Physics is Fun: Physics of Dance Teacher Guide

Episode Description
In Physics of Dance, Jessica directs Cheston in rehearsals for a school
performance of "The Fantastics." Cheston dreams that he is losing his
balance during the performance and falls. Jessica wakes him up, so he
will get to rehearsal on time. Jessica keeps reminding Cheston how physics will improve his balance and dancing ability.

The teens take the viewer for a visit to the Alabama School of Fine Arts Dance Department, where foremost authority on physics and dance, Dr. Ken Laws of Dickinson College, Carlisle Pennsylvania, is teaching class. The hosts discover that physics is not passe in the world of dance!

Concepts Covered

Center of Gravity (Mass)
The center of mass or gravity is the point at which the entire mass of an object may be considered to be concentrated. The center of mass and center of gravity are at the same point; thus, the terms are interchangeable. Objects that have a wide base, a lower center of gravity (mass) with its center of gravity located directly over or under the point of support have greater stability.

Torque
Torque is derived from the Latin word torquere meaning to twist, which is actually what happens when torque is applied. Torque arises when an external force is applied at a point on an object that is some distance from the axis of rotation or pivot point called the 'fulcrum,' causing the object to twist or rotate and can actually make an object's motion more stable (i.e. riding a bicycle). We use torques to our advantage in our everyday lives without thinking about every time we open a door, twist a lid off of a jar, flip a page in a book, throw a football, or row a boat. "What other examples can you think of using torque"?

Conservation of Angular Momentum
Newton's Laws state that force is equal to mass times acceleration, F = m x a, which is a measure of how much an object's linear momentum, p (mass x velocity), is changing over time (F = ?p / ?t). If there is no force, then linear momentum is not changing (?p = 0 Þ pfinal = pinitial) and, thus, it said to be conserved. Similarly, if there are no forces which cause twisting or rotation, then by analogy, it is said that angular momentum is conserved and must not change.

Dance Vocabulary
Choreography- steps, groupings and patterns of a ballet or dance composition

Arabesque - a position of the body, in profile, supported on one leg, which can be straight or demi-plié, with the other leg extended behind and at right angles to it

Plié - a bending of the knee or knees.

Demi - half

Pirouette - a complete turn of the body on one foot, on point or demi-pointe.

Fouette - a term applied to a whipping movement. The movement may be a short whipped movement of the raised foot as it passes rapidly in front of or behind the supporting foot or the sharp whipping around of the body from one direction to another.

En Dehor - turning outward in the direction of the raised leg.
Releve - raising of the body on the points or demi-pointes, point or demi-pointe.

Pointe - on toes

Preview Discussion
What does it mean to be balanced?
What things do you do that require good balance? Generate a list of activities that students must maintain balance to perform.
If you lose balance, what might you do to regain it?
What allows you to be balanced or maintain balance?
Are you familiar with or know someone who participates in ballet?
How do you think balance affects a ballet dancer's performance?
What principles of physics might apply?

Post Viewing Activities and Discussion
Note: Teachers might want to refer to portions of the video during this discussion. Use your video recorder's counter to cue up sections you will reference.

1. Balance
What does it mean to be balanced?
(Center of gravity must be on a vertical line above the area of support at
the floor.)
What IS the center of gravity?
Look at video or locate a photo of a dancer balanced in arabesque position. Discuss what the center of gravity is and its significance.

How does one regain balance if toppling?
(If off balance, one must arrange for something to push against the body to return the center of gravity to the balance condition.)
What is there that can push on the body?
(The ground! One must rotate part of the body one direction, so that the
legs and feet try to rotate the other direction. This produces the needed force against the floor, illustrating Newton's third law: the floor pushes on the body with an equal and opposite force, pushing the center of gravity back to the balance condition.)

Activity:Balance
One person balances on the balls of the feet. Another stands behind and gives a gentle push on the shoulders.
What do instincts tell the pushed person to do?
Rotate the upper body and perhaps the arms forward. This counter-intuitive action results in the feet pushing forward against the floor, which allows balance to be regained by the above logic.

