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.

The physics of the “hardest move” in ballet – Arleen Sugano
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100 thoughts on “The physics of the “hardest move” in ballet – Arleen Sugano

  • May 9, 2018 at 10:45 pm
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    I sucked at fouettes on pointe, but I loved doing them flat footed

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  • May 10, 2018 at 10:44 am
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    They're not actually that hard

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  • May 15, 2018 at 7:45 pm
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    Fouettés are sooooooooooooooooooooooooooooo hard xx

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  • May 20, 2018 at 4:36 pm
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    I can only do 2 sometimes 3 :') i think is enough

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  • May 23, 2018 at 8:35 pm
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    Wow awsome!💃

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  • May 29, 2018 at 8:15 am
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    I do fouetté turns!

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  • May 30, 2018 at 1:29 am
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    “It’s not magic, it’s physics!!!”
    Me: “AND A WHOLE LOT OF HARD FRIKING WORK!!!!!”

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  • June 1, 2018 at 5:28 am
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    The fooettay. I want to die

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  • June 1, 2018 at 6:54 am
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    Oh no, our secrets have been revealed

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  • June 1, 2018 at 10:39 am
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    Wonderful explanations 11/10 but it’s pronounced fwe*tay not foo*et*ay

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  • June 1, 2018 at 11:42 am
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    DAMN THATS HURT

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  • June 1, 2018 at 5:56 pm
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    Can we just talk about these beautiful animations for a sec?

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  • June 1, 2018 at 7:46 pm
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    My mom is a prima ballerina and she actually did 32 fuettes in a row on stage😁😁😁😀😀😃😃🤩🤩🤩😘😘😘😍😍😍

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  • June 2, 2018 at 2:10 am
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    The way he pronounces fouetté is annoying me lol

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  • June 2, 2018 at 5:07 am
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    I can do 34 fouettés….I’m only 13

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  • June 2, 2018 at 6:27 am
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    Who can do a fouette?

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  • June 2, 2018 at 12:49 pm
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    just a helpful note, Fouettes are pronounced For-tays <3

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  • June 2, 2018 at 2:35 pm
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    It's actually not that hard you just have to keep your center

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  • June 2, 2018 at 3:11 pm
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    Just watching the animation of the ballerina is making me tired and dizzy 😂😂😂

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  • June 2, 2018 at 7:54 pm
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    It's called a fouette NOT a "turn"

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  • June 2, 2018 at 9:05 pm
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    it is said like foy tay

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  • June 3, 2018 at 2:28 am
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    Physics of pole vault?

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  • June 4, 2018 at 1:34 pm
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    WHERE IS HER SPOT????

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  • June 4, 2018 at 1:35 pm
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    Doing 32 of these consecutively may be more difficult, but I think a tour jeté is more difficult if you just compare one to one.

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  • June 5, 2018 at 4:58 am
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    It is so bad every other person in the comment section is just complaining

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  • June 5, 2018 at 8:08 am
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    Yall must be scared of pulling your big toe right

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  • June 5, 2018 at 3:11 pm
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    It's not fou-E-tte, it's just fouettes the u and e is quickly said. (Sorry it was bothering me) 😞

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  • June 11, 2018 at 10:45 am
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    You forgot a very important step, the head.

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  • June 13, 2018 at 5:07 am
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    is this a joke? in don quixote you have to do 64. also if you drop your elbows your teacher will smack you

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  • June 13, 2018 at 1:06 pm
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    Omg dancer here the verbs used to describe the movement its making me cringe. Im only 20 seconds in oml. Sooooo let me just say that its a turn she is turning…not spinning it's different. Also she isnt bobbing she is plieing then releveing. Ok I can continue watching in good conscious

    Also to help keep the momentum going you spot duuh

    Omg omg nooooooooo it plies she needs to bend her kneeeeess and there its no twist unless she fall and twist her ancle. It's releve. Releve is to rise she is rising up from the plie spotting to turn again.

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  • June 15, 2018 at 3:51 am
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    why do non dancers think fouettés are so hard? i’ve got 12 year olds doing them on pointe

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  • June 15, 2018 at 11:10 am
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    I sprained my ankle once doing that even though I wasn't a ballerina.

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  • June 16, 2018 at 5:08 am
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    A fouetté is the whip of the leg the other turn the dancer does in that sequence are pirouettes. Good video. Wrong dance terminology

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  • June 19, 2018 at 12:59 pm
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    I’m a dancer, I do every single dance in my dance studio but Ballet is my favorite! I can to a fouetté but not as good as that! I can do it about 16-24 times!

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  • June 20, 2018 at 3:49 am
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    Can u do one of figure skating??

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  • June 20, 2018 at 7:09 am
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    This is the video that made me discover Ted-ed!!!😍

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  • June 23, 2018 at 12:10 am
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    Easy to image!!! I love this video!!! My fouetté became a bit better!!

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  • June 24, 2018 at 4:33 am
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    You done went and forgot about the extra momentum from spotting, no professional (or casual dancer over level 4) doesn't spot their turns. You can easily get in at least one more turn depending on your turning ability, so if you can normally turn once or twice without spotting you can turn more because A. you don't get dizzy, B. your center of balance is kept, and C. you get more momentum from snapping your head around REALLY fast.

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  • June 26, 2018 at 4:16 am
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    This was so interesting!

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  • June 27, 2018 at 6:37 pm
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    Actually, the term is not describing the “incredible ability to whip around” but actually describes the physics of the term, as the ‘whip’ of the other leg. So technically, the video could have stopped there. Also, some momentum is kept in the spotting. You’re also pronouncing fouetté wrong.

