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Name: Nate
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 7/17/2003


Question:
There are several categories of friction commonly described in physics texts. Kinetic friction is when two surfaces slide past each other, such as a sled moving across snow.

Static friction is where the velocity between the two objects is zero, but a frictional force is still present. An example might be a stopped car on a hill.

Now I see another category called "rolling friction." I do not understand this, and do not find it in the Handbook of Chemistry and Physics, not in introductory college physics texts. It would seem to me that it is just static friction since at the point of contact, the relative motion between the item and the surface is zero.


Replies:
Nate,

I have always considered rolling friction as being related to the possible deformation that occurs when the rolling object (and surface upon which it is rolling) is deformed by the weight the rolling object bears. in other words, a tire rolling on a hard concrete surface would encounter less internal friction within the rubber polymer than it would if it were rolling on a softer asphalt surface -- which itself would experience its own internal friction within the asphalt matrix. A steel rail car wheel rolling on a work-hardened steel rail would exhibit very little deformation in either the wheel or rail. Thus, its rolling friction (friction of deformation) would be very much less than that of the tire scenario.

Regards,
ProfHoff 708


The origin of "rolling friction" is exactly what you have assumed, namely "point contact". When a ellipsoid of revolution (a sphere is a special case) is in contact with a "flat" surface there is a finite area of contact. Also on a microscopic scale, there is a depression of the "flat" surface caused by the weight of the rolling object. The forward area of contact depresses the "flat" surface. This reduces the kinetic energy of the rolling object due to an increase in potential energy of the "flat" surface due to compression. In addition, on the rear area of contact there is a further reduction in the kinetic energy of the rolling object required to break the attractive "bonds" that form between the rolling object and the "flat" surface. Two "thought" experiments help to amplify these two mechanisms:

1. Consider rolling a sphere down an incline across a "flat" bed of sponge rubber. The leading edge of the sphere "digs" into the sponge rubber, so that to continue rolling the sphere must continue to compress the sponge rubber as it rolls.

2. Now consider rolling a sphere down an incline across a "flat" bed of adhesive tape (sticky side up). The weight of the sphere forms adhesive bonds to the tape. The trailing edge of the contact must break these adhesive bonds to continue rolling.

Now consider a rolling a sphere down an incline across a "flat" bed of thick honey-like material. Here both mechanisms operate. The forward edge of the rolling sphere depressing a "wave" of honey in front of it as it rolls and the trailing edge of the rolling sphere having to break the adhesive bonding that occurs from the contact of the sphere and the tacky bed material.

You may be interested to know that the length of the trail of a sphere (usually steel or glass) rolled down an essentially friction free incline across a flat bed of adhesive is actually used to characterize the properties of adhesives in lab testing. Certain applications require a balance of these two mechanisms.

Vince Calder


You are absolutely right that there is no relative motion at the point of contact, so it is not kinetic friction. It is also not static friction since the wheel is moving, though the point of contact is not; if there were no rolling friction, the wheel would continue forever on a perfectly level surface.

Rolling friction is due mainly to the deformation of the wheel. Consider a car wheel. The tire is a little flat on the bottom. Therefore, for it to roll, a force must be exerted on the tire to deform it. If it were perfectly elastic, the tire would push forward as it reforms to its round shape. It is not perfectly elastic, however, as is shown by the fact that it gets warm as it rolls along.

There is also friction due to molecular forces holding the wheel to the surface. I believe these are unimportant for car wheels, but could be important for very smooth steel wheels rolling on a smooth steel surface, for example, or if glue is placed on the bottom of the wheel.

Incidentally, if the tire pressure in a car tire is low, the wheel deforms more. The wheel then gets hotter and the gas mileage decreases as more of the car's power goes into deforming the tire. This also explains why bicycle racers use very high pressure (90 lb/in2 or more) tires to reduce the deformation of the tire even though it makes the ride more uncomfortable.

Best, Richard J. Plano Professor of Physics emeritus, Rutgers University
Up-date July 2007
The heating of rolling tires is due to two causes. You have rubber hysteresis (the return path involves less force than the initial path), which consumes energy. But another very significant loss of enery is due to squirming of the tire. The tread surface of an automobile tire is squished inwards by the sidewalls at the contact patch. Regarding very hard surfaces, like train wheels, the rolling resistance is relatively low, considering the amount of downforce on them and their axis. Roll a billard ball (highly elastic with minmal compression, they bounce well) on a very hard surface, and it will roll quite a distance. It's the behavior of rubber hysteresis and squirm that makes it's rolling resitance relatively high.

Jeff



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