  We present spatially resolved stellar rotation velocity and velocity
dispersion profiles form Keck/LRIS absorption-line spectra for 25 galaxies,
mostly visually classified ellipticals, in three clusters at z=0.5. We
interpret the kinematical data and HST photometry using oblate axisymmetric
two-integral f(E,Lz) dynamical models based on the Jeans equations. This yields
good fits, provided that the seeing and observational characteristics are
carefully modeled. The fits yield for each galaxy the dynamical M/L and a
measure of the galaxy rotation rate. Paper II addresses the implied M/L
evolution. Here we study the rotation-rate evolution by comparison to a sample
of local elliptical galaxies of similar present-day luminosity. The brightest
galaxies in the sample all rotate too slowly to account for their flattening,
as is also observed at z=0. But the average rotation rate is higher at z=0.5
than locally. This may be due to a higher fraction of misclassified S0 galaxies
(although this effect is insufficient to explain the observed strong evolution
of the cluster S0 fraction with redshift). Alternatively, dry mergers between
early-type galaxies may have decreased the average rotation rate over time. It
is unclear whether such mergers are numerous enough in clusters to explain the
observed trend quantitatively. Disk-disk mergers may affect the comparison
through the so-called progenitor bias, but this cannot explain the direction of
the observed rotation-rate evolution. Additional samples are needed to
constrain possible environmental dependencies and cosmic variance in galaxy
rotation rates. Either way, studies of the internal stellar dynamics of distant
galaxies provide a valuable new approach for exploring galaxy evolution.
