It's all relative.

Relative to the road the bottom of the wheel is in fact /almost/ stationary.  
There is a tiny bit of slip, depending on whether it's a driven wheel or not.

Obviously if there is a lot of relative motion between the road surface and the 
bottom of the tire, then you've lost all your traction.

Don't forget, the tire is ROTATING.  That means that relative to a fixed point 
(like the road) every part of the circumferece of the tire is moving in a 
different direction at different relative velocities.

> axle is moving at 1x, then the bottom of the tire would have to be standing 
> still. But we all know
> that it isn't, the entire tire is moving forward at 1x. that can't be true 
> either or else the road
> would need to be moving at 1x also or else the tire would be skidding, but 
> it's not. This must be
> what some of those advanced math courses I never took were all about.
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