  Rotational evolution in the pre-main sequence (PMS) is described with new
sets of PMS evolutionary tracks including rotation, non-gray boundary
conditions (BCs) and either low (LCE) or high convection efficiency (HCE).
Using observational data and our theoretical predictions, we aim at
constraining 1) the differences obtained for the rotational evolution of stars
within the ONC by means of these different sets of models; 2) the initial
angular momentum of low mass stars, by means of their templates in the ONC. We
discuss the reliability of current stellar models for the PMS. While the 2D
radiation hydrodynamic simulations predict HCE in PMS, semi-empirical
calibrations either seem to require that convection is less efficient in PMS
than in the following MS phase or are still contradictory. We derive stellar
masses and ages for the ONC by using both LCE and HCE. The resulting mass
distribution for the bulk of the ONC population is in the range 0.2$-$0.3
{\msun} for our non-gray models and in the range 0.1$-$0.3{\msun} for models
having gray BCs. In agreement with Herbst et al. (2002) we find that a large
percentage ($\sim$70%) of low-mass stars (M\simlt 0.5{\msun} for LCE;
M\simlt0.35{\msun} for HCE) in the ONC appears to be fast rotators (P$<$4days).
Three possibilities are open: 1) $\sim$70% of the ONC low mass stars lose their
disk at early evolutionary phases; 2)their locking period is shorter; 3) the
period evolution is linked to a different morphology of the magnetic fields of
the two groups of stars. We also estimate the range of initial angular momentum
consistent with the observed periods. The comparisons made indicate that a
second parameter is needed to describe convection in the PMS, possibly related
to the structural effect of a dynamo magnetic field.
