# Angle of Friction

## (5) Angle of friction

- It is the angle which the normal force N makes with the contact force when the equilibrium is limiting i.e when the condition of maximum Static friction
is reached

- Consider a block of mass "m" resting on a horizontal surface .Weight W=mg of this block is balanced by the normal force (N) of reaction as shown below in
the figure.

Mathematically

W=mg=-N
- if F is the contact force which each body exerts on the another body then this contact force can be resolved into two components

- Perpendicular Components which is normal force N

- Components parallel to the contact surface known as friction which is usually denoted by the f
_{s},f_{k} or f_{ms}

- Angle BCD represented by λ is angle of friction

Since N and f_{ms} are components of the contact force F,so we can write

Fcosλ=N

and Fsinλ=f_{ms}

or we can say

tanλ=f_{ms}/N

Also from the definition of static friction we know that

f_{ms}=μ_{s}N
So tan λ=μ_{s}

Thus we can conclude that coefficient of static friction is equal to the tangent of the angle of friction

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