Translational and rotational velocity

• Josh0768
In summary, for a cylinder rolling down an inclined plane, the tangential velocity of a point at a distance R from the axis of rotation is equal to the velocity of the center of mass. This means that the speed of a point on the edge of the cylinder relative to the axis of rotation is equal to the linear speed of the cylinder. This can be proven for rolling without slipping, and the speed of a point on the edge of the cylinder relative to the surface varies from 0 to twice the linear speed of the cylinder. Drawing a diagram can help visualize this concept.

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?

Josh0768 said:
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?

PeroK said:
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.

Josh0768 said:
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.