We present the first dynamical mass estimates and scaling relations for a sample of Sunyaev-Zeldovich effect (SZE) selected galaxy clusters. The sample consists of 16 massive clusters detected with the Atacama Cosmology Telescope (ACT) over a 455 sq. deg. area of the southern sky. Deep multi-object spectroscopic observations were taken to secure intermediate-resolution (R~700-800) spectra and redshifts for ~60 member galaxies on average per cluster. The dynamical masses M_200c of the clusters have been calculated using simulation-based scaling relations between velocity dispersion and mass. The sample has a median redshift z=0.50 and a median mass M_200c~12e14 Msun/h70 with a lower limit M_200c~6e14 Msun/h70, consistent with the expectations for the ACT southern sky survey. These masses are compared to the ACT SZE properties of the sample, specifically, the match-filtered central SZE amplitude y, the central Compton parameter y0, and the integrated Compton signal Y_200c, which we use to derive SZE-Mass scaling relations. All SZE estimators correlate with dynamical mass with low intrinsic scatter (<~20%), in agreement with numerical simulations. We explore the effects of various systematic effects on these scaling relations, including the correlation between observables and the influence of dynamically disturbed clusters. Using the 3-dimensional information available, we divide the sample into relaxed and disturbed clusters and find that ~50% of the clusters are disturbed. There are hints that disturbed systems might bias the scaling relations but given the current sample sizes these differences are not significant; further studies including more clusters are required to assess the impact of these clusters on the scaling relations.
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