Translational and rotational velocity

AI Thread Summary
In the discussion about a cylinder rolling down an inclined plane, it is clarified that R refers to the radius of the cylinder and tangential velocity denotes the linear velocity of a point on its edge. The speed of a point on the edge of the cylinder, relative to the axis of rotation, matches the linear speed of the cylinder itself. However, the speed of that point relative to the surface varies from zero to twice the linear speed of the cylinder. Participants are encouraged to prove this concept for rolling without slipping and to create diagrams for better understanding. Understanding these velocity relationships is crucial for grasping the dynamics of rolling motion.
Josh0768
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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?
 
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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.
 

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