  We present 0.5" resolution near-IR integral field spectroscopy of the Ha line
emission of 14 z~2 UV-selected BM/BX galaxies obtained with SINFONI at ESO/VLT.
The mean Ha half-light radius r_1/2 is about 4kpc and line emission is detected
over > ~20kpc in several sources. In 9 sources, we detect spatially-resolved
velocity gradients, from 40 to 410 km/s over ~10kpc. The observed kinematics of
the larger systems are consistent with orbital motions. Four galaxies are well
described by rotating disks with clumpy morphologies and we extract rotation
curves out to radii > ~10kpc. One or two galaxies exhibit signatures more
consistent with mergers. Analyzing all 14 galaxies in the framework of rotating
disks, we infer mean inclination- and beam-corrected maximum circular
velocities v_c of 180+-90 km/s and dynamical masses of (0.5-25)x10^10 Msun
within r_1/2. On average, the dynamical masses are consistent with photometric
stellar masses assuming a Chabrier/Kroupa IMF but too small for a 0.1-100 Msun
Salpeter IMF. The specific angular momenta of our BM/BX galaxies are similar to
those of local late-type galaxies. The specific angular momenta of their
baryons are comparable to those of their dark matter halos. Extrapolating from
the average v_c at 10kpc, the virial mass of the typical halo of a galaxy in
our sample is 10^(11.7+-0.5) Msun. Kinematic modeling of the 3 best cases
implies a ratio of v_c to local velocity dispersion of order 2-4 and
accordingly a large geometric thickness. We argue that this suggests a mass
accretion (alternatively, gas exhaustion) timescale of ~500Myr. We also argue
that if our BM/BX galaxies were initially gas rich, their clumpy disks will
subsequently lose their angular momentum and form compact bulges on a timescale
of ~1 Gyr. [ABRIDGED]
