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# Angle and Cone of friction

The relationship between the Angle and Cone of Friction

## Description

Engineers often refer to either the coefficient of friction or the angle of friction. This section describes their relationship and goes on to explain the Cone of friction:

Let R be the normal reaction at a point of contact O and F the frictional force acting in a direction perpendicular to R. Then the total force at O is given by
$\sqrt[]{R^2&space;+&space;F^2}$
acting in a direction making an angle
$tan^{-1}\left(&space;\frac{F}{R}&space;\right)$
with the normal reaction.

If friction is limiting, $\inline&space;&space;F&space;=&space;\mu\:R$ and the action at O makes an angle of $\inline&space;&space;tan^{-1}&space;\mu$ with the normal reaction. This angle is denoted by $\inline&space;\lambda$.

Thus
$\mu&space;=&space;tan\:\lambda$
and the magnitude of the limiting friction can be found if either $\inline&space;&space;\mu$ or $\inline&space;&space;\lambda$ is known.

If the direction in which the body tends to move is varied the the force of limiting friction will always lie in the plane through O perpendicular to the normal reaction and the direction of the total action at O will always lie 0n a cone with it's vertex at O and axis along the line of the normal reaction. The semi vertical angle will be $\inline&space;&space;\lambda$

This cone is called the cone of friction. If friction is not limiting, the angle made by the total action at O will be less than $\inline&space;&space;\lambda$. Hence whether the friction be limiting or not, the direction of the total action at O must be inside or on the cone of friction. It follows that if P is the resultant of the other forces acting on the body which is in equilibrium, the direction of P must lie inside or on the cone o friction, since P must balance the total action at O