Popular Science Blog - Flight of the Pole Dancer:
Newton’s First Law of Motion states that bodies in motion tend to stay in motion. The same holds true for rotating bodies and, as we see in the video below, doubly true for rotating, gyrating bodies.
Consider the body of the body in question. After a quick shake of the head right and left, she leans backward to begin her rotation around the pole. Her pivot points include her right hand, held fast to the pole, and her left foot (disastrously clad, we will soon learn, in three-inch heels). She now has a sizeable amount of angular momentum moving counterclockwise around the pole, and this can be halted only by an external force.