A dancer's spin, especially when he's balanced on one foot, is a pirouette.
A pirouette is a ballet term meaning to whirl or spin while balanced on the toes. In the case of a ballerina, she would pirouette while "en pointe," poised on the very toe of her shoe with the other leg bent. You can also use the word to describe a more casual spin, like an exuberant little boy who pirouettes through the halls of his school. In Old French, the root word pirouet meant "spinning top."