The dynamics of a disc on an inclined plane with friction in the dynamically consistent model of friction

The problem of the motion of a uniform circular disc of non-zero thickness on a fixed rough inclined plane is discussed. It is proved that, if the ratio of the coefficient of sliding friction to the slope of the plane is greater than unity, the disc comes to rest after a finite time. If this ratio is equal to unity, the limit motion of the disc is uniform slip along the line of greatest slope, and if this ratio is less than unity, the slip velocity of the disc increases without limit with time.