the wheel turn on the axle when the automobile maintains a speed of 50 mph?

$v = \dfrac{50 ~ \text{mi}}{\text{hr}} \times \dfrac{5280 ~ \text{ft}}{\text{mi}} \times \dfrac{12 ~ \text{in}}{\text{ft}} \times \dfrac{1 ~ \text{hr}}{60 ~ \text{min}}$

$v = 52,800 ~ \text{in/min}$
 

$v = r\omega$

$52,800 = 15\omega$

$\omega = 3520 ~ \text{rad/min}$

$\omega = 3520 ~ \dfrac{\text{rad}}{\text{min}} \times \dfrac{1 ~ \text{rev}}{2\pi ~ \text{rad}}$

$\omega = 560.225 ~ \text{rpm}$