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.
Click here to see the Physics Photo of the Week Archive.
