Macroscopic diagnostics of microscopic friction phenomena

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on a horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Coulomb friction laws alone, instead it depends on the microscopic details of friction. Hence, we conclude that the macroscopic experiment presented here reveals details about the microscopic processes lying behind friction.

Figure 1

Schematic view of the experiment: a uniform disk of radius $R$ lies on a flat horizontal surface and is subject to an applied torque $\mathbf{T}=2R\mathbf{K}$ and force $\mathbf{F}$.

Figure 2

Measured values of torque and force for a wooden $(+)$ and plastic (◻) disk as a function of the dimensionless variables $\mathcal{F}=F∕{\mu }_{s}N$ and $\mathcal{T}=T∕{\mu }_{s}NR$. The dashed and solid lines represent the theoretical predictions for scenarios (a) and (b), respectively (see text for details).

Figure 3

Geometry used to solve the equations for the coupling of forces and torques. $\mathbf{r}$ is the position of an infinitesimal element of the disk and ${\mathbf{r}}_0$ the position vector of the instantaneous center of rotation $O$.

Figure 4

Schematic plot of (normalized) friction force and torque. The upper curve marks the threshold, below which a static contact is maintained. The lower curve respresents the sliding case. See text for details.