Need help with angular velocity problem. So I have a problem that I just can’t seem to get right and I have only one try remaining. Can someone please help me solve this problem but plz explain if possible. Thanks “Suppose a car runs over a nail while driving at a speed of 57 miles per hour, and the nail is lodged in the tire tread 12 inches from the center of the wheel. What is the angular velocity of the nail in radians per hour? ”

The circumference of the wheel is $2\pi \cdot 12 in$. The wheel must turn $\frac{57 \cdot 63360 in}{2\pi \cdot 12 in}$ times to travel the distance of $57 mi = 57 \cdot 63360 in$. Each full rotation turns the wheel (and thus the nail) by an angle of $2\pi$. This happens in an hour, so the angular velocity of the nail is $2\pi \frac{57 \cdot 63360 in}{2\pi \cdot 12 in}/h = 300960/h$.