Why is the tangential speed of the top of a rotating wheel twice the translational speed at the center?

Quick Background:

This question has baffled me for a while, but when I heard a friend of mine saying that police radar detectors can double your speed it started to make sense to me. Because when I hear physics-related facts in everyday terms they sometimes make more sense.

The answer (with minimal math) is: It all depends on the relative measurement reference point.

Wheels spin, but when you put it against something, like the ground, then they start to push against each other.

If your wheels are not slipping, or sliding, then they are in contact with the ground. This seems obvious, but when you assign a relative speed to two items in contact (with no slippage, or slideage [my new made-up Word of the day]), then their speed relative to each other, is ZERO (pick whatever units you want).

Zero mph

Zero kph

Zero you pick it

This is interesting because the vehicle is still moving, relative to the ground.

If the speed of the vehicle is 30 mph, then the axle of the vehicle is shooting down the road (hopefully with the rest of the car attached) at 30 mph.

The top of the wheel, relative to the road, is double the axle speed (60 mph), so that it can average out with the 0mph at the ground/tire touch poing.

I just came up with the idea, and I'm sure I'm not the first, that a wheel in motion, while contacting a surface (like the ground), is like a lever.

The lever is pulling the vehicle in a direction.

The top of the lever is moving, and in this case, the bottm is not (assuming no slippage). At the center of the lever is the car axle.

See the wheel as a lever that pushes the axle forward and all will make sense.

It's pretty cool.