The angle between the resultant contact force and the normal force exerted by a body on the other is called the angle of friction. Show that, if λ be the angle of friction and μ the coefficient of static friction, λ≤tan−1μ.
Assuming F be the applied force
R be the frictional force'
R be the normal force
u=tanλ=F/R
When F=μR
F is the limiting friction.
When applied force increases, force of friction increases upto limiting friction.
Before reaching limiting friction:
F<μR/F
tanλ=F/R<μR
tanλ≤μ
λ≤tan−1μ