# Physics Photo of the Week

## May 11, 2012

Ballet Leap - Ballet and Photos by Zazie Tobey
The physics of Ballet is complicated and intriguing.    Having danced since she was five years old Zazie has found that learning anatomy and physics has contributed to her dance ability and has made dance easier to learn and to perform well.  She was eager to make the videos of the sport she loves.

We studied the trajectory of her body performing a Sotasha leap.  Zazie is able to maintain a longer "hang time" by raising her arms and legs during the leap. Watch the video clip she made of her leap below.  We tracked her head while she was airborne.   A still shot of the tracks is also shown below.  Careful study of the tracks shows a steeper rise and a shallower descending curve for her head (and body).  An ordinary ball in a trajectory shows a symmetric up and down curve.  The dynamics of ballet (and long jumps, high jumps, and running jump shots in basketball) is modified by the accelerations of the arms and legs.

By raising the legs and arms during the rise, the rising mass of the limbs keeps the body trunk from rising as far.  When the limbs are moved down for the landing, the downward acceleration of the limbs helps keep the body aloft.  The athlete's center of mass follows a simple parabolic trajectory (as does a ball). The extra motion of the arms and legs moves the center of mass higher and lower in the trunk of the body.  Because the trunk of the body follows a lower trajectory than the center of mass, it gives the illusion of greater "hang time".  The asymmetric trajectory of Zazie's head is consistent with several jumps that she made in front of the camera.

Zazie is demonstrating a Sotasha leap in the video - different from a grand jete.  In the Sotasha she fully flexes her right leg before the leap, giving her right leg a quick "flick" to add to her height and the leg dynamics in the leap.  The extra momentum given to her lower leg gives her body more height with less stress on the left leg that is last to leave the ground.

Zazie adds that she will be assisting teaching a dance practicum course at WWC next academic year with dance faculty Julie Gillum.  Interested participants should contact her or Julie.

Zazie filmed herself by placing the video camera on a tripod, starting the recording, then running around in front of the camera to perform one or two leaps, and finally running back to stop the camera.  This all made for an exhausting workout involving several "takes" in an afternoon.

The digital video camera was purchased through a grant by the Pugh Foundation.  Unlike conventional video cameras, this camera can control the exposure time of each frame.   At 30 frames per second stop-action video is possible because each frame of the video was exposed for about 1/500 second in addition to a high sensor sensitivity.

This is the final Physics Photo of the Week for the 2011-2012 academic year.  The Physics Photo of the Week plans to return on August 31, 2012.  Have a nice summer!

Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department. These photos feature interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation. Atmospheric phenomena are especially welcome. Please send any photos to dcollins@warren-wilson.edu.

All photos and discussions are copyright by Donald Collins or by the person credited for the photo and/or discussion.  These photos and discussions may be used for private individual use or educational use.  Any commercial use without written permission of the photoprovider is forbidden.

Observers are invited to submit digital photos to: