The discussion clarifies the relationship between tangential velocity and the velocity of the center of mass for a cylinder rolling down an inclined plane. It establishes that the tangential velocity of a point at distance R from the axis of rotation is equal to the linear speed of the cylinder. Additionally, it highlights that the speed of a point on the edge of the cylinder varies from 0 to twice the linear speed of the cylinder, emphasizing the concept of rolling without slipping. Exercises are suggested to reinforce understanding through proof and diagrammatic representation.
PREREQUISITESPhysics students, mechanical engineers, and educators seeking to deepen their understanding of rotational motion and dynamics, particularly in the context of rolling objects.
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.