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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

ACB
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MSKB
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2 Answers2

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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]

ACB
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  • could you please explain the latter part of your answer further? – MSKB Sep 20 '21 at 10:21
  • I added a link to my answer. Check that please. – ACB Sep 20 '21 at 10:23
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    Are you implying that pure rolling cannot occur on a frictionless surface? Because that is incorrect. – Reet Jaiswal Sep 20 '21 at 10:25
  • @Reet , please check this: https://physics.stackexchange.com/q/515259/305718 – ACB Sep 20 '21 at 10:30
  • @ACB your point being? A cylinder of radius $r$ on a frictionless surface with $v_{CM}=v_0$ and $\omega = v_0/r$ will pure roll without the need for friction. – Reet Jaiswal Sep 20 '21 at 10:35
  • @Reet are you confusing "rolling" with "rotating"? "Rolling" implies there is another agent: i.e. a friction surface, and a gravitation or other pull. – Weather Vane Sep 20 '21 at 10:36
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    @WeatherVane " Rolling where there is no sliding is referred to as pure rolling ." See https://en.wikipedia.org/wiki/Rolling . I have never heard of the notion that rolling implies the existence of another agent. – Reet Jaiswal Sep 20 '21 at 10:46
  • @Reet the cylinder cannot roll without another agent to make it roll. Suppose you release a stationary cylinder on an inclined plane under gravity. If there is no friction, it will not roll: it will slide just as a rectangular section would. There needs to be friction with another agent to make the cylinder roll. – Weather Vane Sep 20 '21 at 10:49
  • @MSKB If you are not getting the latter part of my answer, see this too. https://physics.stackexchange.com/a/660678/305718 (not the exact situation, but it may help) – ACB Sep 20 '21 at 10:54
  • i edited my wues a bit...... I am now considering for a frictional surface – MSKB Sep 20 '21 at 10:54
  • @WeatherVane Indeed I agree. But see my second comment. Will that case, on a horizontal surface, not produce pure rolling? – Reet Jaiswal Sep 20 '21 at 10:58
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    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) – ACB Sep 20 '21 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

Weather Vane
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