  We exploit our formula for the gravitational potential of finite size,
power-law disks to derive a general expression linking the mass of the black
hole in active galactic nuclei (AGN), the mass of the surrounding disk, its
surface density profile (through the power index s), and the differential
rotation law. We find that the global rotation curve v(R) of the disk in
centrifugal balance does not obey a power law of the cylindrical radius R
(except in the confusing case s = -2 that mimics a Keplerian motion), and
discuss the local velocity index. This formula can help to understand how, from
position-velocity diagrams, mass is shared between the disk and the black hole.
To this purpose, we have checked the idea by generating a sample of synthetic
data with different levels of Gaussian noise, added in radius. It turns out
that, when observations are spread over a large radial domain and exhibit low
dispersion (standard deviation less than 10% typically), the disk properties
(mass and s-parameter) and black hole mass can be deduced from a non linear fit
of kinematic data plotted on a (R, Rv 2)-diagram. For a deviation higher than
10%, masses are estimated fairly well from a linear regression (corresponding
to the zeroth-order treatment of the formula), but the power index s is no
longer accessible. We have applied the model to 7 AGN disks whose rotation has
already been probed through water maser emission. For NGC3393 and UGC3789, the
masses seem well constrained through the linear approach. For IC1481, the
power-law exponent s can even be deduced. Because the model is scale-free, it
applies to any kind of star/disk system. Extension to disks around young stars
showing deviation from Keplerian motion is thus straightforward.

Cosmology and Nongalactic Astrophysics