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One of my goals as a science educator is to show students science is not just a classroom subject: Science can be found in most (if not all) human activities. If physics teachers can make connections to the fine arts, they might surprise some students and generate interest in those not excited by car, rocket, or bullet problems. The recent release of Fame, a remake of a 1980 film of the same name, provides an excellent opportunity to discuss the physics of dance and music.
This version of Fame has most of the same characters and basic plot structure of the original film. It follows a group of teens at New York City’s High School of Performing Arts from their auditions through graduation. These students specialize in acting, singing, instrumental performance, or dance. Fame’s core group of students begin as freshmen unsure of themselves, but excited to be with artistically minded peers. The plot unfolds in four sections corresponding to each year of school. By the end of senior year, a few students have left school to pursue paid acting or dance positions, while others are seeking alternative ways to support themselves. The film contains many scenes of rehearsals and performances of songs and dance pieces. These scenes are the most useful for a physics teacher hoping to connect with arts students.
Much of the physics of dance is the physics of rotation, or turning on an axis. To be able to understand rotation, your students will need to be comfortable with terms like force, velocity, mass, and momentum as they apply to linear motion, so adding the complication of rotation will not pose a significant hurdle. Physicists describe a rotating object as having angular velocity and angular momentum. Just as linear momentum is a combination of velocity and mass, and shows you how hard it is to stop the moving object, angular momentum is a combination of angular velocity and mass and helps you realize how hard it is to stop a rotating object. One more wrinkle must be considered : Where the mass is placed in a rotating object is a key factor in angular momentum. The farther the mass is from the axis of rotation, the larger the angular momentum will be (given the same angular velocity). Think of the small merry-go-rounds found on some playgrounds: If two people ride in the center of the merry-go-round, it is easier to set it spinning than if they ride on the edge, even though the mass of the system is the same.
The similarity between the merry-go-round and dancing may not be obvious to some students. When dancers want to turn quickly—that is, with a high angular velocity—they need to bring their arms and legs in close to their axis of rotation to minimize the effect of that mass. They might cross their arms over their chests, for example. When they want to stop turning, they extend their arms and legs because moving that mass away from their center increases its contribution to their angular momentum, and slows their rotation. Gymnasts and divers take advantage of this as well, tucking into a nearly spherical shape when turning, then straightening their bodies to slow the rotation for landing or entering the water.
A factor far more important for dancers than divers is friction. In Fame’s opening segment, when students audition for admission to the school, dancers are shown rubbing the bottoms of their shoes on a block of rosin. Rosin is a processed tree sap used by musicians, dancers, and athletes to maximize friction between two surfaces. String musicians put rosin on their bows to help them “grip” the string, while dancers apply it to their shoes to try to prevent unexpected slipping on the floor.
Friction is not always the dancers’ friend, however. When executing multiple spins, or sliding across the floor on their knees, dancers need minimal friction with the floor to prevent injury from heat and abrasion. For a more complete and mathematical presentation on the physics of dance, see this website.
For students more interested in music than dance, Fame gives teachers the opportunity to point out all sound production starts with a vibration, or oscillation of some material. In a drum, the material is clearly the drum’s surface, but it might be less obvious for other instruments. Brass instruments amplify the vibration of the players’ lips, while the clarinet, bassoon, and saxophone have thin reeds that vibrate to produce a sound. String players draw a bow across a string to produce a vibration that the wooden box amplifies so it can be heard.
All musicians need a way to play a variety of notes, or pitches, that comprise a melody, so they need to change the frequency of the oscillation. With stringed instruments (like violins, violas, and cellos), each string’s length, mass, and tension determine the frequency of oscillation, and players tune their instruments by adjusting the tension. When playing, string musicians change the effective length of the string by the placement of their fingers on the fingerboard. A shorter string vibrates at a higher frequency, so the pitch is higher. Brass and wind players use valves to alter the length of the air column in the instrument, again with a shorter air column producing a higher note. This relationship is probably most obvious in a pipe organ, which can have pipes ranging from 10 centimeters to nearly 10 meters long.
I hope many physics and physical science teachers will turn Fame into an opportunity to show the connections between science and the fine arts, and perhaps spark the interest of students who might otherwise avoid physics.
Jacob Clark Blickenstaff is Assistant Professor of Physics and Assistant Director of the Center for Science and Mathematics Education at the University of Southern Mississippi. He can be reached at jacob.blickenstaff@usm.edu.
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