The discussion revolves around the relationship between the tangential velocity of a point on a rolling cylinder and the velocity of its center of mass, specifically in the context of a cylinder rolling down an inclined plane. The scope includes conceptual clarification and mathematical reasoning related to rotational dynamics.
The discussion includes clarifications and challenges but does not reach a consensus on the implications of the tangential velocity in relation to the center of mass velocity.
Participants express assumptions about the definitions of terms and the conditions of rolling without slipping, but these assumptions remain unresolved.
Is ##R## the radius of the cylinder? And what do you mean by "tangential" velocity?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?
R is the radius yes and by tangential velocity I mean the linear velocity of a point on the edge of the cylinder.PeroK said:Is ##R## the radius of the cylinder? And what do you mean by "tangential" velocity?
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.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.