Why are wheels so good?

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Not just in a car’s context, but more generally. Like what about a curved surface makes things roll better? I’m so confused

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Anonymous 0 Comments

There are 2 important features of a circle that make them roll so well on flat surfaces. And the flat surfaces part is very key, as what I’m about to say is not exactly the case for less uniform surfaces.

One key feature is that circles are continuous and differentiable, meaning there are no gaps in a circle and that any single point along the circle has only one possible tangent line. This is important because the ground will always lie tangent to whatever part of the circle is touching it. This means there’s always a smooth transition from point to point along the circle’s edge as it moves forward, given that there is no sharp angle around which the shape would have to “pivot” as it rotates.

The next is that each point along the perimeter of a circle is the same distance from the center, meaning there would be no jarring up and down movements for a person using the circle as a wheel as it rolls ahead (because they would always be the same distance from the ground).

Again, both of these points rely heavily on the premise that the surface the circle is rolling on is flat. There are lots of cool examples of non-circular wheels that make for a totally smooth ride on different surfaces! Tricycles with square wheels is a classic – https://youtu.be/LgbWu8zJubo

Edit: added “continuous” along with differentiable for extra specificity

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