  The effect of misalignment between the magnetic field $\magB$ and the angular
momentum $\Jang$ of molecular cloud cores on the angular momentum evolution
during the gravitational collapse is investigated by ideal and non-ideal MHD
simulations. For the non-ideal effect, we consider the ohmic and ambipolar
diffusion. Previous studies that considered the misalignment reported
qualitatively contradicting results. Magnetic braking was reported as being
either strengthened or weakened by misalignment in different studies. We
conducted simulations of cloud-core collapse by varying the stability parameter
$\alpha$ (the ratio of the thermal to gravitational energy of the core) with
and without including magnetic diffusion The non-ideal MHD simulations show the
central angular momentum of the core with $\theta=0^\circ$ ($\Jang \parallel
\magB$) being always greater than that with $\theta=90^\circ$ ($\Jang \perp
\magB$), independently of $\alpha$, meaning that circumstellar disks form more
easily form in a core with $\theta=0^\circ$. The ideal MHD simulations, in
contrast, show the the central angular momentum of the core with
$\theta=90^\circ$ being greater than with $\theta=0^\circ$ for small $\alpha$,
and is smaller for large $\alpha$. Inspection of the angular momentum evolution
of the fluid elements reveals three mechanisms contributing to the evolution of
the angular momentum: (i) magnetic braking in the isothermal collapse phase,
(ii) selective accretion of the rapidly (for $\theta=90^\circ$ ) or slowly (for
$\theta=0^\circ$) rotating fluid elements to the central region, and (iii)
magnetic braking in the first-core and the disk. The difference between the
ideal and non-ideal simulations arises from the different efficiencies of
(iii).
