  We use data from the Sydney-AAO Multi-object Integral-field spectroscopy
(SAMI) Galaxy Survey to study the dynamical scaling relation between galaxy
stellar mass $M_*$ and the general kinematic parameter $S_K = \sqrt{K V_{rot}^2
+ \sigma^2}$ that combines rotation velocity $V_{rot}$ and velocity dispersion
$\sigma$. We show that the $\log M_* - \log S_K$ relation: (1)~is linear above
limits set by properties of the samples and observations; (2)~has slightly
different slope when derived from stellar or gas kinematic measurements;
(3)~applies to both early-type and late-type galaxies and has smaller scatter
than either the Tully-Fisher relation ($\log M_* - \log V_{rot}$) for late
types or the Faber-Jackson relation ($\log M_* - \log\sigma$) for early types;
and (4)~has scatter that is only weakly sensitive to the value of $K$, with
minimum scatter for $K$ in the range 0.4 and 0.7. We compare $S_K$ to the
aperture second moment (the `aperture velocity dispersion') measured from the
integrated spectrum within a 3-arcsecond radius aperture
($\sigma_{3^{\prime\prime}}$). We find that while $S_{K}$ and
$\sigma_{3^{\prime\prime}}$ are in general tightly correlated, the $\log M_* -
\log S_K$ relation has less scatter than the $\log M_* - \log
\sigma_{3^{\prime\prime}}$ relation.
