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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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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.

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From Rolling Circles

Weather Vane
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