In the mesmerizing third act of “Swan Lake,” the Black Swan captivates the audience with a stunning display of ballet prowess, executing 32 consecutive spins on a single pointed foot. This sequence, known as fouettés, is renowned for its difficulty, highlighting the dancer’s exceptional skill in maintaining continuous motion.
The dancer begins the fouetté by pushing off with her foot to create torque, which is the force that initiates her spin. However, the real challenge lies in sustaining this rotation. As she spins, friction between her pointe shoe and the floor, along with air resistance, gradually reduces her momentum. So, how does she keep turning?
Between each spin, the dancer momentarily pauses, facing the audience. Her supporting foot flattens and then twists as it rises back onto pointe, generating a small amount of new torque. At the same time, her arms extend to help maintain balance. The success of these turns depends on keeping her center of gravity stable, allowing her to maintain a vertical turning axis.
The dancer’s extended arms and the torque from her foot both play crucial roles in the fouetté. The illusion of continuous motion is achieved by keeping her other leg in motion. During the brief pause, the elevated leg straightens and moves from the front to the side before folding back into her knee. This movement allows the leg to store some momentum from the turn. When the leg returns towards the body, the stored momentum transfers back to the dancer, propelling her as she rises back onto pointe.
As the ballerina extends and retracts her leg with each turn, momentum shifts between her leg and body, keeping her in motion. A skilled ballerina can achieve multiple turns from each leg extension in one of two ways. First, she can extend her leg sooner, allowing it to store more momentum, which can then be transferred back to the body. More angular momentum means she can perform additional turns before needing to compensate for losses due to friction.
The second method involves bringing her arms or leg closer to her body once she returns to pointe. This technique is based on the principle of angular momentum, which is the product of the dancer’s angular velocity and her rotational inertia. Except for what is lost to friction, angular momentum must remain constant while the dancer is on pointe, a principle known as the conservation of angular momentum.
Rotational inertia refers to a body’s resistance to rotational motion. It increases when mass is distributed further from the axis of rotation and decreases when mass is closer to the axis. By bringing her arms closer to her body, the dancer reduces her rotational inertia. To conserve angular momentum, her angular velocity, or the speed of her turn, must increase, allowing her to utilize the stored momentum for multiple turns.
Similar principles can be observed in ice skaters, who spin faster by drawing in their arms and legs. In Tchaikovsky’s ballet, the Black Swan is portrayed as a sorceress, and her 32 captivating fouettés appear almost magical. However, the reality is that it is physics that makes these extraordinary movements possible.
Explore an online physics simulation that demonstrates the principles of torque and angular momentum. Adjust variables such as friction, mass distribution, and initial torque to see how they affect a dancer’s ability to perform fouettés. Reflect on how these principles apply to the Black Swan’s performance.
Form small groups to discuss the role of rotational inertia and angular momentum in ballet. Analyze video clips of professional dancers performing fouettés, and identify the techniques they use to maintain balance and momentum. Share your insights with the class.
Conduct a simple experiment using a spinning chair. Sit on the chair with your arms extended and have a partner spin you. Then, pull your arms in and observe the change in your spinning speed. Relate your observations to the conservation of angular momentum in ballet.
Work individually or in pairs to create a mathematical model that calculates the angular velocity of a dancer based on different arm and leg positions. Use this model to predict how changes in body position affect the number of fouettés a dancer can perform.
Apply your understanding of physics by creating a short dance sequence that incorporates principles of torque and angular momentum. Perform your sequence for the class, explaining how you used physics to enhance your choreography.
In the third act of “Swan Lake,” the Black Swan performs a remarkable series of turns, spinning around 32 times on one pointed foot. This sequence, known as fouettés, is one of the most challenging in ballet, showcasing the dancer’s incredible ability to maintain motion.
The dancer initiates the fouetté by pushing off with her foot to generate torque. However, the challenge lies in sustaining the rotation. As she turns, friction between her pointe shoe and the floor, as well as some resistance from the air, reduces her momentum. So, how does she continue to turn?
Between each turn, the dancer briefly pauses and faces the audience. Her supporting foot flattens and then twists as it rises back onto pointe, generating a small amount of new torque. Simultaneously, her arms extend to help maintain balance. The effectiveness of the turns relies on keeping her center of gravity stable, and a skilled dancer can maintain a vertical turning axis.
The extended arms and the torque-generating foot both contribute to the fouetté. The key to the illusion of continuous motion is that her other leg remains in motion. During the brief pause, the elevated leg straightens and moves from the front to the side before folding back into her knee. This movement allows the leg to store some momentum from the turn. When the leg returns towards the body, that stored momentum transfers back to the dancer, propelling her as she rises back onto pointe.
As the ballerina extends and retracts her leg with each turn, momentum shifts between her leg and body, keeping her in motion. A skilled ballerina can achieve multiple turns from each leg extension in one of two ways. First, she can extend her leg sooner, allowing it to store more momentum, which can then be transferred back to the body. More angular momentum means she can perform additional turns before needing to compensate for losses due to friction.
The second option involves bringing her arms or leg closer to her body once she returns to pointe. This works because the fouetté is governed by angular momentum, which is the product of the dancer’s angular velocity and her rotational inertia. Except for what is lost to friction, angular momentum must remain constant while the dancer is on pointe, a principle known as conservation of angular momentum.
Rotational inertia refers to a body’s resistance to rotational motion. It increases when mass is distributed further from the axis of rotation and decreases when mass is closer to the axis. By bringing her arms closer to her body, the dancer reduces her rotational inertia. To conserve angular momentum, her angular velocity, or the speed of her turn, must increase, allowing her to utilize the stored momentum for multiple turns.
Similar principles can be observed in ice skaters, who spin faster by drawing in their arms and legs. In Tchaikovsky’s ballet, the Black Swan is portrayed as a sorceress, and her 32 captivating fouettés appear almost magical. However, the reality is that it is physics that makes these extraordinary movements possible.
Physics – The branch of science concerned with the nature and properties of matter and energy. – In the physics lecture, we explored the fundamental forces that govern the universe.
Ballet – A highly technical form of dance with its own vocabulary based on French terminology. – The physics of ballet involves understanding the balance and center of mass to execute graceful movements.
Momentum – The quantity of motion of a moving body, measured as a product of its mass and velocity. – In the physics lab, we calculated the momentum of a dancer as she leaped across the stage.
Torque – A measure of the force that can cause an object to rotate about an axis. – The physics professor explained how torque is crucial in understanding the mechanics of a pirouette in ballet.
Rotation – The action of rotating around an axis or center. – The dancer’s rotation was analyzed to understand the physics behind her spins and turns.
Friction – The resistance that one surface or object encounters when moving over another. – In physics, we studied how friction affects the movement of ballet shoes on different surfaces.
Inertia – The resistance of any physical object to any change in its velocity. – The concept of inertia is important in physics to explain why a dancer continues to move even after the initial force is removed.
Gravity – The force that attracts a body toward the center of the earth, or toward any other physical body having mass. – Understanding gravity is essential in physics to analyze how dancers maintain balance during jumps.
Motion – The action or process of moving or being moved. – The physics of motion is crucial in choreographing sequences that require precise timing and coordination.
Conservation – A principle in physics that states certain properties of isolated physical systems do not change over time. – The conservation of angular momentum is a key concept in physics that explains how a dancer can spin faster by pulling in her arms.
