  We present a detailed study of rotational asymmetry in galaxies for both
morphological and physical diagnostic purposes. An unambiguous method for
computing asymmetry is developed, robust for both distant and nearby galaxies.
By degrading real galaxy images, we test the reliability of this asymmetry
measure over a range of observational conditions, e.g. spatial resolution and
signal-to-noise (S/N). Compared to previous methods, this new algorithm avoids
the ambiguity associated with choosing a center by using a minimization method,
and successfully corrects for variations in S/N. There is, however, a strong
relationship between the rotational asymmetry and physical resolution (distance
at fixed spatial resolution); objects become more symmetric when less
well-resolved. We further investigate asymmetry as a function of galactic
radius an rotation. We find the asymmetry index has a strong radial dependence
that differs vastly between Hubble types. As a result, a meaningful asymmetry
index must be specified within a well-defined radius representative of the
physical galaxy scale. We enumerate several viable alternatives, which excludes
the use of isophotes. Asymmetry as a function of angle (A[phi]) is also a
useful indicator of ellipticity and higher-order azimuthal structure. In
general, we show the power of asymmetry as a morphological parameter lies in
the strong correlation with (B-V) color for galaxies undergoing normal star
formation, spanning all Hubble types from ellipticals to irregular galaxies.
Interacting galaxies do not fall on this asymmetry-color ``fiducial sequence,''
as these galaxies are too asymmetric for their color. We propose to use this
fact to distinguish between `normal' galaxies and galaxies undergoing an
interaction or merger at high redshift.
