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?

 

[PeroK]

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.

 

[PeroK]

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.