So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)

$\displaystyle 100 km/h = 27.78 m/s$

$\displaystyle \pi 64=201.06 cm = .201 m$ is the circumference of the circle in meters.

$\displaystyle \frac{27.78}{.201}=138.5$ is the number of rotations per second.

So the circle makes approximately 138.5 rotations per second. I know that an entire circle is $\displaystyle 2\pi$ radians so I just multiple 138.5 by $\displaystyle 2\pi$ and that works out to be 870.22 radians/s.

The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?

I have no idea how to start this one. Help!