# Coefficient of friction (mu) is not dependent on the area

1. Aug 31, 2007

### FedEx

Hi
If i am not wrong than coefficient of friction (mu) is not dependent on the area of the surface of the body in contact with other body. Then why is that rolling friction is less than static friction

2. Aug 31, 2007

### quetzalcoatl9

the coefficient of friction is not, but the frictional force certainly is dependent upon the area of contact. when rolling, the area of contact is much less, hence less frictional force.

3. Aug 31, 2007

### rcgldr

This is only true under ideal conditions, perfectly "clean", smooth surfaces, and possibly only in a vacuum. In real life you get results similar to those shown 4:45 into this video clip:

http://www.gyros.biz/lecture/wmv/2.wmv [Broken]

From this web site:

http://www.gyroscopes.org/1974lecture.asp

Under ideal conditions it's the same. If one of the surfaces is flexible, like rubber in a tire, it's virtually the same (if the tire and surface are reasonably clean). In the case of tires, even though the contact patch increases slightly with increased load, heavy loads reduce the cornering coefficient of friction (probably related to the deformation of a tire during cornering loads), which is how suspension systems are used to "tune" the handling of a car, the stiffer end gets less grip, because more downforce force is applied to the outer tire at the stiffer end.

Last edited by a moderator: May 3, 2017
4. Aug 31, 2007

### FedEx

But the frictional force is in turn dependent on the coefficient of friction

5. Aug 31, 2007

### rcgldr

My point is the coefficient of friction varies depending on the circumstances, such as contact area, pressure, cleanliness, deformation, static, ...

6. Aug 31, 2007

### quetzalcoatl9

of course the frictional coefficient is not really "constant", it is dependent upon the molecular composition of the material and it's response to the "environment".

but that is not what the OP is asking. The OP is asking why, under ideal circumstances, would the frictional force affect sliding to a greater extent that rolling (at least, that's what I think the OP is asking). my response is that the OP is confusing the coefficient of friction with the frictional force.

7. Aug 31, 2007

### FedEx

I know,but f=(mu)(normal reaction). So here f is proportional to mu. And so as mu changes f changes. And mu is independent of the area of contact. So mu sholud not be less for a rolling body according to the given concept. B ut we have that mu for rolling is always smaller than mu of sliding . So why?

Last edited: Sep 1, 2007
8. Sep 1, 2007

### quetzalcoatl9

let's take the simplest case: if there were NO area of contact, would you still have a frictional force opposing?

9. Sep 1, 2007

### Staff: Mentor

I don't think that the coefficient of static (or sliding) friction is simply related to the coefficient of rolling friction, which is largely due to the deformation of the surfaces.

10. Sep 1, 2007

### FedEx

Hi
we donot have a direct relation between coefficient of rolling and sliding friction. But we have a relation that rolling friction is less than sliding friction.

11. Sep 7, 2007

### Shooting Star

There is no direct relationship between rolling and static friction. Static friction allows one body to roll on another without slipping. Experimentally, rolling friction is always found to be less than sliding or kinetic friction, which is in turn slightly less than static friction.

The static friction is independent of the area of contact, depending only on the normal reaction. I don't really know within what limits this is valid.

12. Sep 8, 2007

### AlephZero

It's a fairly good assumption provided the stress-strain behaviour of the material stays linear (e.g. no plastic deformation), the work done by the friction doesn't abrade the surfaces (which can make them either rougher or smoother), the work converted into heat doesn't cause local chemical reactions or melting/vaporization of the material, and the relative movements are large compared with the local flexibility of the objects caused by internal stresses (e.g. for metal to metal contact and displacements of the order of 0.01mm, the friction coefficient is very amplitude dependent - bolted or riveted joints carrying large oscillating loads, for example)

In other words, for blocks of wood sliding down inclined planes in physics labs, it's OK.... but for many other situations, it's not so good.