The physics of the "hardest move" in ballet - Arleen Sugano
-
0:07 - 0:09In the third act of "Swan Lake,"
-
0:09 - 0:14the Black Swan pulls off a seemingly
endless series of turns, -
0:14 - 0:17bobbing up and down on one pointed foot
-
0:17 - 0:23and spinning around, and around,
and around 32 times. -
0:23 - 0:25It's one of the toughest sequences
in ballet, -
0:25 - 0:27and for those thirty seconds or so,
-
0:27 - 0:31she's like a human top
in perpetual motion. -
0:31 - 0:34Those spectacular turns
are called fouettés, -
0:34 - 0:36which means "whipped" in French,
-
0:36 - 0:40describing the dancer's incredible
ability to whip around without stopping. -
0:40 - 0:44But while we're marveling at the fouetté,
can we unravel its physics? -
0:44 - 0:49The dancer starts the fouetté by pushing
off with her foot to generate torque. -
0:49 - 0:52But the hard part
is maintaining the rotation. -
0:52 - 0:53As she turns,
-
0:53 - 0:56friction between her pointe shoe
and the floor, -
0:56 - 0:58and somewhat between her body and the air,
-
0:58 - 1:00reduces her momentum.
-
1:00 - 1:02So how does she keep turning?
-
1:02 - 1:07Between each turn, the dancer pauses
for a split second and faces the audience. -
1:07 - 1:09Her supporting foot flattens,
-
1:09 - 1:12and then twists as it rises
back onto pointe, -
1:12 - 1:17pushing against the floor to generate
a tiny amount of new torque. -
1:17 - 1:21At the same time, her arms sweep open
to help her keep her balance. -
1:21 - 1:26The turns are most effective if her center
of gravity stays constant, -
1:26 - 1:30and a skilled dancer will be able to keep
her turning axis vertical. -
1:30 - 1:33The extended arms
and torque-generating foot -
1:33 - 1:35both help drive the fouetté.
-
1:35 - 1:39But the real secret and the reason
you hardly notice the pause -
1:39 - 1:42is that her other leg never stops moving.
-
1:42 - 1:44During her momentary pause,
-
1:44 - 1:48the dancer's elevated leg straightens
and moves from the front to the side, -
1:48 - 1:51before it folds back into her knee.
-
1:51 - 1:56By staying in motion, that leg is storing
some of the momentum of the turn. -
1:56 - 1:59When the leg comes back in
towards the body, -
1:59 - 2:02that stored momentum gets transferred
back to the dancer's body, -
2:02 - 2:06propelling her around as she rises
back onto pointe. -
2:06 - 2:10As the ballerina extends and retracts
her leg with each turn, -
2:10 - 2:14momentum travels back and forth
between leg and body, -
2:14 - 2:16keeping her in motion.
-
2:16 - 2:21A really good ballerina can get more
than one turn out of every leg extension -
2:21 - 2:22in one of two ways.
-
2:22 - 2:25First, she can extend her leg sooner.
-
2:25 - 2:28The longer the leg is extended,
the more momentum it stores, -
2:28 - 2:33and the more momentum it can return
to the body when it's pulled back in. -
2:33 - 2:35More angular momentum means
she can make more turns -
2:35 - 2:39before needing to replenish
what was lost to friction. -
2:39 - 2:41The other option is for the dancer
-
2:41 - 2:44to bring her arms
or leg in closer to her body -
2:44 - 2:46once she returns to pointe.
-
2:46 - 2:47Why does this work?
-
2:47 - 2:49Like every other turn in ballet,
-
2:49 - 2:51the fouetté is governed
by angular momentum, -
2:51 - 2:57which is equal to the dancer's angular
velocity times her rotational inertia. -
2:57 - 2:59And except for what's lost to friction,
-
2:59 - 3:03that angular momentum has to stay
constant while the dancer is on pointe. -
3:03 - 3:07That's called conservation
of angular momentum. -
3:07 - 3:09Now, rotational inertia can be thought of
-
3:09 - 3:13as a body's resistance
to rotational motion. -
3:13 - 3:18It increases when more mass is distributed
further from the axis of rotation, -
3:18 - 3:23and decreases when the mass is distributed
closer to the axis of rotation. -
3:23 - 3:25So as she brings her arms closer
to her body, -
3:25 - 3:28her rotational inertia shrinks.
-
3:28 - 3:30In order to conserve angular momentum,
-
3:30 - 3:33her angular velocity,
the speed of her turn, -
3:33 - 3:34has to increase,
-
3:34 - 3:36allowing the same amount
of stored momentum -
3:36 - 3:39to carry her through multiple turns.
-
3:39 - 3:42You've probably seen ice skaters
do the same thing, -
3:42 - 3:46spinning faster and faster
by drawing in their arms and legs. -
3:46 - 3:50In Tchaikovsky's ballet, the Black Swan
is a sorceress, -
3:50 - 3:55and her 32 captivating fouettés do seem
almost supernatural. -
3:55 - 3:58But it's not magic that
makes them possible. -
3:58 - 3:59It's physics.
- Title:
- The physics of the "hardest move" in ballet - Arleen Sugano
- Speaker:
- Arleen Sugano
- Description:
-
View full lesson: http://ed.ted.com/lessons/the-physics-of-the-hardest-move-in-ballet-arleen-sugano
In the third act of "Swan Lake", the Black Swan pulls off a seemingly endless series of turns, bobbing up and down on one pointed foot and spinning around and around and around ... thirty-two times. How is this move — which is called a fouetté — even possible? Arleen Sugano unravels the physics of this famous ballet move.
Lesson by Arlene Sugano, animation by Dancing Line Productions.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:17
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Jessica Ruby edited English subtitles for The physics of the "hardest move" in ballet - Arleen Sugano | ||
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