  We measure the pitch angle ($\varphi$) of spiral arms in a sample of 79
galaxies to perform a systematic study of the dependence of $\varphi$ on galaxy
morphology, mass, and kinematics to investigate the physical origin of spiral
arms. We find that $\varphi$ decreases (arms are more tightly wound), albeit
with significant scatter, in galaxies with earlier Hubble type, more prominent
bulges, higher concentration, and larger total galaxy stellar mass ($M_*^{\rm
gal}$). For a given concentration, galaxies with larger stellar masses tend to
have tighter spiral arms, and vice versa. We also find that $\varphi$ obeys a
tight inverse correlation with central stellar velocity dispersion for
$\sigma_c$$\gtrsim$$100$ km s$^{-1}$, whereas $\varphi$ remains approximately
constant for $\sigma_c\lesssim100$ km s$^{-1}$. We demonstrate that the
$\varphi$-$\sigma_c$ and $\varphi$-$M_*^{\rm gal}$ relations are projections of
a more fundamental three-dimensional $\varphi-\sigma_c-M_*^{\rm gal}$ relation,
such that pitch angle is determined by $\sigma_c$ for massive galaxies but by
$M_*^{\rm gal}$ for less massive galaxies. Contrary to previous studies, we
find that $\varphi$ correlates only loosely with the galaxy's shear rate. For a
given shear rate, spirals generated from $N$-body simulations exhibit much
higher $\varphi$ than observed, suggesting that galactic disks are dynamically
cooler (Toomre's $Q \approx 1.2$). Instead, the measured pitch angles show a
much stronger relation with morphology of the rotation curve of the central
region, such that galaxies with centrally peaked rotation curves have tight
arms, while those with slow-rising rotation curves have looser arms. These
behaviors are qualitatively consistent with predictions of density wave theory.
