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Both of my sisters used to dance and when I was younger I went to their dance recitals.  Every year I went, there was always that one dancer who would spin on her toe for the longest time.  I always notice that when ever the dancer slowed down while spinning, she whipped her legs around in a circle again and then she started to spin faster.  I have always wondered how one leg motion could keep you spinning for the longest time.  Well this simple spinning of a dance can be explained through angular momentum.  When the dancer starts she extends her legs out to have a larger radius.  With this larger radius, her angular speed is small, but when she whips her legs around and tightened up her leg to her body, the radius is smaller.  The angular momentum is the angular speed times moment of inertia initial equals the final.  The dancer with the large radius has a large moment of inertia and low angular speed.  When she brings her legs together, the moment inertia becomes less and the angular speed increases.  Therefore she can spin faster when she puts her legs out and then whips it back into her body. 

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