**Laws of Frction**

The limiting (or maximum) force of friction is proportional to the normal force that keeps the 2 forces in contact with each other, and is independent of the area of contact between the 2 surfaces. Mathematically

f_{max} = μN

**Properties of friction**

- If the body does not move, then the static frictional fore f
_{s}and the external force F parallel to the surface are equal in magnitude and f_{s}is directed to the opposite to F. If the external force F increases then f_{s}also increases. - The maximum value of static friction is given by

f_{s}_{(max)} = μ_{s}N Here, μ_{s }is the static coefficient of friction and N is the magnitude of the normal reaction. If the external force F exceeds f_{s}_{(max) }then the body slides on the surface.

- If the body begins to slide along the surface then, the magnitude of the frictional force rapidly decreases to a constant value of f
_{k}given by

f_{k} = μ_{k}N Here, μ_{k }is the coefficient of kinetic friction.

**Angle of Friction**

It is the angle which the resultant of the limiting friction and the normal reaction makes with the normal reaction i.e μ_{s} = tan θ, where θ is the angle of friction.

**Angle of Repose**

It is the minimum angle that an inclined plane makes with the horizontal when a body placed on it just begins to slide down. If φ is the angle of repose, then tan φ = μ_{s}. Angle of repose (φ) = Angle of friction (θ)