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So, let's take the situation where a perfect cylinder or ball is rolling, without slipping, to the right. The ball is rolling clockwise from our perspective viewing it rolling to our right.

There's a static friction force at the point of contact, preventing relative motion of the instantaneous point of contact.

From the center of mass perspective, this friction force is the only horizontal force (and the only net force) on the rolling object. So, it slows down and stops.

From the torque about the center of mass perspective, this friction force exerts a torque about the C.O.M. The direction of this torque would increase the angular velocity in the counter-clockwise direction — so the ball would increase in linear speed if this were true.

I suspect the paradox is trying to evaluate the torque about the C.O.M when the fixed point of rotation is elsewhere? Is there a pseudo-torque? Do truly ideal balls never stop rolling?

The math works itself out from either perspective if there's an incline...

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closed as unclear what you're asking by Steeven, sammy gerbil, Jon Custer, Anders Sandberg, AccidentalFourierTransform Jul 30 '18 at 16:26

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  • $\begingroup$ Something is wrong here: "a perfect cylinder or ball is rolling, without slipping, to the right. The ball is rolling counter-clockwise from our perspective viewing it rolling to our right." If it rolls without slipping, then it must roll clockwise while moving rightwards. Were it rolling counter-clockwise while moving rightwards, then it would be sliding (not rolling). $\endgroup$ – Steeven Jul 26 '18 at 6:14
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    $\begingroup$ A diagram would be helpful. $\endgroup$ – Krishnanand J Jul 26 '18 at 6:14
  • $\begingroup$ Right, edited to correct counter-clockwise to clockwise. It is rolling without slipping. $\endgroup$ – sulliOS Jul 26 '18 at 14:26
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Your false assumption is that there is a non-zero static friction force at the point of contact.

If an ideal ball is rolling at a constant velocity on an ideal level surface with no rolling resistance, then there is no friction force. The surface's only function is to provide a normal force to prevent the ball from falling due to gravity.

If there is no gravity, then the surface is not needed and the ball will simply translate to the right while spinning at a constant angular velocity.

For ideal contact, the friction force will only exist if the ball is accelerating (such as with the inclined surface that you mentioned).

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  • $\begingroup$ You know what, I buy this. The ideal ball in ideal contact wouldn't stop. Real rolling objects come to a stop due to non-ideal effects. Thanks James. $\endgroup$ – sulliOS Jul 26 '18 at 14:30

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