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Let a cylinder is made to roll in such a way that the velocity of its center of mass is $v$ $m/s$. Are the particles of its surface supposed to move with equivalent tangential velocity? It is to be noted that the cylinder is rolling on a non frictional surface(negligible amount of friction).Isn't tangential velocity independent on translational velocity in this circumstance?

The scenario is like the cylinder is being taken from one place to another along a flat surface by rolling it and with respect to a stationary object like a tree its linear velocity is v m/s

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  • $\begingroup$ I don't get what is meant by "rolling on a non frictional surface". $\endgroup$ Sep 20 at 10:09
  • $\begingroup$ negligible amount of friction $\endgroup$
    – MSKB
    Sep 20 at 10:17
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    $\begingroup$ Then it can't be rolling "on the surface". It is rotating adjacent to the surface. $\endgroup$ Sep 20 at 10:34
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    $\begingroup$ Related (meta): Exit strategies for "chameleon questions". Someone else can elaborate. $\endgroup$ Sep 20 at 13:28
  • $\begingroup$ I rolledback your last edit, because you have accepted an answer and it matches the original question. $\endgroup$
    – ACB
    Sep 20 at 23:36
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What I want to imply first is that rolling motion cannot happen on a frictionless surface (neglegible friction). It merely slides if no friction. Then the all particles are moving with $v$ linear velocity. If the friction is enough to provide external torque for rolling motion, then we can analyze it as a combination of two motions: linear motion and rotational motion. The all particles has the same $v$ linear velocity. And every particle on the same circumference has the same tangential velocity. If it is a rolling without slipping motion, the bottommost particle has zero velocity, therefore tangential velocity is equal to linear velocity and they are opposite in direction.[1]

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  • $\begingroup$ could you please explain the latter part of your answer further? $\endgroup$
    – MSKB
    Sep 20 at 10:21
  • $\begingroup$ I added a link to my answer. Check that please. $\endgroup$
    – ACB
    Sep 20 at 10:23
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    $\begingroup$ Are you implying that pure rolling cannot occur on a frictionless surface? Because that is incorrect. $\endgroup$ Sep 20 at 10:25
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    $\begingroup$ @WeatherVane " Rolling where there is no sliding is referred to as pure rolling ." See en.wikipedia.org/wiki/Rolling . I have never heard of the notion that rolling implies the existence of another agent. $\endgroup$ Sep 20 at 10:46
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    $\begingroup$ Please don't edit questions that makes its answers invalid. If you want ask a new question.(but your new question has been asked numerous times on PSE) $\endgroup$
    – ACB
    Sep 20 at 11:13
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Instantaneously:

  • a particle in contact with the ground has velocity $0$

  • a particle on the opposite end of that diameter (at the top) will have a velocity $2v$.

The locus of any point on the cylinder is a cycloid.

enter image description here

From Rolling Circles

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