## Friday, November 30, 2012

### Physics of a Fouetté Turn in Ballet

Physics of a Fouetté Turn

In ballet, there are several types of turns a dancer can do. One of the most difficult types is a Fouetté. The video below describes the motions involved in such a turn.

As the dancer turns, she brings her leg inward which decreases her moment of inertia. This in turn increases her angular velocity. I decided to calculate what the dancer's velocity would be right after she brings her leg in. To do this, I timed how long it took the dancer to turn with her leg extended. She completed one turn in 0.8 seconds, which is about 2.5*pi rad/s. Additionally, I considered the dancer with her leg close to the body as a uniform cylinder, giving a moment of inertia as I=1/2MR^2 (Even though the dancer does not bring her leg all the way in, I did this to simplify my calculations). I considered her leg to be a uniform rod rotating about its end.

Here are my knowns:

Mass of person= 60 kg
Mass of leg= 6 kg
Length of leg= 0.762 meters

To solve for the angular velocity of the dancer with her leg brought in:

I1w1=I2w2

(1/2)MR^2(w1) = (1/2MR^2 + 1/3mL^2)(w2)
1/2(60)(0.1524^2)(w1)= (1/2(60)(0.1524^2)+1/3(6)(0.762^2))(7.85)