# If the friction coefficients depend on the object's property, why do they change in sliding & rolling, despite the object being same? [duplicate]

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I know that when you roll an object instead of sliding it reduces the friction you can easily move an object. Consider the object to have a weight $W$ on a horizontal surface and the two objects have coefficient of friction of $\mu$. Thus the friction force $f$ should be: $$f=\mu W$$ In order for the friction to change, either $\mu$ or $W$ has to change and since $W$ does not change when rolling $\mu$ changes. My question is ,$\mu$ depends on the property of the materials not their orientation or their surface area of contact. So what has changed in order for $\mu$ to change? Does $\mu$ depend on other factors. The same question for static friction $\mu_{s}$and kinetic friction $\mu_{k}.$

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## 1 Answer

When two objects are pressed together and then slid against each other there is a force which opposes the 'sliding force' called friction. This force is parallel to, and located at, the contact plane of the surfaces. It is also opposite in direction to the 'sliding force'. The part of the "moving force" which contributes to the frictional force is perpendicular to the surfaces contact and called the normal force. The amount of the frictional force is usually stated as the product of the normal force and a coefficient (usually determined empirically) called the coefficient of friction, thus your formula f=μW.

The coefficient of friction depends on many factors, for example; surface texture, composition, adhesion etc. The actual mechanism is still debated and in some cases poorly understood. For example surfaces can 'pressure weld' and breaking these welds is a major contributor to frictional forces. There has even been conjuncture that the van der Waals forces may be a contributing factor.

In the case of the rolling wheel you have your "moving force" but many of the contributing elements of the coefficient of friction are different or missing; there is no sliding, contact area is reduced to a line in the ideal case, as the wheel rolls the surfaces are separated nor rubbed, and so on. (As an aside and contrary to popular belief, mu varies with contact area. That's why drag race cars use wide tires.)

In an ideal case the value of mu can be reduced to a almost zero. For example, gears with properly formed teeth and correct lubrication. The teeth roll off each other and never slide. The oil film prevents physical contact. If a gearbox was sealed and completely free of contaminants the gears should last indefinitely.