  We study numerically the collapse of rotating, magnetized molecular cloud
cores, focusing on rotation and magnetic braking during the main accretion
phase of isolated star formation. Motivated by previous numerical work and
analytic considerations, we idealize the pre-collapse core as a magnetized
singular isothermal toroid, with a constant rotational speed everywhere. The
collapse starts from the center, and propagates outwards in an inside-out
fashion, satisfying exact self-similarity in space and time. For rotation rates
and field strengths typical of dense low-mass cores, the main feature remains
the flattening of the mass distribution along field lines -- the formation of a
pseudodisk, as in the nonrotating cases. The density distribution of the
pseudodisk is little affected by rotation. On the other hand, the rotation rate
is strongly modified by pseudodisk formation. Most of the centrally accreted
material reaches the vicinity of the protostar through the pseudodisk. The
specific angular momentum can be greatly reduced on the way, by an order of
magnitude or more, even when the pre-collapse field strength is substantially
below the critical value for dominant cloud support. The efficient magnetic
braking is due to the pinched geometry of the magnetic field in the pseudodisk,
which strengthens the magnetic field and lengthens the level arm for braking.
Both effects enhance the magnetic transport of angular momentum from inside to
outside. The excess angular momentum is carried away in a low-speed outflow
that has, despite claims made by other workers, little in common with observed
bipolar molecular outflows. We discuss the implications of our calculations for
the formation of true disks that are supported against gravity by rotation.
