Precession, which is the rolling motion of the drillstring on the walls of the borehole, is investigated by considering the various possible motions of a rotating disk in a circular hole. Due to the simplicity of the model, closed-form results are derived on the stability of precession and on the evolution of impacting motions towards precession. It is found that increasing coefficients of friction and contact damping have a favoring effect on precession, while the stiffness and damping of the drillstring bending mode have an opposing effect.