Suppose a body is placed on an inclined surface whose angle of inclination q varies between 0 to p/2. The coefficient of friction between the body and the surface is µ. Let the initial value of q be zero and if we slowly start increasing the value of q, then at a particular value of q = f the block just starts to move. This value of q =f is called the angle of friction.
Mathematically, if the block is just about to move, then
mg sin q = f
When q = f, mg sin f =fmax
or mg sin f = µN = µmg cos f
or tanf = µ
Thus f = tan-1µ
The angle of friction is that minimum angle of inclination of the inclined plane at which a body placed at rest on the inclined plane is about to slide down.
When q £ f (or tan‑1µ) the body is in equilibrium.
When the angle of inclination is more than the angle of friction (q > f) the block starts sliding down with acceleration. And, if we wish to keep it in equilibrium an external force has to be applied.
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