Angle of friction; laws of static friction

Angle of friction

The angle of friction φ is the angle between the normal reaction N and the resultant R of the normal reaction and the limiting friction force F_max. At the point of impending motion, tan φ = F_max / N = μₛ, so φ = tan⁻¹ μₛ.

        N
        ^   /R
        |  /
        | / φ
 -------+/-------> F_max

A body on an inclined plane is just on the point of sliding when the angle of the incline equals φ (angle of repose).

Laws of static friction

1. The friction force always acts opposite to the direction of the impending motion.
2. Friction is self-adjusting: it equals the applied force until the limit is reached, so F ≤ μₛN.
3. The limiting friction is proportional to the normal reaction: F_max = μₛN.
4. It is independent of the area of contact.
5. It depends on the nature and roughness of the surfaces, which give the value of μₛ.
6. When motion starts, the friction force drops to the kinetic value μₖN (μₖ < μₛ).