The Physics Behind Ballet's Hardest Move: The Fouetté

\The fouetté, a dazzling display of athleticism and artistry, is a move often seen as one of the most challenging in ballet. In the third act of "Swan Lake," the Black Swan executes a seemingly endless series of these turns, spinning 32 times on one pointed foot. But what makes this feat of physics possible?

Understanding the Fouetté

The term fouetté translates to "whipped" in French, perfectly describing the dancer's ability to whip around continuously. During these approximately thirty seconds, the ballerina resembles a human top in perpetual motion. Let's break down the physics involved.

Generating and Maintaining Rotation

The dancer initiates the fouetté by pushing off with one foot, generating torque. However, maintaining this rotation is the real challenge. Several factors work against the dancer:

• Friction: The friction between the pointe shoe and the floor, as well as air resistance, gradually reduces momentum.

The Secret to Continuous Turns

To counteract these forces, the dancer employs several clever techniques:

• The Pause and Twist: Between each turn, the dancer momentarily pauses, facing the audience. The supporting foot flattens and then twists as it rises back onto pointe, providing a small amount of new torque.
• Arm Movement: The arms sweep open, aiding in balance and control.
• Core Stability: Maintaining a constant center of gravity and a vertical turning axis is crucial for efficient turns.
• The Moving Leg: The seemingly paused leg is actually in constant motion. As the supporting foot twists, the elevated leg straightens and moves from front to side before folding back into the knee. This continuous motion stores momentum.

Momentum Transfer

As the leg retracts, the stored momentum is transferred back to the dancer's body, propelling her around as she rises back onto pointe. This constant exchange of momentum between leg and body is what sustains the fouetté.

Maximizing Turns

A highly skilled ballerina can achieve multiple turns per leg extension through two primary methods:

1. Early Leg Extension: Extending the leg sooner allows it to store more momentum, which, in turn, provides a greater boost when retracted.
2. Reducing Rotational Inertia: By bringing the arms or leg closer to the body upon returning to pointe, the dancer decreases her rotational inertia.

The Physics of Rotational Inertia

The fouetté, like all turns in ballet, is governed by angular momentum. Angular momentum is the product of angular velocity (the speed of the turn) and rotational inertia (a body's resistance to rotational motion).

Rotational inertia increases when mass is distributed further from the axis of rotation and decreases when mass is closer. Therefore, by bringing her arms closer, the dancer shrinks her rotational inertia. To conserve angular momentum, her angular velocity must increase, allowing her to complete more turns.

An Ice Skating Analogy

This principle is also seen in ice skating, where skaters spin faster by drawing in their arms and legs.

More Than Just Magic

While the Black Swan's 32 fouettés may appear supernatural, they are rooted in the principles of physics. It's a testament to the dancer's skill and understanding of these principles that allows them to execute this challenging move with such grace and precision.