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- Thread starter Josh0768
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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.

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Is ##R## the radius of the cylinder? And what do you mean by "tangential" velocity?Josh0768 said:

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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?

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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.

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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