# Translational and rotational velocity

Josh0768
For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?

## Answers and Replies

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For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
Is ##R## the radius of the cylinder? And what do you mean by "tangential" velocity?

Josh0768
Is ##R## the radius of the cylinder? And what do you mean by "tangential" velocity?
R is the radius yes and by tangential velocity I mean the linear velocity of a point on the edge of the cylinder.

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R is the radius yes and by tangential velocity I mean the linear velocity of a point on the edge of the cylinder.
The speed of a point on the edge of the cylinder relative to the axis of rotation is the same as the linear speed of the cylinder.

Exercise: prove this for rolling without slipping.

The speed of a point on the edge of the cylinder relative to the surface, therefore, varies from ##0## to twice the linear speed of the cylinder.

Exercise: draw a diagram to convince yourself of this.