Dynamics of a light hoop with an attached heavy disk: Inside an interaction pulse

An analysis of motion of a light hoop with a heavy circular disk attached to the inner side of its rim over a rough horizontal surface is presented. When the radius of the disk is small relative to the radius of the hoop, the motion is characterized by the sequence of sharp interaction pulses between the hoop and the horizontal surface, during which a complex transition between stick, slip, and reversed slip takes place. This is accompanied by the corresponding changes in the frictional force, which include abrupt reversal of its direction, and rapid increase and discontinuous changes of the normal component of the reactive force. The intensity of the interaction rapidly diminishes with an increase of the radius of the disk or the mass of the hoop. The effects of the coefficient of friction on the dynamic interactions, stick and slip transitions, and the energy dissipation are discussed.