Spivak, Classical Mechanics: rolling disc

Question

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?

The center of mass of the disc doesn't accelerate because it doesn't rotate. It moves at a constant speed. — John Douma, Dec 15 '23 at 23:10

score 0 · Accepted Answer · answered Dec 19 '23 at 23:12

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.

Spivak, Classical Mechanics: rolling disc

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