Rolling friction on a horizontal surface

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Rolling friction is only necessary at the initiation of motion for a cylindrical rod rolling on a horizontal surface. Once the push is removed, the rod experiences only gravitational and normal forces. If the surface becomes frictionless after the rod starts rolling, it can maintain a constant linear velocity and angular velocity indefinitely. The relationship between linear velocity and angular velocity remains valid as long as there is no slipping. Thus, rolling friction is not needed to sustain motion once it has begun.
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Suppose a cylindrical rod is given a push such that it rolls without slipping on a horizontal plane. Am I right to say that rolling friction is only required at the start when the push is applied to initiate the rolling motion? Once the push is removed, the only forces acting on the rod are its weight and normal contact force? So the rod could continue rolling indefinitely at the same velocity ##v## and the same angular velocity ##\omega## without slipping (with ##v=r\omega##) if the plane is replaced by a frictionless one after rolling begins?
 
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Yes, that's correct.
 
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