  We study the rotational properties of magnetized and self-gravitating
molecular cloud cores formed in 2 very high resolution 3D molecular cloud
simulations.The simulations have been performed using the code RAMSES at an
effective resolution of 4096^3.One simulation represents a mildly
magnetically-supercritical cloud and the other a strongly
magnetically-supercritical cloud.A noticeable difference between the 2
simulations is the core formation efficiency (CFE) of the high density cores.In
the strongly supercritical simulations the CFE is ~33 % per free-fall time of
the cloud tff,cl, whereas in the mildly supercritical simulations this value
goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular
momentum j3D distributions of the cores with the distribitions of j2D derived
using synthetic 2D velocity maps of the cores,shows that the synthetic
observations tend to overestimate the true value of j by a factor of ~10.The
origin of this discrepancy lies in the fact that contrary to the intrinsic
determination which sums up the individual gas parcels contributions to j, the
determination of j using the observational procedure which is based on a
measurement on the global velocity gradient under the hypothesis of uniform
rotation smoothes out the complex fluctuations present in the 3D velocity
field. Our results provide a natural explanation for the discrepancy by a
factor ~10 observed between the intrinsic 3D distributions of j and the
corresponding distributions derived in real observations.We suggest that
measurements of j which are based on the measurement of the observed global
velocity gradients may need to be reduced by a factor of ~10 in order to derive
a more accurate estimate of j in the cores.
