Fig. 1

• It is defined as the angle which the resultant of the normal reaction and limiting force of friction makes with the normal reaction.

• With reference to Fig.1.

         Let;     R= Normal Reaction

                     F= Limiting force of friction

                    $S=\sqrt{R^2+F^2}=\ Total\ or \ Resultant\ reaction$

                    $tan \phi =\dfrac{F}{R}\\ where, \ \phi \ is \ angle\ of\ friction$

• The ratio of F/R is also called the coefficient of friction,

               $\mu =tan \phi $

• The angle of friction ($\phi$) is measure of the limiting position of total reaction between the two contacting surfaces.

Fig. 2

• Consider a block of weight W resting on an inclined plane making an angle$\alpha $ with the horiziontal.
• Let the angle$\alpha $ be increased gradually till the block is just at the point of sliding. The block is then in equilibrium state under the influence of following set of forces:

1. Weight W of the block acting vertically downward.
2. Normal reaction R acting at right angles to the inclined plane, and
3. Limiting forces of friction$F=\mu R$ acting up the plane as the block is to slide downwards

Resolving these forces along and perpendicular to the plane

$\mu R=Wsin \alpha \\ R=Wcos \alpha $

• These two expressions gives:$\mu =tan \alpha $
• In terms of