  Nearby associations are excellent objects for the study of the initial spin
up phase during the PMS evolution. An empirical approach is adopted here to
infer their rotations properties and relations to X-ray emission. Three nearby
associations are considered. The TW Hya association with an age of 8 Myr, the
Beta Pictoris moving group with 12 Myr and a combination of Tucana and
Horologium associations (30 Myr). Two low and high rotation modes are
considered for each association with stellar masses less than 1.5M and greater
than 1.5M respectively. We infer representative equatorial rotation velocities
Vo from the observed distribution of projected rotational velocities vsini. A
spin up is found for the high rotation mode, whereas in the low rotation mode
the Vo do not increase significantly. This insufficient increase of Vo is
probably the cause of a decrease of the total mean specific angular momentum
for the low mass stars between 8 and 30 Myr. However, for the high mass stars,
where a sufficient spin up is present, the specific angular momentum is
practically conserved in this same time interval. By supposing that the
distribution of masses of these three associations follows a universal mass
function, we estimate the number of members of these associations that remain
to be detected. The analysis of rotation and stellar masses using luminosity
X-rays indicators present similar properties, as the dependence on stellar mass
and rotation, at least for the younger associations, to those obtained for T
Tauri stars in the ONC. A strong desaturation effect appears at 30 Myr. This
effect seems to be provoked by the minimum configuration of the stellar
convection layers, attained for the first time for the higher mass stars at 30
Myr. The desaturation appears to be independent of rotation at this stage.
