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tbn032

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rolling friction

rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and R is radius of sphere and w in angular velocity).It increases the angular acceleration and decreases the translational velocity or vice versa till the condition v=Rw is reached.

Rolling resistance

Rolling resistance is the counter torque provided to the rolling object due to the deformation of the object or the surface, causing the normal forces to shift from the centre of mass and thus providing counter torque.

Now my question is.

Suppose a non deforming sphere of radius R initially is kept on a non deforming rough horizontal surface(frictional surface). Then it is provided with translation velocity v and angular velocity w such that v=Rw.will the static frictional force(rolling friction) be applied on the sphere?will the sphere continue to roll forever?(there is no air resistance and there is no rolling resistance due to non deforming sphere and non deforming horizontal surface)(gravitational forces acts on the sphere perpendicular to the horizontal surface)