Placeholder Image

Subtitles section Play video

  • 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 32 times.

  • It's one of the toughest sequences in ballet,

  • and for those thirty seconds or so,

  • she's like a human top in perpetual motion.

  • Those spectacular turns are called fouettés,

  • which means "whipped" in French,

  • describing the dancer's incredible ability to whip around without stopping.

  • But while we're marveling at the fouetté, can we unravel its physics?

  • The dancer starts the fouetté by pushing off with her foot to generate torque.

  • But the hard part is maintaining the rotation.

  • As she turns,

  • friction between her pointe shoe and the floor,

  • and somewhat between her body and the air,

  • reduces her momentum.

  • So how does she keep turning?

  • Between each turn, the dancer pauses for a split second and faces the audience.

  • Her supporting foot flattens,

  • and then twists as it rises back onto pointe,

  • pushing against the floor to generate a tiny amount of new torque.

  • At the same time, her arms sweep open to help her keep her balance.

  • The turns are most effective if her center of gravity stays constant,

  • and a skilled dancer will be able to keep her turning axis vertical.

  • The extended arms and torque-generating foot

  • both help drive the fouetté.

  • But the real secret and the reason you hardly notice the pause

  • is that her other leg never stops moving.

  • During her momentary pause,

  • the dancer's elevated leg straightens and moves from the front to the side,

  • before it folds back into her knee.

  • By staying in motion, that leg is storing some of the momentum of the turn.

  • When the leg comes back in towards the body,

  • that stored momentum gets transferred back to the dancer's body,

  • propelling her around as she rises back onto pointe.

  • As the ballerina extends and retracts her leg with each turn,

  • momentum travels back and forth between leg and body,

  • keeping her in motion.

  • A really good ballerina can get more than one turn out of every leg extension

  • in one of two ways.

  • First, she can extend her leg sooner.

  • The longer the leg is extended, the more momentum it stores,

  • and the more momentum it can return to the body when it's pulled back in.

  • More angular momentum means she can make more turns

  • before needing to replenish what was lost to friction.

  • The other option is for the dancer

  • to bring her arms or leg in closer to her body

  • once she returns to pointe.

  • Why does this work?

  • Like every other turn in ballet,

  • the fouetté is governed by angular momentum,

  • which is equal to the dancer's angular velocity times her rotational inertia.

  • And except for what's lost to friction,

  • that angular momentum has to stay constant while the dancer is on pointe.

  • That's called conservation of angular momentum.

  • Now, rotational inertia can be thought of

  • as a body's resistance to rotational motion.

  • It increases when more mass is distributed further from the axis of rotation,

  • and decreases when the mass is distributed closer to the axis of rotation.

  • So as she brings her arms closer to her body,

  • her rotational inertia shrinks.

  • In order to conserve angular momentum,

  • her angular velocity, the speed of her turn,

  • has to increase,

  • allowing the same amount of stored momentum

  • to carry her through multiple turns.

  • You've probably seen ice skaters do the same thing,

  • spinning faster and faster by drawing in their arms and legs.

  • In Tchaikovsky's ballet, the Black Swan is a sorceress,

  • and her 32 captivating fouettés do seem almost supernatural.

  • But it's not magic that makes them possible.

  • It's physics.

In the third act of "Swan Lake,"

Subtitles and vocabulary

Click the word to look it up Click the word to find further inforamtion about it