Contact Point of a Rolling Tire Does Not Move

How to read tire codes. Copied from this website that has additional info on tire.

That's right. Although a tire moves, the contact point between the tire and the surface does not move. This fact often confuses students. They see the tire gains distance as it moves, so how come the contact point of a tire does not move while the tire gains distance? Let me offer a simple explanation to this problem.

When a tire rolls and completes one full revolution over a time interval t, its perimeter covers a distance of 2πR, where R is the tire radius. The speed v of the tire is equal to the distance covered 2πR divided by the time interval t. That is, v = (2π/t)R. The quantity (2π/t) is called angular velocity and is typically denoted as ω.

The tire speed ωR causes the tire to gain distance. It moves. The center of the tire also moves with this speed, which can be confirmed by experiment. The contact point moves and gains distance as well. But the speed of the contact point is zero (i.e., it does not move). How come?

The key to understand this confusion is that a single point on the tire perimeter touches the surface only once every one full revolution. When it touches the surface, it becomes the contact point. But it leaves the surface as soon as it touches it. This contact point thus has zero velocity as it never moves relative to the surface. It just touches and goes fleetingly. If you follow the path of motion of this point, you get a curve called cycloid (click for animation).

Since there is always available one point on the tire perimeter touching the surface as the tire rolls, then you can always match one such contact point - that does not move - with the center of the tire that moves with the speed ωR. Hence, the statement that the contact point of a rolling tire does not move.