We present a MUSE and KMOS dynamical study 405 star-forming galaxies at redshift z=0.28-1.65 (median redshift z=0.84). Our sample are representative of star-forming, main-sequence galaxies, with star-formation rates of SFR=0.1-30Mo/yr and stellar masses M=10^8-10^11Mo. For 49+/-4% of our sample, the dynamics suggest rotational support, 24+/-3% are unresolved systems and 5+/-2% appear to be early-stage major mergers with components on 8-30kpc scales. The remaining 22+/-5% appear to be dynamically complex, irregular (or face-on systems). For galaxies whose dynamics suggest rotational support, we derive inclination corrected rotational velocities and show these systems lie on a similar scaling between stellar mass and specific angular momentum as local spirals with j*=J/M*propto M^(2/3) but with a redshift evolution that scales as j*propto M^{2/3}(1+z)^(-1). We identify a correlation between specific angular momentum and disk stability such that galaxies with the highest specific angular momentum, log(j*/M^(2/3))>2.5, are the most stable, with Toomre Q=1.10+/-0.18, compared to Q=0.53+/-0.22 for galaxies with log(j*/M^(2/3))<2.5. At a fixed mass, the HST morphologies of galaxies with the highest specific angular momentum resemble spiral galaxies, whilst those with low specific angular momentum are morphologically complex and dominated by several bright star-forming regions. This suggests that angular momentum plays a major role in defining the stability of gas disks: at z~1, massive galaxies that have disks with low specific angular momentum, appear to be globally unstable, clumpy and turbulent systems. In contrast, galaxies with high specific angular have evolved in to stable disks with spiral structures.
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