Pirouette The Aspects

of Physics Victoria Culver Science Fair 2012 Purpose To determine the amount of torque required to execute a pirouette.

Find the torque, momentum, tangential velocity, and centripetal force of the pirouette. Hypothesis As the number of pirouettes increases, the amount of torque, momentum and tangential velocity required to perform the pirouette will increase. About Pirouettes A pirouette, one of the most common turns in all forms of dance, is a ballet move that relies heavily on the mechanics of physics. Form of a Pirouette A pirouette is a rotation that has one leg in the retire position, and the other leg supporting the weight of the dancer. Front View Side View Leg in Retire Position Supporting Leg Why? Dancers unintentionally use and require certain mechanics of physics. For example:

- balance: demonstrating body movements with motionless poses

- projectile motion: performing a gande jete, a leap, involving vertical forces and accelerations

In this experiment, the aspects of physics in a pirouette, which requires rotational motion, are being studied. Methods/Procedure 1) Video tape a quadruple pirouette from above within a four count.

2) Video tape a single and a double pirouette in the same amount of time/ four count.

3) Video tape the single, double, and quadruple pirouette from a front view with the dancer facing the camera. Use the same counts for these pirouettes.

4) Upload both front and above views of the 3 different pirouettes to "Tacker".

5) For the above view shots: Use "Tacker" to determine the position magnitude, the x- and y-velocity, the velocity magnitude, the x- and y- acceleration, the acceleration magnitude, the angular velocity, the angular acceleration, the x- and y-momentum, and the momentum magnitude.

6) Put obtained data into a table.

7) Determine the tangential velocity, centripetal acceleration, centripetal force, torque and momentum for the 3 pirouettes. Methods/Procedure

8) Determine the difference in the amount of torque, momentum, and tangential velocity required for the different pirouettes.

9) For the front view shots: Use "Tacker" to determine the position magnitude, the x- and y-velocity, the velocity magnitude, the x- and y- acceleration, the acceleration magnitude, the angular velocity, the angular acceleration, the x- and y-momentum, and the momentum magnitude.

10) Put the obtained data into a table.

11) Determine the tangential velocity, centripetal acceleration, centripetal force, torque and momentum for the 3 pirouettes.

12) Determine the difference in the amount of torque, momentum, and tangential velocity required for the different pirouettes. Cont. Data Data Notes: m= 60 kg

r & d = .2150 m

r & d = .8750 m top top front front 1P= Single Pirouette

2P= Double Pirouette

4P= Quadruple Pirouette Key: Formulas Used Tangential Velocity: Centripetal Acceleration: Centripetal Force: Torque: v=r t . c c a =v

r I t 2 c F =mv

r c I t 2 l =F d l . tangential velocity=

radius x angular velocity centripetal acceleration=(tangential velocity)

radius 2 centripetal force=(mass) x (tangential velocity)

radius 2 [ ] [ ] [ ] [ ] torque=Force x distance Data Analysis of the Results

from the Top View Data Analysis of the Results

from the Top View Data Analysis of the Results

from the Front View Data Analysis of the Results

from the Front View Tangential Velocity: Centripetal Force: Torque: Momentum: Tangential Velocity: Centripetal Force: Torque: Momentum: 1P: v =454.4191195 m/s

2P: v =410.0245435 m/s

4P: v =487.412955 m/s The difference between 1P and 4P was found to be v = 32.9938255 m/s. 1P: F =57569202.31 N

2P: F =46917244.55 N

4P: F =66298992.2 N The difference between 1P and 4P was found to be F = 8723789.89 N. 1P: =12377378.5 N m

2P: =10087208.58 N m

4P: =14254283.32 N m The difference between 1P and 4P was found to be = 13015303 N m. l

l

l l l l l l 1P: p=4.4714353 kg m/s

2P: p=4.0264852 kg m/s

4P: p=4.3465285 kg m/s . l . . . . . . t t t t c c c c The difference between 1P and 4P was found to be p= 0.1261503 kg m/s. . 1P: v =2222.3978 m/s

2P: v =27.526675 m/s

4P: v =2279.409476 m/s The difference between 1P and 4P was found to be v = 57.011675 m/s. 1P: F =338677850.1 N

2P: F =51950.21347 N

4P: F =272774646.6 N The difference between 1P and 4P was found to be F = 65903203.5 N. t t t t c c c c 1P: =296343118.8 N m

2P: =45456.43679 N m

4P: = 238677815.8 N m The difference between 1P and 4P was found to be = 57665303 N m. 1P: p=11.440014 kg m/s

2P: p=12.119554 kg m/s

4P: p=15.414525 kg m/s The difference between 1P and 4P was found to be p= 3.974511 kg m/s. l l l

l

l l l l . . . . . . . . Top View Front View *from center of head to shoulder *from center to finger tip Results Top View: Single Pirouette Double Pirouette Quadruple Pirouette Front View: Single Pirouette Double Pirouette Quadruple Pirouette Conclusion The hypothesis was proven to be true, and the results can be seen through the differences between a single pirouette and a quadruple pirouette, allowing a greater difference to be observed. All amounts of torque, momentum, and tangential velocity that was required to perform a single pirouette needed to be increased in order to perform a quadruple pirouette. Bibliography http://www.abt.org/education/dictionary/index.html

www.algaria.org/Phys1PP/C8_Rotation.ppt

http://www. artofballet.com/jpg/pir2.jpg

www.asbweb.org/conferences/2012/abstract/533.pdf

www.dance-teacher.com/content/perfect-pirouette

www.ehow.com/video_12238370_make-pirouettes-better.html

www.ezintearticles.com/?How-to-Do-a-Perfect-Pirouette&id=3285329

www.fitforafeast.com/dance-lessons-pirouette-tutorial.html

www.iceskatingresources.org/PhysicsBallet.pdf

www.meriam-webster.com/dictionary.pirouette

www.physicsofdance.homestead.com/ballet2~ns4.html

http://schmeightschmatchers.files.wordpress.com/2012/06/pirouette.jpg

www.the-perfect-pointe.com/PointeShoePhysics.jtml Acknowledgments - Dan & Company Dance Studio- a local dance studio in Dunwoody, for the accommodations to film the pirouettes on a standard dance floor.

- Jaspin Newell- Dan & Company Dance Studio instructor, company dancer at "Dancer's Studio Backstage", graduate from Marymount Manhattan College in New York with a dance and academic scholarship, for performing the pirouettes used in this experiment.

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# Pirouette: The Aspects of Physics

Science Fair 2012

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