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In this paper we consider the combined effect of rotating and non-rotating asymmetries on a rotor under non-conservative loading, motivated by technical applications in which breaking of symmetries may be used to avoid self-excited vibrations. We consider a rotating disk with two translatory degrees of freedom describing the displacements of the center of the disk with respect to the axis of rotation and two rotational degrees of freedom describing the tilting angles with respect to the axis of rotation. It is shown that breaking of symmetries of the rotating and non-rotating restoring terms has opposite effects for the stability behavior of translatory and rotational motions. Thus, if neither the translatory nor rotational degrees of freedom are dominant, it will be difficult to find robust designs against self-excited vibrations using the approach of breaking symmetries. [ABSTRACT FROM AUTHOR]