Activity:Walk the Line
a) Using chalk or masking tape, draw or place a line on the floor that spans the classroom or other area.
b) In groups of three, students should take turns attempting to walk along the straight line, arms outstretched, with an activity partner walking along each side.
c) As each student attempts their walk, the partners should take turns 'gently' nudging the student that is walking.
With each nudge, have students pay special attention to what body adjustments (arms specifically) they have to make in order to keep balanced? "Did you attempt to shift or move your weight (i.e. center of gravity)? If so, how? How easy was it for your partners to 'nudge' you off balance? What factors do you think affect or influence how hard a 'nudge' should be in order to knock you off balance"?

How does one start accelerating linearly?
(Balance must be destroyed in order for the body to start toppling. Then a horizontal force can be exerted against the floor producing the acceleration, without also allowing the toppling to continue.)
How does one start toppling if initially balanced?
(Students may describe various ways, using different forces.)

Activity:Turns
How does a dancer exert forces against the floor to produce a torque that initiates a pirouette?
How does the torque depend on the separation of the feet on the floor in
the preparation position?
How does a dancer control the rate of turn after a torque initiates the turn?
How does a dancer continue turning in a 32-turn pirouette?
All of these questions can be answered with a combination of demonstrations and explanations.

First, what is a torque?
(Anyone can feel a torque if another person pulls on one shoulder and pushes on the other. You tend to turn. Equal and opposite forces with some distance between the lines along which they act -- that's torque!)
What determines the magnitude of torque?
Try opening a door by pushing near the hinge; that's hard. (That's why
door handles are at the opposite edge.) And the same reasoning applies to the distance between the feet in a preparation position for a pirouette.

Activity: Conservation of Momentum
Materials Needed:
2 free weights, books, or bricks per 2 students
Revolving stool or chair

Procedure:
Divide students in pairs
One student will sit on stool with arms extended laterally and holding free weights. The other student will spin the stool of chair by providing a torque and move away.

The student should then draw his/her arms in close to see what happens. Outstretching and drawing the arms in alternately should make a difference in the motion.
What happens?
(Controlling the rate of turn -- that's the ice skater effect; the closer
the mass of the body is to the axis of rotation, the faster the turn. This
also explains movement in the pirouette.)

The 32-turn pirouette question refers to the fouette turn sequence; the
dancer and Dr. Laws carry out a dialogue that describes the logic of the
analysis.
"Caroline, I want you to do a 32-turn pirouette at a constant
tempo."
"I can't do that!"
"Why not?"
"Because I'd slow down due to friction, and I'd lose balance and fall."
"OK, if you'd slow down, that means you need to regain the lost momentum once each turn."
"But I'm turning en pointe. How can I get a torque from the floor?"
(Review this portion of the tape to answer questions)

3. Vertical jumps.
How is the height of a vertical jump related to the time in the air?
Jumps are carried out with different magnitudes of effort, producing
different heights. Time is measured, showing that twice the time in the
air (2t) relates to four times the height (4h) and has a profound impact on dancers' remarkable sense of tempo.

Another concept predicts the effect of the use of arms in a vertical jump. If the arms are used to store vertical momentum, greater height can be achieved. Timing of the arms is crucial.

Activity: Vertical Jumps
Materials needed:
Meter stick and a stopwatch

Principles: Jumps are carried out with different magnitudes of effort, producing different heights. Time can be measured showing a definite relationship between the heights one can achieve and the time spent in the air; this has a profound impact on a dancer's remarkable sense of tempo. Can you determine this relationship?

For the Teacher: In general, the relationship between the time spent in the air and the height achieved is such that height is proportional to the square of the time. For example, twice the time in air (2t) relates to four times the height (4h). You may want to share this with your students at any time that you feel is appropriate. Another concept predicts the effect of using your arms during the jump where greater heights can be achieved but timing is crucial!

Procedure: In groups three or more students, have one student perform vertical jumps with your arms held at your side. As one student jumps, the other two students should record the height and total time spent in the air for each jump. Repeat this step at least three (3) times and compute an average value for the height and the time. Students should all take a turn jumping. After all have jumped and computations have been completed, compare your data. Can you determine the relationship between time and height? Repeat the same activity but now swing your arms as you jump. What effect does this have on the height of your jump? How exactly should you time the swing your arms in order to have a positive and a negative effect on the height of your jump?

Dance Over to These Sites:

American Ballet Theatre Online Ballet Dictionary http://www.abt.org/dictionary/

Dance @the Alabama School of Fine Arts
http://www.asfa.k12.al.us/Programs/Dance/cover.asp

Center of Gravity http://www.exploratorium.edu/snacks/center_of_gravity.html