# Rotation without slipping and the direction of friction?

## Main Question or Discussion Point

sorry, this is is a general question about a conceptual definition I read in my textbook, i hope that's ok.
"an object that rolls without slipping at a constant velocity over a surface with friction experiences no frictional force"
is this true?
i understand that on a frictionless surface, the object wouldn't need any external force or torque to keep it rolling, but on a surface with friction, why would the same situation apply?

and, in addition, how does an object slip while it has angular velocity? does that mean that for every instant that a particle is in contact with the ground, it slides for an infinitesmall distance? I don't get how that could happen from a macroscopic view.

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rcgldr
Homework Helper
"an object that rolls without slipping at a constant velocity over a surface with friction experiences no frictional force" I understand that on a frictionless surface, the object wouldn't need any external force or torque to keep it rolling, but on a surface with friction, why would the same situation apply?
If an objects angular velocity is such that there is no relative motion between the object and the surface the object is "rolling" on, then there is zero "friction" force. Note that this ignores issues related to deformation, such as rolling resistance.

How does an object slip while it has angular velocity?
A common example of this would be spinning the driven tires on a car during acceleration.

If an objects angular velocity is such that there is no relative motion between the object and the surface the object is "rolling" on, then there is zero "friction" force. Note that this ignores issues related to deformation, such as rolling resistance.
yes, there is no relative motion between the object and the surface, but wouldn't there be static friction, or at least some sort of external torque to keep the object spinning?
or maybe you're right, i can understand that no relative motion means no friction, but then how would we use friction to calculate rotation without slipping? in that case, does friction only apply when the object is accelerating?

and...sorry, "driven" tires?

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WannabeNewton
If you choose your origin as say the center of mass of the object then relative to this origin the friction at the contact point will cause a torque of course. What's being said is that if the no slipping constraint is indeed imposed, there will be no relative velocity between the contact point and the ground so there will be no deceleration due to friction unlike say the case of a block sliding across a rough surface in which case friction will effect a deceleration on the block.

rcgldr
Homework Helper
yes, there is no relative motion between the object and the surface, but wouldn't there be static friction, or at least some sort of external torque to keep the object spinning?
This is an idealized situation, with no losses. The object keeps rolling at the same speed because there is zero force and zero torque on the object. In real life, the object would slow down due to rolling resistance unless there was a torque or force to counter that resistance.

"driven" tires?
"Driven tires" are the ones that are turned (driven) by the engine of a car.

"Driven tires" are the ones that are turned (driven) by the engine of a car.
ok, I get this, thank you.

What's being said is that if the no slipping constraint is indeed imposed, there will be no relative velocity between the contact point and the ground so there will be no deceleration due to friction.
so even on a surface with friction, as long as the object is rolling without slipping at a constant speed, there is no friction between the object and the surface, because there is no relative motion at the point of contact?
wait. but at the point of contact, wouldn't the particle be inclined to move in a certain direction, causing static friction in the opposite direction?

A.T.
rolling without slipping at a constant speed ... causing static friction in the opposite
If there was static friction, there would be a torque that would change the speed.

If there was static friction, there would be a torque that would change the speed.
bingo.
I think i get it a lot better now.
one last question---
if an object was rolling without slipping at constant speed on a surface with friction, it wouldn't experience any friction at all, but this situation isn't possible, because as long as an object is rolling on a surface with friction, friction would cause a torque to change the angular acceleration thus making it impossible for rolling without slipping...is this right?
no. wait. then...how would anything be able to roll without slipping if there was no external force...i'm never going to really get it, am i...