Answer
$114.59\frac{\text{rev}}{\text{hour}}$.
Work Step by Step
We know that circumference$=2\pi\cdot r$, where $r=\text{radius}$, and the radius is the half of the diameter
Here $C=2\pi\frac{1}{4}=\frac{\pi}{2}$.
We can get the angular speed by: $\frac{v}{C}=\dfrac{180\text{mph}}{\frac{\pi}{2}\frac{\text{miles}}{\text{rev}}}\approx114.59\frac{\text{rev}}{\text{hour}}$.
