Angle of friction
Given two surfaces, the angle of friction (sometimes also termed the angle of repose, though that term has another meaning in a related context) between the two surfaces is defined numerically as:
where is the limiting coefficient of static friction.
Here, is the arc tangent function, i.e., is the acute angle such that .
It can be defined in the following ways:
- It is the angle that a fixed inclined plane made up of one surface must make with the horizontal so that a body with the second surfaces placed on it just starts slipping. In other words, for any angle smaller than , slipping does not begin on its own and for any angle larger than , slipping begins on its own. Further information: sliding motion along an inclined plane
- Consider a block placed on a fixed horizontal plane such that the surfaces of contact are the two desired surfaces. Then, is the angle such that the force needed to pull the block in a particular horizontal direction is minimum if the block is pulled at an angle with that horizontal direction.
For more information about motion on an inclined plane, refer sliding motion along an inclined plane.
The angle of friction is a strictly increasing function of the limiting coefficient of static friction , taking the value for the case and approaching the value as .
Range of values
|First surface||Second surface||Condition||(radians)||(degrees)||(radians)||(degrees)|
|Aluminimum||Mild steel||Dry and clean|
|Aluminimum||Aluminimum||Dry and clean|
|Copper||Steel||Dry and clean|
|Copper||Copper||Dry and clean||?||?||?|
|Wood||Concrete||Dry and clean||?||?||?|
|Wood||Metal||Dry and clean||?||?||?|
|Wood||Wood||Dry and clean||?||?||?|
|Mild steel||Mild steel||Dry and clean|
|Hard steel||Hard steel||Dry and clean|
- MIT OCW lecture on friction by Walter Lewin does not explicitly introduce the term "angle of friction" but derives the expression for it and also demonstrates an experiment to calculate it (time interval: 02:24 -- 08:58; continue on for more)