# Static Friction Coefficient

on . Posted in Dimensionless Numbers

Static friction coefficient, abbreviated as $$\mu_s$$ (Greek symbol mu), a dimensionless number, also called coefficient of static friction, is the amount of force required to overcome the initial resistance between two surfaces in contact before they start to slide or move relative to each other.  It's a fundamental concept in physics and engineering that characterizes the interaction between surfaces under static conditions.

The static friction coefficient varies depending on the nature of the surfaces in contact and their roughness.  Rougher surfaces generally have a higher static friction coefficient because the irregularities in the surfaces interlock and resist relative motion more effectively.  Smoother surfaces tend to have a lower static friction coefficient.

The static friction coefficient sets the threshold for whether an object will stay at rest or start moving when a force is applied to it parallel to the surface.  If the applied force is less than or equal to the product of the normal force and the static friction coefficient, the object remains at rest.  Once the applied force exceeds this threshold, the object overcomes static friction and begins to move.

The static friction coefficient is an essential consideration in various real world scenarios, such as designing machinery, calculating the force needed to initiate motion, and understanding the behavior of objects on inclined surfaces.  It's important to note that the static friction coefficient is just one aspect of the frictional interaction between surfaces, dynamic friction comes into play once the surfaces are in motion.

### Static friction coefficient formula

$$\mu_s \;=\; f_s \;/\; F_n$$     (Static Friction Coefficient)

$$f_s \;=\; \mu_s \; F_n$$

$$F_n \;=\; f_s \;/\; \mu_s$$

Symbol English Metric
$$\mu_s$$  (Greek symbol mu) = Static Friction Coefficient $$dimensionless$$ $$dimensionless$$
$$f_s$$ = Static Friction           $$lbf$$ $$N$$
$$F_n$$ = Normal Force $$lbf$$ $$N$$

Tags: Coefficient Friction