Friction - Aetherwisp

Friction is a Dissipative force between two objects that occurs when one objects slides over the surface of the other. Typically, the second object is static. This force is tangent to the surface and opposes motion. Its magnitude is assumed to be proportional to the normal force between the objects (usually weight) and independent of both the area of contact and the velocity of the moving object once it is in motion.

Mathematically, dynamic friction can be described as

\mathbf{F}=\begin{cases} -c_{k} \frac{\mathbf{v}}{|\mathbf{v}|}, \quad &\mathbf{v}\neq0 \\ 0,\quad &\mathbf{v}=0 \end{cases}

where $c_{k}$ is called the coefficient of dynamic friction. The coefficient is the ratio between the magnitudes of the friction and the normal force, $c_{k}=F_{friction}/F_{normal}$ , multiplied by a unit constant to make the units of measurements those of a force.

It is also known that an object also requires a minimum force to start sliding; if it didn't, every surface would feel like slippery ice. This obstruction to movement from a standstill is called static friction and is modeled in the same way as dynamic friction. The difference is that static friction is dependent on a different parameter, called the coefficient of static friction, $c_{s}$ , which is equal to the ration of the maximum frictional force over the normal, $c_{s}=\max (F_{friction})/F_{normal}$ . It also only occurs when the object is static; when it begins moving, friction becomes dynamic.