ANGULAR MOMENTUM: blog 8 :)

http://www.youtube.com/watch?v=2gYEtBwmiPE

Physics affects many aspects of dance, including one of the hardest parts- turns. There are many types of turns: pirouettes, coupe turns, fouette turns, pencil turns, etc. etc. The speeds at which a dancer turns for each type differs- fouette turns are much slower than coupe turns. This is because Angular momentum is equal to moment of inertia times angular velocity, and because angular momentum is conserved. In a fouette turn, a straight leg is extended parallel to the ground. This increases the radius of the dancer, which causes the dancer's moment of inertia to increase, due to the fact that moment of inertia is equal to mass times radius squared. When moment of inertia is larger, then the angular velocity is less. In a pirouette, however, the radius is smaller because the leg is bent so that the foot is at the knee, which means moment of inertia is smaller. The angular velocity of a dancer doing a pirouette is larger than if the dancer were doing fouette turns, which is why pirouettes are faster than fouette turns.
This is a video from Winter Showcase two years ago, and it includes alesicon turns (which are like fouette turns because the leg is fully extended) and goes straight into pirouettes. The change in speed is a little hard to see, but when you are doing the turns, the change in velocity is very noticable.