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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.^[ref]

In the horizontal $2\mathrm{kg}$ example, an observed state balancing a $2\mathrm{N}$ pull would only establish ${\mu }_s\ge 2/19.6\simeq 0.10204$ 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.

At the final state of the slump test for yield stress, an axisymmetric deposit of height $h(r)$ is just able to support itself. Hydrostatic pressure gives radial pressure gradient $\rho g{h}^{\prime }(r)$, while lubrication theory makes the magnitude of the basal shear stressThe marginally yielded final profile therefore satisfiesIntegration givesUsing mass conservation, the known volume isSolving for the yield stress produces the estimateThus one measures the final radius $R$ and inserts it with $V$ and $\rho$. The estimate assumes a thin deposit, negligible surface tension, complete initial yielding, and a spatially uniform yield stress.

Dry sand is a granular material governed primarily by frictional stability. Its final free surface reaches the angle of repose ${\theta }_r$, so the deposit is approximately a cone,This constant-slope profile differs from the square-root edge of the yield-stress-fluid model.