The Dance Of Physics

We all are familiar with many types of dance forms such as Kathak ( India form of dance) and Ballet. We have also seen the dancers taking endless turns at a particular position without any disturbance in their movement. How do they do it? Practice? Yes but their is something else also. So what is that something else? And how does it helps the dancer to perform those spectacular turns?

In the third act of the swan lake the black swan pulls of an endless series of thirty two turns at one pointed foot. It is probably the most toughest sequence in ballet. She is like a human top for the next few seconds. The dancer starts the motion by pushing the toe to generate torque but the friction between her pointed toe and the floor and also the friction between her body and the air reduces her momentum. So how does she manages to take those turns known as fouette?

While taking the turns the dancer stops for a very small fraction of second. In that second her foot flattens and then she pushes her foot against the floor which leads to the generation of a tiny amount of torque. Her arms also keep moving in order to maintain the balance. The fouettes are most effective when her center of gravity stays constant. Her pointed foot and the extended arm helps her to takes those turns.

Their is one more thing which most of the people fail to notice and that is that her other leg ( apart from the pointed foot) never stops moving. Her other leg helps her to gain momentum. When the leg is moving a certain amount of momentum gets stored in it and when she pulls that leg back towards her body the momentum gets transferred to her body.The more area the leg sweeps the more momentum she gains.

Their is one more way by which the ballerina can take turns that is by bringing her arms and legs closer to her body.The fouette is governed by the angular momentum (L) which is equal to the product of the angular velocity and the rotational inertia (I) i.e L= angular velocity X I. It is necessary for the angular momentum to stay constant while the dancer performs that means that her angular momentum needs to be conserved. 

Rotational inertia is a body's resistance to rotational motion. It increases when more mass gets distributed further the axis of rotation i.e the radius increases and it decreases when the mass is distributed closer to the axis of rotation i.e the radius decreases. So when the ballerina brings her arms and legs closer to her body the rotational inertia decreases and in order to keep her angular momentum constant the angular velocity increases which allows her to take multiple turns similar situation can be noticed in ice skating also .

In Kathak also while taking the chakkars (turns at one leg) the dancer pushes her foot against the ground to gain torque and her hands keep coming closer to her body after a certain interval of time which increases her angular momentum and decreases the rotational inertia. This allows the dancer to perform the magical dance which does not happens due to some magic but Physics. 

Bibliography-
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