Friction

Static Friction

Static friction is the resistive force between an object and its environment when the object is not moving with respect to its environment. It is represented as $\vec{f}_{s}$, and can be calculated with the following formula:

$$\vec{f_s}_{max} = \mu_s F_N$$

where $\mu_s$ is the coefficient of static friction

Static friction opposes the motion that the object would have without friction; that is to say, it acts in opposition to the applied force.

$$\text{If } \vec{F_{applied}} < \vec{f_s}_{max}, \vec{f_s} = \vec{F_{applied}}$$

The exact instant in time when static friction is overcome by the applied force is known as the slipping point, or the point of impending motion, after which kinetic friction takes its place.

Kinetic Friction

Static friction is the resistive force between an object and its environment when the object is sliding across a surface with respect to its environment. It is represented as $\vec{f}_{k}$, and can be calculated with the following formula:

$$\vec{f_k} = \mu_{k} F_{N}$$

where $\mu _{k}$ is the coefficient of kinetic friction^[1]

$\vec{f}{k}$ has one constant value^[2].

Notes

$\mu_{k}$ and $\mu _s$ are dimensionless (i.e. they do not possess units).

$\mu_{k}$ and $\mu _s$ are nearly independent of the amount of area undergoing friction

$\mu_{k}$ is nearly independent of velocity