# Impact of speed on the coefficient of rolling friction

• e2m2a
No. The rolling resistance would be different because the deformation of the surfaces and energy loss due to heat generation would be different. In summary, the object rolls on four fixed caster wheels that are made of some kind of rigid material. The object at one time attains a maximum velocity of about .5 meters per second. In another phase of the experiment the object attains a maximum velocity of about 1.2 meters per second. The change in velocity of the object from about .5 meters per second to 1.2 meters per second has no appreciable impact on the coefficient of rolling friction of the wheels or would the coefficient be relatively constant?f

#### e2m2a

I have conducted an experiment that measures the velocity of an object that is moving on a flat surface. The object rolls on four fixed caster wheels. The wheels are made of some kind of rigid material. Maybe nylon, maybe hard rubber. The total mass of the object, including the wheels, is about 1.5 kilograms. In the experiment the object at one time attains a maximum velocity of about .5 meters per second. In another phase of the experiment the object attains a maximum velocity of about 1.2 meters per second. My question is this: Will the change in velocity of the object from about .5 meters per second to 1.2 meters per second have any appreciable impact on the coefficient of rolling friction of the wheels or would the coefficient be relatively constant? Or would the change in speed of the object or the range of the speed of the object have to be much larger to have any appreciable effect on the coefficient of rolling friction?

What's a coefficient of rolling friction? Do you mean like bearing friction? What kind of bearings do the wheels have? High quality bearings will not have much of a difference in friction versus a reasonable speed range. Cheap or poorly-fitting bearings will "rattle" more at higher speeds, which could increase the bearing friction effects.

What's a coefficient of rolling friction? Do you mean like bearing friction? What kind of bearings do the wheels have? High quality bearings will not have much of a difference in friction versus a reasonable speed range. Cheap or poorly-fitting bearings will "rattle" more at higher speeds, which could increase the bearing friction effects.
I mean the friction due to the wheel in contact with the surface as it rolls along the flat surface. My understanding is this friction is actually due to some kind of deformation of the surface and wheel as they make contact. This deformation "moves" with the wheel and remains pretty much constant. More specifically, I am asking would this friction between the wheel and the surface be constant for the case when the wheels begin at rest and reach a max velocity of .5 m/s and for the case when the wheels begin at rest and reach a max velocity of 1.2 m/s? In both cases would the friction between the wheel and the surface be the same?

I mean the friction due to the wheel in contact with the surface as it rolls along the flat surface.
It sounds like you are wondering about "rolling resistance", which is not really a friction effect:

https://en.wikipedia.org/wiki/Rolling_resistance

I don't see speed as a variable in that Wikipedia article about the things that affect rolling resistance...

The reference you gave me brings up an interesting point. Friction technically refers to forces that arise when there is relative motion between two surfaces. But in the case of a wheel rolling on a surface where there is no slipping, there is no relative motion. The wheel is instantly at rest with respect to the surface. So the resistance has to be due to a differenct phenomena as the article points out: deformation of surfaces and energy loss due to heat generation.

I bring this up because I conducted an experiment which involved measuring the maximum velocity of an object due to an external force applied to the object In case one the object with wheels began at rest and attained a final velocity of about .5 m/s. In the second case the same object with wheels began at rest and attained a final velocity of about 1.2 m/s. A "critic" of the experiment pointed out that I did not account for the increase in rolling resistance for the second case which might be significant. Could this be possible? At speeds of .5 and 1.5 m/s, could these two results result in any appreciably change in rolling resistance?

I conducted an experiment which involved measuring the maximum velocity of an object due to an external force applied to the object In case one the object with wheels began at rest and attained a final velocity of about .5 m/s. In the second case the same object with wheels began at rest and attained a final velocity of about 1.2 m/s.
So the applied forces were different to get to the two different terminal velocities? How were these constant forces applied?

Yes. There were two different applied forces. In the second case there was more force applied then the first case, but this should not change the rolling resistance, right? The rolling resistance would effectively be the same, right? They were not constant forces in each case.

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The rolling resistance would effectively be the same, right?
Yes, I believe so. In modeling cars and motorcycles, for example, the retarding forces that limit velocity are rolling resistance (which is constant with velocity to a first order), bearing friction (which may be included in rolling resistance), and air resistance (which does depend on velocity).

ok. thanks.

My understanding is this friction is actually due to some kind of deformation of the surface and wheel as they make contact. This deformation "moves" with the wheel and remains pretty much constant

This deformation it self does not produce rolling resistance. The resistance is produced due to internal damping of the materials. The vertical forces behind the wheels are a little smaller than those in front of them. So a little braking torque is produced. The damping I mentioned above depends on the velocity of the materials deformation, but I suppose that it can't be noticeable at your experiment.

P.S. there is one more phenomenon that produces the rolling resistance

What is the other phenomenon. Interested.

The contact surface, is not linear, but somewhat flattened. To make it more simple to explain, let's suppose that the floor is undeformable.

Supposing you stand on the moving object, the wheel points should have a relative velocity u = ω * R. The R of the wheel point in contact whit the floor is variable (because the wheel is deformed at that area). So, the velocity of the wheel contact point "i" is not ui = - u, as it should supposed to be in order to have no friction. Its velocity is ui = ω * Ri
There is only one line on the contact surface that there is clear rolling. On the rest surface there exist sliding friction.

I hope I wrote it in understandable manner...

Well, this phenomenon is more complicated than I thought originally. Thanks for the insight.