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The Physics of Ballet


  Dancing is one of the most beautiful but equally difficult art forms. Ballet, in particular, is the foundation of all genres of dance. It teaches correct placement of the body, self-discipline, and dedication. Not many people know that in order for the dancers to perform, they need to demonstrate many fundamental parts of physics. Every graceful leap and turn is an application of projectile and rotational motion. Dancing is a unique art form, as it allows the dancer to express their emotions and to be able to use their capabilities to the fullest. In order to use their body, the fundamentals of mechanical physics are needed to ensure that the art form is definitely an amazing one.

The concepts of the following are the most prominent examples of physics applications in ballet:
  • the center of gravity and balance
  • projectile motion and the grande jete 
  • rotational mechanics and the pirouette

Center of Gravity and Balance
         Ballet consists of movements of the body as well as motionless poses. These poses demonstrate a balance of the body over a small area of support on the floor. The perfect balance will be achieved only if the center of gravity is on a vertical line passing through the area of support in the floor.
        If the dancer is motionless, the sum of all the forces and torques acting on the body must be zero. The force of gravity vertically downward will be balanced by the force upward from the floor to the foot (the Normal force), acting on the same vertical line.
        If the center of gravity is not in line with the other forces, the dancer will be unbalanced and experience an angular acceleration towards the ground (in other words the dancer will fall to one side).
        A dancer almost never achieves a true balance condition. If the center of gravity is close to that “balance area” that is if the forces are almost but not perfectly vertical, the acceleration away from vertical is initially quite small and the dancer appears to be balanced. Also, as the dancer balances, even if the arm moves an inch, it can throw off the whole center of balance, leading the dancer to counterbalance. After the counterbalance, there is another counterbalance to the first counterbalance which is why when balancing the dancer never stays completely still.

Rotational Mechanics and the Pirouette
        Turning movements are common in all forms of dance. One of the most common turns is the pirouette. The pirouette is a rotation where the dancer supports herself on one leg while the other leg is in a passe position (the foot is touching the opposite knee with the leg turned out). Any pirouette begins with some form of preparation position followed by a torque exerted against the floor. This torque of the floor against the dancer causes the angular acceleration that produces turning motion.
        In ballet, pirouettes are commonly done from one of two positions, fourth position or fifth position. A turn from fifth position, which has a smaller distance, will require more force to produce the same torque than a turn from fourth position, which has a larger distance. This is because torque is equal to the force multiplied by the distance used in the preparation of the turn.
        Using the equation: T=Ia, we can calculate the T used for the turn.


Projectile Motion and the Grand Jete
        All jumps involve vertical accelerations and forces. Because gravity acts vertically downward on our bodies at all times, we can only remain motionless if there is a vertical supporting force equal to our weight (the normal force). In order to jump off the ground, we need to exert a force downward against the floor greater than our weight (mg=mass * acceleration due to gravity for long enough to achieve the vertical upward velocity.
        Jumps combined with horizontal motions such as the grand jete (a leap in which the weight of the body is thrown from one foot to the other) have projectile motion. Once the body loses contact with the floor, the center of gravity will follow a parabolic trajectory that is determined by the initial conditions starting from the ground.
        The trajectory will follow the path of a normal projectile. It will begin with an initial velocity, which will decrease as the dancer rises into the air until it reaches zero. This is at the maximum height during the leap. Following this maximum is the descent to the floor which is an accelerating downward motion until the dancer reaches the ground again.
Image result for ballet dancers grand jete
         Image result for trajectory of a grand jete
Overall, dance and ballet, in particular, are very dependent on physics. Without physics, ballerinas would not be able to do half of the moves that they are able to do. The correct technique uses physics to maintain the gracefulness and strength required for the dancers to look beautiful and effortless.
        



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