  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.
