  The angular momentum of a molecular cloud core plays a key role in star
formation, since it is directly related to the outflow and the jet emanating
from the new-born star and it eventually results in the formation of the
protoplanetary disk. However, the origin of the core rotation and its time
evolution are not well understood. Recent observations reveal that molecular
clouds exhibit a ubiquity of filamentary structures and that star forming cores
are associated with the densest filaments. Since these results suggest that
dense cores form primarily in filaments, the mechanism of core formation from
filament fragmentation should explain the distribution of the angular momentum
of these cores. In this paper we analyze the relation between velocity
fluctuations along the filament close to equilibrium and the angular momentum
of the cores formed along its crest. We first find that an isotropic velocity
fluctuation that follows the three-dimensional Kolmogorov spectrum does not
reproduce the observed angular momentum of molecular cloud cores. We then
identify the need for a large power at small scales and study the effect of
three power spectrum models. We show that the one-dimensional Kolmogorov power
spectrum with a slope -5/3 and an anisotropic model with reasonable parameters
are compatible with the observations. Our results stress the importance of more
detailed and systematic observations of both the velocity structure along
filaments and the angular momentum distribution of molecular cloud cores to
determine the validity of the mechanism of core formation from filamentary
molecular clouds.
