Authors: Margaret Wilson and Jennifer Deckert on behalf of the IADMS Dance Educators' Committee

Successful completion of a pirouette (turn on one leg) can sometimes feel like an impossible task, but understanding more about the mechanics behind the turn may help you find more stability, produce more rotations and have better balance. There are several principles from physics that are useful in understanding the preparation and turning action in a pirouette.

1. Torque – a turning force that helps start the turn (test)
2. Force couple – torque that is created in the placement of the legs and feet in the preparation for the turn
3. Angular acceleration – how to build up turning speed
4. Conservation of angular momentum – how to maintain the desired turning speed.

But first, let’s examine Newton’s laws of motion to help put these principles into context and help describe our understanding of dance movement. The first law has to do with inertia (the tendency to maintain the current state of motion or a resistance to change). Newton's second law deals with acceleration and momentum and the third law describes action/reaction. Each of these laws comes into play in the preparation and continued turning motion in pirouette. To start turning we must overcome inertia through the creation of torque – and we do this in the preparation for the turn. While turns can start from a variety of positions of the legs, if we look at 4th position in external rotation, we can see easily see how the dancer creates torque to overcome inertia and begin the turn. The distance between the two feet, rotating away from each other creates an equal and opposite force which is transferred to the supporting leg in the turn. This generation of torque can be described as a force couple. In 4th position plié a moderate amount of torque is created, in 5th position, where the distance between the feet is very small, less torque is created. If a dancer takes an open fourth allongé (a lunge position where one leg is bent and the other extended), the torque generated is greater (Sugano and Laws 2002).

The force couple and torque help start the turn, but angular acceleration also determined by the contribution of all related body parts in a turn. For example, when the arms and legs are extended away from the center of the body, as when the arms and gesture leg are à la seconde, rotation is slower since more mass further away from the body’s center of rotation. As that mass gets pulled closer to the center of rotation, conservation of angular momentum dictates that the dancer must turn faster. Dancers can feel this when they pull their arms in tight, and it is clearly visible on a low-friction surface like when watching figure skaters. Angular momentum is lost to friction – the amount of surface contact for the turning foot. A dancer will experience less friction en pointe than on a low relevé in plié as is sometimes seen in a jazz turn. The interaction of the surface of the shoe and the floor also contribute to the coefficient of friction: a satin pointe shoe on a vinyl surface has relatively low friction when compared to a bare foot on the same surface. The more friction the slower the turn, and therefore fewer rotations are possible.

Take Away Ideas:

1. Develop a strong supporting leg: In a pirouette the dancer is rotating around a vertical axis so balance in the turning position is important. Imura and Iino (2018) found that dancers need good strength in the supporting leg to help find balance and endurance for multiple revolutions.
2. Focus on the arms in the preparation –Kim, et al, (2015) found that skilled dancers generated larger vertical angular momentum by skillfully using rotation of the upper trunk and arms. The closing arm after the moment of inertia makes the largest contribution to whole-body angular momentum – not the arm that opens as the trunk begins to rotate.
3. While the supporting leg should be strong, the body should be slightly relaxed. The same is true in pirouette. If a dancer holds the body rigid, the slightest displacement from equilibrium will cause gravity to exert a torque on the body, and the dancer will topple. Keeping the body somewhat relaxed enables the dancer to make the slight adjustments necessary to correct for small perturbations from balance.

Additional Reading

1. Laws, K. Physics and the Art of Dance (2002)
2. Sugano A and Laws K. Physical analysis as a foundation for pirouette training. Med Probl Perfom Art, 17 (1) 29-32.
3. Imura A. and Iino Y. Regulation of hip joint kinetics for increasing angular momentum. The results suggest that dancers need to regulate hip joint torques along with the thigh angles in the pirouettes depending on the number of revolutions. Human Movement Science 60(2018)18-31.
4. Kim J, Wilson M, Singhal K, Gamblin S, Suh CY and Kwon YK Generation of vertical angular momentum in single, double and triple-turn pirouette en dehors in ballet. Sports Biomechanics, Volume 13, 2014 - Issue 3
5. Lott, MB and Laws KL The physics of toppling and regaining balance during pirouette. Journal of Dance Medicine & Science 2012, 16(4) 167-174.

Margaret Wilson, PhD
Professor, University of Wyoming

Jennifer Deckert, MFA
Associate Professor, University of Wyoming

Margaret and Jennifer are the co-directors of the Dance Science Program at the University of Wyoming in Laramie, WY USA