No, most spinning objects hold together rigidly while they are spinning. Some objects will fall apart if you spin them too fast, but they are either just too loosely held together or cracked or otherwise easily break apart.
Angular momentum does not depend on mass being ejected from a spinning object. Tops which are spinning wobble because of a phenomenon called precession. Here is one answer
on our web site covering precession, and also the subject of gyroscopes
for another description of how precession works.
The faster an object is spinning, the more angular momentum it has, and the more torque it will take to change this direction, making bicycles more stable at higher speeds, and tops also more stable at higher speeds.
The force of gravity tugs on all objects and some force is always needed to counteract it, or an object will fall. Some demonstrations involving spinning bicycle wheels or gyroscopes on long poles seem to defy gravity because the upwards force is applied at a point rather far away from the center of mass. But the force has to be applied somewhere, and the turning motion is governed by the the fact that the torque
is the rate of change of angular momentum.
(republished on 07/13/06)