## Bryn Mawr College Dissertations and Theses

2012

#### Degree

Doctor of Philosophy (PhD)

Physics

#### Abstract

All forms of dance incorporate examples of the human body in motion or standing in an aesthetically appealing pose. While balancing in a static position, dancers make small adjustments to avoid toppling. Balancing when the body is rotating around a vertical axis with one supporting foot at the floor (a pirouette) is more complex. Dancers are often taught to perform pirouettes by beginning the movement as close to balanced as possible and holding the body rigid throughout the turn. Theoretically, if the body is initially perfectly balanced, the number of revolutions will be limited only by friction. However, the research reported here demonstrates that dancers who perform pirouettes without making adjustments to correct for loss of balance will likely be unable to complete more than a two or three turn pirouette.

The topple angle (θ) as function of time was predicted for a model of a rigid body dancer. When θ becomes large enough, dancers must compensate for loss of balance or end the turn. That limiting angle was determined experimentally and set as the upper limit to θ. It was found that performing more than a three-turn, rigid-body pirouette requires the dancer to begin unreasonably close to perfectly balanced (θ<0.1°).

To successfully perform more than a three turn pirouette, dancers must employ one of three strategies for regaining balance: (1) Return the center of mass (CM) to a location vertically above the supporting foot (SF), which requires a horizontal force on the body from the floor; (2) Hop the SF to a position vertically under the CM, which compromises the aesthetic of the movement; or (3) slide the SF under the CM, which moves the area of support and produces a horizontal force to move the CM to a revised location.

An experimental analysis of dancers’ pirouettes was performed in order to determine what adjustment mechanisms were successfully employed to regain balance. Sliding the SF was the most common and effective technique used by advanced dancers. The SF slides were accompanied by a decrease in normal force, so the instruction to “lift” when performing a pirouette may be useful.