How wheels go at three different speeds simultaneously

Some sciences prove that everything you know is wrong. Physics doesn't. It just proves that everything you know is relative. A good example of this is the motion of the wheel. Although it was one of humankind's earliest machines, it still has some tricks up its sleeve.

One of those tricks is the fact that any given wheel is going at many different speeds, at least from the road's point of view.

Photo via Jalopnik — read about this six-wheeled supercar on Jalopnik.

When we measure speed, we generally measure the distance an obect goes over time. For an overall car, that's a fine measurement. But the wheels are in different kinds of motion. When a wheel skids, it's moving over the road without any traction. The rubber of the wheel is sliding with respect to the surface of the road. Tires don't usually, or optimally, skid. They aren't usually moving over the ground - at least the part that touches the ground isn't. It's gripping, and staying still.

The car is moving forward at a certain speed, S, with respect to the ground. The bottom of the wheel is motionless in respect to the ground. In order for the bottom of the wheel to have a speed of zero when the car is racing forward, it has to be going backwards just as much as the car is going forwards. It's like someone on a moving sidewalk walking backwards as fast as the sidewalk is pushing them forwards, so they don't appear to move when observed from someone off the sidewalk. The wheel's speed, with respect to the car, is negative S. To the road, it's motionless.

Here's where things get weird. The exact center of the wheel moves at the same speed of the car, of course. So looked at from the road, it is moving at speed S. But the top of the wheel is moving with the speed of the car, and it is also moving forward at exactly the speed that the bottom of the wheel is moving backward. Since the bottom of the wheel is spinning backwards at negative S, so the top of the wheel is spinning forwards at speed positive S, and also moving with the car at speed positive S, making for a combined speed of 2S.

And that is how a single wheel, all in one piece and attached to a car going at a steady pace can have a measured speed of 0, S, and 2S, all at the same time.

The moral of the story is, if anyone tries to ticket you for speeding, you can make a case that certain parts of your car were not only not over the limit, but completely motionless.

Further Reading: Sydney School of Physics and Davidson.