Angle of Friction

For certain applications it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the angle of friction or friction angle. It is defined as:

 Tan θ = μ

where θ is the angle from horizontal and μ is the static coefficient of friction between the objects. This formula can also be used to calculate μ from empirical measurements of the friction angle. Another way to define the friction is by the angle of the opposing force.

The friction angle θ is defined as; tan θ = F_f / F_n  so, tan θ = μ When two objects are in rough contact and friction is limiting, two contact forces act on each object; one is the normal reaction R and the other is the frictional force uR. The resultant of R and uR, which is sometimes called the resultant contact force. The angle between this resultant and the normal reaction is also called as the angle of friction The angle of repose, or more precisely the critical angle of repose, is the minimum angle made by the inclined plane with the horizontal surface such that the body lying on the inclined plane is just at the verge of sliding down along the inclined plane. When bulk granular materials are poured onto a horizontal surface, a conical pile will form. The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose and is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. Material with a low angle of repose forms flatter piles than material with a high angle of repose. In other words, the angle of repose is the angle between the surface of a pile and the ground