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I have been reading "variational principles in classical mechanics" by Douglas Cline and the following page rather confused me. It states that for a cylinder rolling without slipping, the velocity of rolling point of contact is not zero. What am I missing here? rolling

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    $\begingroup$ Hi, welcome to Physics SE! Can you convert the picture of the text into typed-out, formatted text? It makes the content index-able by search engines, and shows up better on different devices' displays. For formulae, try MathJax instead. $\endgroup$ – user191954 Aug 28 '18 at 12:37
  • $\begingroup$ I will edit my post as soon as I do that. $\endgroup$ – physicsguy19 Aug 28 '18 at 12:39
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    $\begingroup$ Hint: The point of contact is not a material point fixed relative to the cylinder nor the ground. $\endgroup$ – Qmechanic Aug 28 '18 at 12:39
  • $\begingroup$ The velocity of the contact point for a rolling motion must be zero, otherwise we have slipping motion $\endgroup$ – Eli Aug 28 '18 at 14:01
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    $\begingroup$ Not clear what you are asking. You have not explained what is confusing about the text which you have quoted. $\endgroup$ – sammy gerbil Sep 1 '18 at 19:58
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The contact point is stationary when the wheel (or cylinder) is rolling. Otherwise it wouldn't be rolling, but sliding. The "without slipping" part is emphasizing this - if the two surfaces slide over one another, then we have slipping. If they don't, then we have no slipping.

And if they don't slide over one another, well, then they are stationary relative to each other.

But only for a moment.

To roll, the wheel therefor isn't sliding over the surface. Rather, the point-of-contact on the wheel is "placed on" the surface and the rest of the wheel moves over this point. Then this point is "lifted off" from the surface. A new point takes over right away, so that there is basically always contact. This contact point is stationary in each moment, but is constantly replaced by a new point on the wheel.

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