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In rolling without slipping motion we know that the friction acting is static friction and so we treat it as an unknown while solving equations of dynamics.

Question: Is the static friction during pure rolling the same as rolling friction?

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Rolling friction result from for example small changes in the surface or in the wheel material (the rubber in a tire).

The surface is not perfectly flat and rigid so there will be some small forces trying to stop the rotating motion:

enter image description here
(source: davidson.edu)

On the contrary, the static friction is not trying to stop the rotation of the wheel.

Static and rolling friction are different things.

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No.

Rolling friction is the fraction of resistive force to normal load. It is a fudge factor, lumping all rolling related resistances into one dimensionless value. This applies to rolling only.

Static friction is a measurable quantity relating to the maximum resistance an interface provides before sliding occurs. This applies to sticking only.

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