Angle of Repose (Or) Angle of Sliding
The angle of repose or angle of sliding is defined as the minimum angle of inclination of a plane with the horizontal such that a body placed on the plane just begins to slide down. Its value depends on the material and nature of the surfaces in contact.
From the above figure we can say that, AB is an inclined plane such that a body placed on it just begins to slide down. ∠BAC = α = Angle of repose.
The various force involved are:
1. Weight (mg), of the body acting vertically downwards.
2. Normal reaction (RN), acting perpendicular to AB.
3. Force of friction (F), acting upon the plane AB.
Now, mg can resolve into two rectangular components: mg cosα opposite to R and mg sinα opposite to F. In equilibrium:
F = mg sinα … (1)
N = mg cosα … (2)
Dividing equations (1) by (2), we get: f/ N = mg sinα/ mg cos α = µ,
i.e. µ = tanα
Hence, the coefficient of limiting friction between any two surfaces in contact is equal to the tangent of the angle of repose between them.