Rolling Friction: Understanding the Catch

[Tin]

I'm not sure whether I understood rolling friction properly. First, I'll assume that both surface and the body are completely rigid (no deformations of body nor surface will happen, thus vector N won't be dislocated creating an opposite momentum). So, rolling friction (assuming there is friction between the body and surface) will only "act" if the velocity of any point on the body rotating is not the same in magnitude as the velocity of the center of the mass (motion including both rotating and translating) because then the contact point of the body and the surface is not equal to zero, meaning that the rolling friction will only "act" until those two speeds (velocities) hit the same value and that point of contact will not be moving. Few friends of mine said that the rolling friction is present at all times (assuming that there is friction between the body and surface), but that doesn't make sense to me because then there would be a ∑F≠0 and the body would've had an acceleration that would've slowed the motion of the CM down. So, where's the catch?

 

[Dale]

First, I'll assume that both surface and the body are completely rigid (no deformations of body nor surface will happen, thus vector N won't be dislocated creating an opposite momentum).

I think this assumption is incompatible with rolling friction.

 

[Tin]

I think this assumption is incompatible with rolling friction.

I'm aware of that, but this is more of a conceptual question, we neglect other effects all the time in some of the easier calculations, for example ignoring friction, air resistance, etc. I'm aware that avoiding deformations in actual world is impossible, but in a shell of basic mechanics I'd say that's plausible.

 

[PeroK]

I'm not sure whether I understood rolling friction properly. First, I'll assume that both surface and the body are completely rigid (no deformations of body nor surface will happen, thus vector N won't be dislocated creating an opposite momentum). So, rolling friction (assuming there is friction between the body and surface) will only "act" if the velocity of any point on the body rotating is not the same in magnitude as the velocity of the center of the mass (motion including both rotating and translating) because then the contact point of the body and the surface is not equal to zero, meaning that the rolling friction will only "act" until those two speeds (velocities) hit the same value and that point of contact will not be moving. Few friends of mine said that the rolling friction is present at all times (assuming that there is friction between the body and surface), but that doesn't make sense to me because then there would be a ∑F≠0 and the body would've had an acceleration that would've slowed the motion of the CM down. So, where's the catch?

There's a difference between friction "being present" and friction "acting". Just imagine an object at rest on a flat surface.

There's also a difference between friction acting and friction doing work. Imagine an object a rest on a slight slope where gravity down the slope is less than the maximum static friction. Gravity and friction are both acting on the object, but neither does any work.

When something is rolling without slipping it means that, as I think you've understood, the rotational speed of the object's rim is the same as the speed of its centre of mass. When the rim touches the surface it is instantaneously at rest and friction neither acts not does any work. But, I;d say, friction is still "present" in the sense that it has the potential to act beween those two surfaces.

Finally, consider something rolling without slipping on a frictional surface, which then becomes a non-frictional surface. The object keeps rolling. It doesn't need friction to keep rolling. That shows that friction does not need to be present for something to keep rolling.

 

[Dale]

we neglect other effects all the time in some of the easier calculations

Sure, I have no problem with that. I do that all the time too. But you can't "assume it stays dry" if you want to study "what happens when it gets wet".

There is a bit of an art to picking assumptions. You want to pick ones that simplify your calculations but still leave the essence of the problem intact. I think this assumption negates the very thing you want to study.

This link explains how the assumption of rigidity is incompatible with the phenomenon of rolling resistance.

http://www.real-world-physics-problems.com/rolling-resistance.html

 

[Nidum]

 

[Tin]

@PeroK First of all thanks for the reply. I am aware that work is defined as ∫F⋅dr and in case of the contact patch having a velocity=0, meaning that even the dr is 0 so no work is being done (the point is not moving). And yes, that was my question in fact, that it is "present" at all times, but it is not "acting" at all moments (when the velocity of CM is as same as the velocity of the rotation). Also, as English is not my first language, I'm not sure if I'm using the term of velocity properly here. In my language, speed and velocity have the same meaning. I know that speed is the magnitude of the velocity (at least in a of time dt), so I'm not sure whether I'm using it properly here. Maybe I should've said that the velocity of the rotation at the point of contact has the same speed (magnitude), but the opposite direction. And yes, I thought about that. For example, I could spin a wheel with some speed and then "launch" it on ice (as if there was friction between the wheel and ice) with a starting velocity same as the velocity of the rotation, then it would roll without slipping, right?

@Dale Thanks for the reply as well. At the moment I'm not trying to apply this into the actual world situations, I'm just thinking of some concepts, but I do get your point. Deformations are not something that I could ignore because as you said, But you can't "assume it stays dry" if you want to study "what happens when it gets wet". Friction and air resistance are some things that will only change your calculations a bit (or a lot, depending on the given situation), but deformations here are something that is simply in the core of the rolling itself, if that's what you meant. I'm aware that in the actual world where something like this is unavoidable.

 

[PeroK]

@PeroK First of all thanks for the reply. I am aware that work is defined as ∫F⋅dr and in case of the contact patch having a velocity=0, meaning that even the dr is 0 so no work is being done (the point is not moving). And yes, that was my question in fact, that it is "present" at all times, but it is not "acting" at all moments (when the velocity of CM is as same as the velocity of the rotation). Also, as English is not my first language, I'm not sure if I'm using the term of velocity properly here. In my language, speed and velocity have the same meaning. I know that speed is the magnitude of the velocity (at least in a of time dt), so I'm not sure whether I'm using it properly here. Maybe I should've said that the velocity of the rotation at the point of contact has the same speed (magnitude), but the opposite direction. And yes, I thought about that. For example, I could spin a wheel with some speed and then "launch" it on ice (as if there was friction between the wheel and ice) with a starting velocity same as the velocity of the rotation, then it would roll without slipping, right?

First, about speed and velocity. Speed is the magnitude of the velocity. Velocity is a vector quantity and has a direction. I only used the word speed, because a point on the rim has a constant speed of rotation (relative to centre of mass). I think you understand this.

In answer to your question, if launched on ice with the right combination of linear and rotational motion, an object would roll (as it would on a frictional surface). But, of course, if it was slipping on the ice, it would remain slipping (assuming no friction); whereas, if it was slipping on a frictional surface, the excess linear motion would be converted by the friction into additional rotational motion until the rolling with slipping equilibrium is established. Or, of course, the excess rotational motion would be converted to linear motion.

 

[Dale]

Deformations are not something that I could ignore because as you said, But you can't "assume it stays dry" if you want to study "what happens when it gets wet".

Yes,exactly. Here are a couple of links that might be helpful.

http://www.real-world-physics-problems.com/rolling-resistance.html

https://www.lhup.edu/~dsimanek/scenario/rolling.htm

 

[sophiecentaur]

There was no comment attached to this picture so I'm not sure what message was intended but there would always be some sliding friction as the gear moves along the rack because the paths along the two mating surfaces are different lengths.