We investigate the dynamical state of a new class of extended star clusters, known as "Faint Fuzzies", that were discovered in two nearby S0 galaxies, NGC 1023 and NGC 3384. It is shown that the Faint Fuzzies of NGC 1023 lie in a fast rotating ring-like structure within the galactic disk with mean radius of 5 kpc, rotational velocity of 200 km/s and velocity dispersion of 115 km/s. We propose a scenario for the origin of Faint Fuzzies that is connected to the origin of S0 galaxies as a result of galaxy-galaxy interactions in dense environments. As is apparent in the Cartwheel galaxy, and is confirmed by numerical simulations, the passage of a small galaxy through, or close to, the center of a disk galaxy can form a ring of clumpy star formation with a radius comparable to the Faint Fuzzy ring radius in NGC 1023. In this case, the Faint Fuzzies are signposts for the transformation of spiral galaxies into lenticulars via such interactions.

11 pages, 4 figures, ApJ, in press