Sliding Friction - Coefficient of friction and angle of friction.

Coefficient of friction and angle of friction. When rigid bodies in contact slide one after the other, at the point of contact, with the normal force $F_N$, the bodies interact with the tangential friction forces $F_T$ as shown in the Figure 1.1.

Figure 1.1 - The reaction of rough substrate on a body at rest.

These forces are directed so as to impede mutual movement. The forces do not depend on the size of the contact surface or its shape, they depend only on the normal force $F_N$ and it is proportional to it, ie: $$F_T = \mu F_N,$$ where $\mu$ is the coefficient of friction. Therefore, the total reaction of the substrate $F$ consists of two components $F_N$ and $F_T$, and with the perpendicular to the contact surface the angle $\varphi$ is called the angle of friction.

Figure 1.2 - The base reaction on the sliding body.

According to the Figure 1.2, the angle of friction is determined by the expression: $$\begin{eqnarray} \tan \varphi &=& \frac{F_T}{F_N} = \mu. \end{eqnarray}$$