Question

How can a blackhole be stabilized by adding to its angular momentum

Answer 1

Well, I suppose, but only in the sense that it is hard to change the direction of the axis of rotation.

A bicycle is also stabilized by the rotation of the tires. The faster the spin, the more torque is needed to turn or tip the wheels. (torque = rate of change of angular momentum, either in magnitude or direction)
Try Google - gyroscopic stabilization

Answer 2

ah - cute demo :

http://www.youtube.com/watch?v=az1_4WjadlU