Definition:Friction/Coefficient
Definition
Let $B$ be a body at rest on a plane surface $S$ on which friction acts.
Let $N$ be the normal reaction of $S$ on $B$.
Let a force be applied to $B$ parallel to $S$.
Coefficient of Static Friction
Let $F$ be the magnitude of that force in the limiting case when $B$ is just about to move.
Then the coefficient of static friction is defined and denoted:
- $\mu_s = \dfrac F N$
Coefficient of Kinetic Friction
Let $F$ be the magnitude of that force needed to keep $B$ moving at a constant velocity.
Then the coefficient of kinetic friction is defined and denoted:
- $\mu_k = \dfrac F N$
These coefficients of friction depend upon the materials out of which $B$ and $S$ are made.
It is usual for $\mu_s$ to be greater than $\mu_k$.
It is noted that the coefficients of friction is independent of the area of contact between the two materials.
Also see
- Results about coefficients of friction can be found here.
Linguistic Note
The word friction comes from the Latin word for rub.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): coefficient of friction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coefficient of friction
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): coefficient of friction
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): friction
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): coefficient of friction
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): friction (frictional force)