Define limiting friction, angle of friction, coefficients

Limiting friction

The maximum value of the static friction force that can be developed between two surfaces in contact, just when sliding is about to begin (impending motion). F_max = μₛ N, where N is the normal reaction. If the applied force exceeds it, motion starts.

Angle of friction (φ)

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

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

Coefficient of static friction (μₛ)

The ratio of the limiting friction force to the normal reaction when the body is just about to slide: μₛ = F_max / N. It depends on the materials and the surface condition, not on the area of contact.

Coefficient of dynamic (kinetic) friction (μₖ)

The ratio of the friction force to the normal reaction when the body is sliding: μₖ = F_k / N. It is slightly less than μₛ, and nearly independent of speed at low speeds.