= Coefficient of static friction
{title2=$\mu_s$}
= Granular friction coefficient
{synonym}
The <coefficient of static friction> is the nonnegative <dimensionless quantity> $\mu_s=|f_s|_{\max}/N$, with $N>0$, in the ideal dry-contact model. It characterizes the pair of surfaces under specified conditions. It describes the largest supported tangential <force>, whereas the <coefficient of kinetic friction> describes sliding. It is an empirical approximation, not a universal material constant.<University Physics Volume 1 by William Moebs and others/6.2 Friction>[Equations 6.1–6.2; unitless coefficient and dependence on both surfaces; empirical-law limitations immediately before Example 6.10]{ref}
In the horizontal $2\,\mathrm{kg}$ example, an observed state balancing a $2\,\mathrm N$ pull would only establish $\mu_s\ge2/19.6\simeq0.10204$ under the model assumptions. It would not establish $\mu_s=0.10204$: the actual <static friction> is below its limit. Identifying the coefficient needs an onset measurement, such as <inclined-plane measurement of static friction>, or the starting peak in a suitably controlled horizontal pull. The sustained sliding part of <constant-speed measurement of kinetic friction> measures a different coefficient.
In a simple grain model, the existing name <granular friction coefficient> represents resistance to downstream motion. That model excludes lift and detailed contact <torques>. Its coefficient should not automatically be identified with a bulk pile's <angle of repose>: individual contact geometry and collective rearrangement can matter.
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