# Amontons' first law of friction

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## Name

This law is sometimes termed Amontons' first law of friction after Guillaume Amontons, but is often attributed to Leonardo da Vinci, and is hence sometimes termed Leonardo da Vinci's law of friction. Often, the law is studied without an explicit name, but rather, by its statement.

## Statement

The friction force experienced by two dry bodies whose planar surfaces are in contact is independent of the area of contact between the bodies.

Amonton's first law of friction is implicit in the Coulomb model of friction, and is closely related to Amonton's second law of friction, which says that the friction force is (limiting value for static friction, actual value for kinetic friction) proportional to the normal force.

## Apparent counterexamples

Formulation of apparent counterexample Resolution Possible empirical tests
Rolling a wheel is easier than dragging a box of the same weight and material Rolling is a fundamentally different operation from dragging because there is no slipping at the surface of contact (so static friction operates). Dragging a wheel is just as hard as dragging a box  ?
With the same material, the same type of surface, and the same shape, objects with larger area encounter more friction Area is related to volume (assuming a similar shape), which is related to mass (assuming the same density), which is related to weight (since $g$ is the same), which in turn affects the normal force experienced to balance the weight, which then affects the friction force that can operate. Same object, same kind of surface, different sides of different areas; for more, expand below.
In case of multiple supports, the support with larger contact area contributes more in friction The larger contact area, as well as further geometrical details, affect the relative distribution of the normal force. It is not the contact area per se that is playing a role.

Below are more details of these apparent counterexamples.