  Using hydrodynamic simulations we investigate the rotational properties and
angular momentum evolution of prestellar and protostellar cores formed from
gravoturbulent fragmentation of interstellar gas clouds. We find the specific
angular momentum j of prestellar cloud cores in our models to be on average
comparable to the observed values. A fraction of prestellar cores is
gravitationally unstable and goes into collapse to build up protostars and
protostellar systems. Their specific angular momentum is one order of magnitude
lower than their parental cores and in agreement with observations of
main-sequence binaries.
  The ratio of rotational to gravitational energy of protostellar cores in the
model turns out to be very similar to the observed values. We find, that it is
roughly conserved during the main collapse phase. This leads to j proportional
to M^{2/3}, where j is specific angular momentum and M core mass. Although the
temporal evolution of the angular momentum of individual protostars or
protostellar systems is complex and highly time variable, this correlation
holds well in a statistical sense for a wide range of turbulent environmental
parameters. In addition, high turbulent Mach numbers result in the formation of
more numerous protostellar cores with, on average, lower mass. Therefore,
models with larger Mach numbers result in cores with lower specific angular
momentum. We find, however, no dependence on the spatial scale of the
turbulence. Our models predict a close correlation between the angular momentum
vectors of neighboring protostars during their main accretion phase. Possible
observational signatures are aligned disks and parallel outflows. The latter
are indeed observed in some low-mass isolated Bok globules.
