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I am having a hard time understanding a very simple principle involving a rolling wheel. I know that the velocity at the bottom "contact point" of a rolling wheel is zero relative to a stationary observer.. yet I don't see how this is true.

So I made a quick sketch and here is my reasoning: As the wheel rolls, it translates horizontally over time. The contact point is no exception. Thus it must have a non-zero velocity, otherwise the wheel is stationary. Basically, the 'delta d'/dt will give the velocity of the contact point, which is non-zero. Why am I wrong? Any light anybody could shed on the matter would be much appreciated!

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# Very Simple Conceptual Question About Rolling

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