  The angular momentum of molecular cloud cores plays an essential role in the
star formation process. However, the time evolution of the angular momentum of
molecular cloud cores is still unclear. In this paper, we perform
three-dimensional simulations to investigate the time evolution of the angular
momentum of molecular cloud cores formed through filament fragmentation. As a
result, we find that most of the cores rotate perpendicular to the filament
axis. The mean angular momentum of the cores changes by only around 30% during
the initial stage of their formation process and then remains almost constant.
In addition, we analyze the internal angular momentum structure of the cores.
Although the cores gain angular momentum with various directions from the
initial turbulent velocity fluctuations of their parent filaments, the angular
momentum profile in each core converges to the self-similar solution. We also
show that the degree of complexity of the angular momentum structure in a core
slightly decreases with time. Moreover, we perform synthetic observations and
show that the angular momentum profile measured from the synthetic mean
velocity map is compatible with the observations when the filament inclination
is taken into account. The present study suggests a theory of core formation
from filament fragmentation where the angular momentum structures of the cores
are determined by the velocity fluctuation along the filaments and both are
compatible with the observations. This theory also provides new insights on the
core properties that could be observationally tested.
