# eli5 how a complete rotation of wheel measures the length of circumstance with the same rotation the inner portion having less circumstance also covers the same distance.

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Sorry circumference.

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The only reason why the inner portion covers the same distance is because it is the part of the larger wheel. If you had a wheel that was only the smaller portion in total size, it would cover a smaller distance.

The distance traveled is essentially the amount of wheel that touches the road/surface that the wheel is traveling on (which is the outermost part of the wheel which has the largest circumference/radius)

Only the outermost surface determines the distance travelled. The math is very simple. Diameter of the wheel x Pi = circumference and thus distance travelled for one revolution. All the portions of the wheel are making exactly one revolution too, but they are not covering the same distance. Think about you standing on the north pole for 24 hours. You’d cover no distance, your body would just spin. But if you were on the equator you’d cover 25000 miles in the same time.

The inner part of the wheel is not rotating along the ground, it is rotating a couple of inches off the ground

Imagine two ants that want to race by getting on the wheel of a bike. One is on the tire and one is near the hub.

At the beginning, the tire ant is near the ground. As the wheel starts to turn, the hub ant moves forward while the tire ant just kind of moves upward. Hub ant thinks he’s gonna win for sure.

As the wheel keeps turning, tire ant picks up speed upward and forward. When the tire ant is at the top of the rotation, he’s going twice as fast as the hub ant! Tire ant thinks he’s got the race in the bag and hub ant is shocked.

As the wheel keeps turning, the tire ant slows down again and starts moving downward. At the bottom of the rotation, the tire ant comes to a complete stop. The hub ant takes the lead again.

Ultimately, both ants travel the same average speed, with the tire ant going twice as fast and then coming to a stop over and over again while the hub ant maintains a more constant speed.

If you had a wheel with a removable inner ring and you removed that ring and rolled it next to the wheel, one rotation of that removable ring would not cover the same amount of distance as the wheel it came out of because it is smaller.