In page 231 of his brilliant classical mechanics book ("Physics for Mathematicians 1"), Spivak considers the setting where we have a disc rolling on a planar floor such that the plane of the disc is always perpendicular to that of the floor (i.e. imagine a coin rolling on a table). There, he says something that makes absolutely no sense to me:
"In the simplest case, where there are no external forces, it is easy to guess from the symmetry of the situation that the disc of mass $m$ and angular momentum $L$ will roll with constant speed along a circle of radius $m/\|L\|$, or along a straight line when $L=0$".
I mean, in order the disc to trace a circular path, the center of mass must be accelerated so we must have external forces. Does anyone have any idea about what he tried to say?
OK, I figured out what he wants to say: he assumes there is a force that constraints the disc so that it stays perpendicular to the floor. With such a constraint force, if the disc has an initial rolling angular velocity and an initial angular velocity around the axis perpendicular to the floor, then it will trace a circle.