How a ballet dancer spins rapidly at one place?

Ballet dance, one of the most entertaining form of dance that we like to watch. If you had ever watched ballet , you must had watched the performer to rotate rapidly at one place. But have you ever thought how she do that easily. What is the technique behind this, that a normal person don't know and fails to perform this act.So let's explore this topic today. But before that we have to be clear about some basic concepts of motion of a body. So let's begin that first step by step:-

1.Momentum as you all know is the product of the mass of an object and it's velocity. This definition of momentum is limited to the linear motion of the object. But when the  object is rotating about an axis, it is undergoing rotational motion.

                  It should be clear that rotational analogue of momentum is called angular momentum. We should now learn about the conservation of momentum which states that:-

"Momentum neither be created nor be destroyed".

So from the above law angular momentum also remains conserved. Because it is just the rotational analogue of linear momentum.

              So far we have learn about momentum and it's conservation. Now let's move ahead.

2.Moment of inertia :- It is just the rotational analogue of inertia (the tendency of an object to resist change in its state of rest or motion). In linear motion, mass plays role of inertia and in rotational motion Moment of inertia plays the role of inertia.

So the main conclusion here is mass in linear motion is equivalent to  Moment of inertia in rotational motion.

             Now, linear momentum is the product of mass and velocity. So angular momentum is the product of Moment of inertia and angular velocity. Moment of inertia(I) can be calculated by following formulae:-

                            I= MR² (here I is moment of inertia , M is mass of object and R is radius of object).

 Above stated two concepts is sufficient to understand the technique used by ballet dancer to rotate on its axis. So now, let's learn that:-

During the ballet dance when dancer wants to rotate , she folds  her arms and brings leg closer to her body. By doing this she reduces moment of inertia.

                As angular momentum is always conserved , so here angular velocity increases to maintain this result.This is because , the angular momentum is the product of moment of inertia and angular velocity. So if one of angular velocity or moment of inertia decreases the other will increase and vice- versa. 

Due to increase in angular velocity the dancer able to rotate rapidly at her axis.

           This same reason is responsible for increase in angular velocity of a planet when it comes near the sun.

Some common application of the above result:-

i) The springboard diver able to perform Sommersaults after jumping towards water.

ii) Increase in angular velocity of a planet after coming near to sun.

iii) Cat jumping from a height stretches it's body.

iv) A circus acrobat able to perform feats.

Author:- Nayan Jyoti

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