What is the speed of a wheel when/where it touches the pavement?

120 mph with respect to the road.

From inside the car you see the wheel’s bottom going 60 mph backward and its top going 60 mph forward.

The speed of the wheel “where it touches the pavement” is essentially zero (plus whatever small component of friction causes it to move slightly as it touches), at that instant. Is that what you were looking for?

At the top of the rotation I think it will depend on the diameter of the wheel / tire.

In one sense, “all of the wheel” is moving at 60 mph, same as the rest of the car. If you’re asking “What is the angular velocity at various points on the wheel?” then that’s a different question.

I think you hit it @CWOTUS. Otherwise the tire would not lift from the road in the same place it was put down.

Diameter is irrelevant. The top of the wheel moves forward at twice the speed as the car itself.

An old riddle is which part of a train is always moving backward? The answer is the rim of the flange at the bottom of travel, where it dips below the top of the rail.

Yes, relative to the road (or someone observing from the ground), the tire is moving at 0 mph at the point it touches the ground and moving twice the speed of the car, 120 mph, at the highest point of the tire.

Relative to the driver of the car, the “rim” of the tire is moving at the speed of the car, 60 mph. Any other point on the tire has the velocity v r / R, where r is the distance between the point and R is the total radius of the tire.

However, relative to a meteoroid, a biker on the road, a car going in the opposite direction, etc. all these values are different. There is a level of ambiguity when the question “What is the speed of . . . ?” is asked without stating the observer.

Relative to the ground, it’s going 120mph at the top (which is what you asked), and 0 mph on the ground, plus any slippage.

Relative to the car, it’s going 60mph forward at the top, and 60 mph backwards on the bottom.