Stand on the turning disk and push yourself with your leg! As you start turning, lean back and put out one of your legs backwards like ice-skaters!
Then put your other leg on the disk, too, and pull your body slowly to the handhold!
Why does the speed of whirling grow when you hunch?

The cause of the phenomenon is the conservation of angular momentum.
Angular momentum depends on the rotating body's (angular) velocity, weight and the distance between its center of mass and the axis of rotation..
"Conservance" means that if there is no outside force acting on, momentum is constant.

The law is valid on a "greater scale", too: planets of the Solar System obeying this law started whirling with great speed when at their formation thanks to gravity the material cloud they consisted of pulled together.

A black hole turns around its axis thousands of times per second. Stars of great mass at the end of their life -thanks to a supernova-explosion - collapse and they become black holes. According to the conservance of angular momentum their rotation accelerates immensely.