# The Physics of Ballet

## The Physics of Ballet

Physics + Dance

Sounds interesting, right?

This blog of Terminal Stack unfolds before you the amazing physics concepts hidden behind the beautiful moves of a Ballet Dancer.

## What is Ballet?

Ballet is a very graceful dance form, originated in Italy about 500 years ago. The Moves in Ballet seem smooth, graceful, and effortless, but behind this, it involves a great amount of strength, balance, technical skill, and flexibility. Traditionally, female ballet dancers perform ‘en Pointe’ that is on the points of their tiptoes. Hence said, that Ballet is a very elegant but very physically strenuous style of the dance form.

Understanding the physics behind ballet only enhances the appreciation of the artistry and skill that it takes to create the illusion of grace and effortlessness.

## The Physics elements in Ballet

Ballet is a complex art form that incorporates many stylized elements which correlate with the law of physics. The most prominent out of them are- Balance, Jump, and Turn.

• Balance:

A Dancer needs to balance their gravity while performing different movements. As the position of the dancer changes, the position of the Centre of Gravity changes to maintain balance. Static equilibrium occurs when the net force and net torque of the object are zero. To balance en pointe, the dancer must be in static equilibrium.

A professional ballet dancer has a complete idea of when, where, and how much to bend forward or backward while keeping in mind to balance the center of gravity.

• Jump:

This Concept is based on Newton’s first law of motion that states, “An Object will not change its motion unless acted on by an unbalanced force.” When a dancer jumps, they first exert a force on the ground which is balanced by the normal force and make the dancer move through the air. This exerted force sets them into motion, but after some time, the gravity gets unbalanced and exerts a gravitational force on the dancer. Hence dancer lands on the ground.

Jumping forms a projectile motion, where the vertical motion is only affected. Once the dancer is airborne, their center of gravity follows a parabolic path, whose vertex is the highest point of their jump. Due to conservation of momentum, the final velocity and initial velocity of the dancer remain equal, except the sign of final velocity turns negative.

mu + mv = 0

m (u + v) =0

u+v =0

Hence, u= -v

Where,

m – Mass of the dancer

u – Initial velocity of dancer

v – Final velocity of dancer

• Turn:

This concept deals with Newton’s third law of motion. Torque applied by the dancer’s feet on the ground gives a rotational motion to the dancer’s body. How long the motion continues depends on the conservation of angular momentum.

“Efficiency of a dancer results from the dancer’s knowing where and how to generate momentum and then how to engage with the forces that result.”

## Role of Angular Momentum

Momentum is mass in motion and moving in a constant direction creates momentum. Rotational Motion gives rise to Angular Momentum. When no torque is applied, angular momentum remains constant that keeps the body in rotational motion. Angular momentum depends on Inertia and Angular velocity.

Inertia: It is the measure of an object’s resistance to a change in its state of motion.

Angular velocity: It is the time rate at which a body rotates about an axis.

For continuing the rotational motion, angular momentum must be conserved. That is, increasing inertia decreases angular velocity, and decreasing inertia increases angular velocity, to keep angular momentum constant.

A Ballet dancer increases its rotational speed by decreasing the moment of inertia. And it is done by contracting or folding the arms inwards, thus reducing the distribution of mass around the axis of rotation. Similarly, to slow down the motion dancer stretches their arms outwards to increase distribution of mass.

## Forces acting on a Ballet dancer:

Various forces act on the dancers which are needed to be balanced to maintain a posture for a certain period.

• Centripetal Force:

Net forces that act on the body to keep it moving along a circular path is called Centripetal Force. It keeps the body in a circular motion. The dancer provides the initial force by pushing off the ground but centripetal force keeps her body spinning.

• Gravitational Force:

Force of attraction between two masses, especially attraction between earth and bodies present over it is called Gravitational force. It pulls the dancer towards the earth’s surface. Dancers need to balance their center of gravity as it is the point where all object’s mass is concentrated. It is also the rotating point of any object.

• Frictional Force:

The force that restricts the motion of the body is called Frictional force. It acts sideways and it is necessary to avoid it as much as possible. It is done by using slippy bottoms on the bottom of the shoes to dance fluently.

## Physics behind Fouette’s

Foeutte means whipped in French.

Foeutte’s is considered as one of the hardest moves in Ballet. It includes endless series of turns, bobbing up and down on one pointed foot and spinning around and around several times. The Dancer starts the foeutte by pushing off the ground to generate torque. Now slowly the friction between the toe and ground and between the body and air tends to reduce the dancer’s momentum.

So, for spinning continuously, the dancer pauses for a moment and flattens their foot, and then twits back on to en pointe. This flattening of the foot generates new torque to overcome the law of momentum. During her momentary pause, the dancer’s other elevated leg straightens and moves from the front to the side, and then it folds back into her knee. This act stores a certain amount of momentum, which helps in spinning.

While if a dancer tilts in a direction, then sweeps her arms starting from front to side. This sweeping movement of the arm maintains the body balance.

“Hidden behind the ribbons and tulle, we see the theories and principles of physics come alive right before our eyes!”

Reference: https://bit.ly/39XpdWr