@inna
When I refer to 'mass of the platter', I am referring to suspended mass. That is, loosely speaking, the mass supported by the thrust bearing, including spindle and mat (usually negligible).
A physicist would normally speak of the moment of inertia, which is the physical analogue of mass in a rotating system, and which is most relevant to rotational stability. Moment of inertia is maximized when all the mass is on the outer ring, which is why some TT have mass distributed on the periphery.
But mass is easier to understand, and is highly correlated with moment of inertia in a solid object. Also, mass determines the weight which must be supported by the thrust bearing. The remaining forces acting on the spindle are radial, arising from asymmetrical rotation and belt tension, and are sometimes dealt with more casually.