What is the Difference Between Angle of Friction and Angle of Repose?

The angle of friction and the angle of repose are related concepts, but they have distinct differences:

• Angle of Friction: This is defined as the angle between the normal reaction force and the resultant force of the normal reaction force and friction when an object just begins to move. It is related to the static friction coefficient between an object and the surface it rests on. The angle of friction can be calculated using the formula $$\theta = \tan^{-1} \mus$$, where $$\theta$$ is the angle of friction and $$\mus$$ is the static friction coefficient.
• Angle of Repose: This is defined as the minimum angle of an inclined plane which causes an object to slide down the plane. It refers to the angle that the slopes of a stable mount of granular material forms under gravity. The angle of repose is related to the internal friction between the particles that make up the granular material, preventing them from sliding.

The main difference between the angle of friction and the angle of repose is that the angle of friction deals with the coefficient of static friction between an object and the surface it rests on, while the angle of repose deals with the static friction between the particles that make up an object preventing them from sliding. Although these concepts are related, they are distinct and should not be confused with each other.

Comparative Table: Angle of Friction vs Angle of Repose

The main difference between the angle of friction and the angle of repose lies in the way they are described and the types of surfaces they are applied to. Here is a table comparing the two concepts:

In summary, the angle of friction is defined for rigid bodies and measures the angle at which an object starts to move along a surface, while the angle of repose is defined for granular particles and measures the shallowest angle of an incline where an object starts to slide down. Although these two angles are essentially the same, given by the inverse tangent of the coefficient of friction between two surfaces, their applications and descriptions differ.