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]
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