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We exploit our formula for the gravitational potential of finite size,power-law disks to derive a general expression linking the mass of the blackhole in active galactic nuclei (AGN), the mass of the surrounding disk, itssurface density profile (through the power index s), and the differentialrotation law. We find that the global rotation curve v(R) of the disk incentrifugal balance does not obey a power law of the cylindrical radius R(except in the confusing case s = -2 that mimics a Keplerian motion), anddiscuss the local velocity index. This formula can help to understand how, fromposition-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 syntheticdata with different levels of Gaussian noise, added in radius. It turns outthat, when observations are spread over a large radial domain and exhibit lowdispersion (standard deviation less than 10% typically), the disk properties(mass and s-parameter) and black hole mass can be deduced from a non linear fitof kinematic data plotted on a (R, Rv 2)-diagram. For a deviation higher than10%, masses are estimated fairly well from a linear regression (correspondingto the zeroth-order treatment of the formula), but the power index s is nolonger accessible. We have applied the model to 7 AGN disks whose rotation hasalready been probed through water maser emission. For NGC3393 and UGC3789, themasses seem well constrained through the linear approach. For IC1481, thepower-law exponent s can even be deduced. Because the model is scale-free, itapplies to any kind of star/disk system. Extension to disks around young starsshowing deviation from Keplerian motion is thus straightforward.

AGN disks and black holes on the weighting scales