Question

What is the basic difference between angle of friction and angle of repose?

Answer 1

,Angle of Friction is the angle between the normal force (N) and the resultant force (R) of normal force and friction. Angle of Repose is the angle of maximum slope, where an object placed just begins to slide. Angle of friction is applicable between the rigid surfaces.
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Answer 2

Suppose angle of friction = alpha and angle of repose = theta

Let us suppose a body is placed on an inclined plane as in the above figure.

Various forces involved are:-

1. weight,mg of the body,acting vertically downwards.

2.normal reaction,R,acting perpendicular to inclined plane.

3.Force of friction,F, acting up the plane.

Now, mg can be resolved in two components:-

mgcos theta opposite to R

and mgsin theta opposite to F

In equilibrium,

F = mgsin theta -------- eq.1

R = mgcos theta ---------eq.2

On dividing eq.1 by eq.2 we get,

F/R = mgsin theta/mgcos theta

mu = tan theta