Ok, the bottom part of the wheel is actually stationary relative to road frame.
But how does this wheel look for a moving observer (the observer where this wheel is stationary)?
If all points along the wheel are moving at some tangential speed, they should all be contracted in the direction of their movement. After all, bottom point of the wheel is contracted along with the road, because it is moving at speed -v.
So, how do these tiny parts of the wheel contract? Shouldn't the wheel still have the same circular shape and same radius?
Furthermore, shouldn't points closer to the axle contract less (their speed is lower)?