  Here we present the analysis of the distribution of rotation periods and
light curve amplitudes based on 2859 family asteroids in 16 Main Belt families
based on 9912 TESS asteroid light curves in the TSSYS-DR1 asteroid light curve
database. We found that the distribution of the light curve properties follow a
family-specific character in some asteroid families, including the Hungaria,
Maria, Juno, Eos, Eucharis, and Alauda families. While in other large families,
these distributions are in general very similar to each other. We confirm that
older families tend to contain a larger fraction of more spheroidal,
low-amplitude asteroids. We found that rotation period distributions are
different in the cores and outskirts of the Flora and Maria families, while the
Vesta, Eos, and Eunomia families lack this feature. We also confirm that very
fast spinning asteroids are close to spherical (or spinning top shapes), and
minor planets rotating slower than ~11 hour are also more spherical than
asteroids in the 4--8 hour period range and this group is expected to contain
the most elongated bodies.
