The Physics of Dance
Physics as science and dance as art may seem unrelated, but the two share much in common and may even benefit each other. Exploring dancers’ movements enables physicists to gain tangible experience of their subject matter. Dancers, in turn, may improve their skills by becoming familiar with the physics that underlie basic dance movements, such as spins, jumps, and balance.
Balancing in relevé (on the toes) results from a net-zero force acting on a dancer’s body long the line connecting the center of gravity and the pivot point (the toes). Dancers are in a constant push-pull relationship created by the different forces that act on them in their surroundings. The force exerted against the floor by the dancer equals the force of gravity exerted on them.
To start moving or accelerating, a motionless dancer must put one leg forward while exerting a backward force on the other foot. The repetition of this process is walking. By increasing the applied force with each motion and gaining momentum, dancers can make the process more dramatic.
Momentum is created by placing mass into motion. The amount of momentum is proportional to the amount of moving mass and its velocity. By strengthening their legs, dancers can increase their speed. Moving across the floor creates linear momentum, while spinning creates angular momentum.
The two principles of physics that influence the speed and balance of a dancer’s turn are called torque and rotational inertia. Torque is the amount of force acting on an object that causes it to rotate about an axis. Torque is significant for the rate at which turns can be executed by a dancer. The greater the friction from pushing off the floor, the faster a dancer will spin. Another way a dancer can affect her or his rate of rotation is by extending and retracting a leg during turns. This influences the rotational inertia of the turn so that the dancer slows when extending a leg and speeds when retracting it.
Acceleration describes a change in speed or direction of motion. In ballet, a common change in direction is motion in a circular path. As dancers move around the stage in a circular path and push off the floor, the force exerted on the body is directed toward the center of the circle. This force sustains the constant change in motion that enables dancers to move on the curve. Slightly leaning toward the center of the circular path prevents them from leaving it.
Every jump includes vertical acceleration and force. To jump, dancers must apply a force greater than their weight downward against the floor. They can increase that force by starting the jump from a plié or bending their legs. The motion preceding the jump is equally important. A jump moving into and out of a plié is more effective than a jump starting from a plié at rest.
Jumps also can be horizontal. Such movements create trajectories or paths of motion through space. Multiple forces, including friction and gravity, play roles. Once dancers are off the ground, their center of gravity follows a parabolic trajectory determined by the initial conditions of the jump. The path remains unchanged even if dancers move their bodies while in the air. The jump combines a rising motion with decreasing speed, a moment with no vertical speed, and an accelerated downward motion. The strength, height, and weight of dancers influence the effectiveness of the jumps they perform.
