# What is the tangential velocity of a cylinder which is moving with a translational/ linear velocity (of center of mass)? [closed]

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

• I don't get what is meant by "rolling on a non frictional surface". Sep 20 at 10:09
• negligible amount of friction
– MSKB
Sep 20 at 10:17
• Then it can't be rolling "on the surface". It is rotating adjacent to the surface. Sep 20 at 10:34
• Related (meta): Exit strategies for "chameleon questions". Someone else can elaborate. Sep 20 at 13:28
• I rolledback your last edit, because you have accepted an answer and it matches the original question.
– ACB
Sep 20 at 23:36

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]

– MSKB
Sep 20 at 10:21
– ACB
Sep 20 at 10:23
• Are you implying that pure rolling cannot occur on a frictionless surface? Because that is incorrect. Sep 20 at 10:25
• @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. Sep 20 at 10:46
• 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 $$2v$$.