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  • June 27, 2018 at 6:50 pm
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    And I thought I doing 8 was good :c cri

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  • July 2, 2018 at 5:07 am
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    Watching the dancers feet makes me cringe

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  • July 2, 2018 at 6:36 pm
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    I do pont

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  • July 4, 2018 at 9:39 am
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    You know her point shoe is made out of fabric,wood and metal.Her tummy and her legs must be in pain.

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  • July 4, 2018 at 4:58 pm
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    This is interesting and accurate but he forgot to mention that ballerinas have to find a point and whip their head which helps them get round and stay in the same place

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  • July 8, 2018 at 9:28 pm
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    I thought it’s called a pirouette

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  • July 9, 2018 at 3:21 am
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    I can do fouttes a letter secondes and pirrhouettes but Im not yet mastered them

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  • July 9, 2018 at 4:21 am
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    This is technically a ballet lesson

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  • July 12, 2018 at 2:06 am
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    as a dancer i would def day this is a better way of explaining the turn than my teacher explained it lol

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  • July 12, 2018 at 3:18 am
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    Amazing

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  • July 12, 2018 at 3:10 pm
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    Sorry but that not how you pronounce fouettés

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  • July 12, 2018 at 4:32 pm
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    I've got to keep practicing my fouetté at barre

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  • July 13, 2018 at 12:16 am
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    Im in dance and this is totally not the hardest move

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  • July 17, 2018 at 4:23 pm
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    I’m 11 and I make swan lake coda with 32 fouettés on pointe
    ( ◠‿◠ )

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  • July 17, 2018 at 4:23 pm
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    exposed

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  • July 19, 2018 at 4:39 pm
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    U don't always use pòint shoes u can use leather canvas also known as split shoes

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  • July 22, 2018 at 3:12 am
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    its not fu-ette its said like fwette

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  • July 22, 2018 at 5:29 am
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    This gonna help me try do one properly lmao

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  • July 24, 2018 at 2:03 am
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    uuuuuuuu

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  • August 10, 2018 at 5:09 am
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    I'm glad they talked about the Fouettes. The ballerina drawing is so cute!

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  • August 13, 2018 at 6:50 am
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    So does that mean i can say

    i’m fouetté

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  • September 5, 2018 at 11:47 pm
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    I remember I did that move (not gracefully ofcourse; ) when I was 12, yet I coudn't do it too many times as I am not a ballet dancer. This is amazing! also very helpful for dancers who wishes to analyze their own movements.

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  • September 6, 2018 at 2:27 pm
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    Physics makes it possible? Hmm and here I thought physics was only a way to explain how it's done. Not what makes it possible.

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  • September 11, 2018 at 11:20 pm
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    Oh trust me these are impossible.

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  • September 11, 2018 at 11:31 pm
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    COMO BAILARINA DEVO CORREGIR NÃO É BALÉ E SIM BALLET

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  • September 27, 2018 at 5:36 am
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    Neither tops nor ballet dancers are ever in perpetual motion.

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  • September 27, 2018 at 7:37 am
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    now what now what now?

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  • October 3, 2018 at 2:36 am
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    FAIL! Your cartoon ballerina isn't spotting!! One of the most crucial elements in any type of dance turns is spotting in order to do multiple turns without falling off balance and to keep from getting dizzy. Your body turns first while, while you focus in the direction your moving, then you whip your head around to complete the turn. Its dance 101.

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  • October 3, 2018 at 3:07 pm
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    I personally dont think fouettes are the most difficult thing in classical ballet…. There might be many things that demands a very higher level of technique…

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  • October 7, 2018 at 8:59 pm
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    Ooh I love the animations

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  • October 15, 2018 at 3:51 am
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    Pls do alisicones next

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  • October 25, 2018 at 6:04 pm
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    fu-wet-tay lol its fwet-tay

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  • November 7, 2018 at 3:20 am
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    Thanks

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  • November 15, 2018 at 8:05 pm
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    Lol I'm looking at this so if can get my doubles lol

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  • November 21, 2018 at 1:53 am
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    Actually, they’re not all THAT hard, once you get the rhythm going. Although I must admit that I’ve never done 32 in a row. Then again it’s more of a female move anyway. That’s my excuse and I’m sticking to it. 😉

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  • November 30, 2018 at 5:30 pm
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    The drawing style is adorable <3

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  • December 1, 2018 at 9:51 pm
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    How can she not be dizzy???
    Can any ballet person tell me???

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  • December 3, 2018 at 1:21 am
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    physics, plus a massive amount of stamina. like the most ridiculous stamina ever.

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  • December 6, 2018 at 5:56 pm
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    SHOUT OUT TO MISS ABBIE FROM JULI KELLS IF U R READING THIS U ROCK U R THE BEST EVER AT FOUETTES RILLLY RILLY GOOD! 🙂 🙂 🙂

    Reply
  • December 22, 2018 at 7:54 am
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    im very proud of my record of six thank you very much now i just need 30 more

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  • December 22, 2018 at 12:13 pm
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    I can barely do a triple pirouette but ok-

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  • December 31, 2018 at 10:38 am
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    Odile secrets revealed

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  • January 31, 2019 at 5:20 am
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    The animation looks like the people from the Red Bull commercials 💀

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  • February 7, 2019 at 6:37 am
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    The heads too! We spot one place and whip our head to it in every turn!

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  • February 17, 2019 at 3:15 am
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    The most important thing about turning in dance is SPOTTING. If you can’t spot, you can’t turn!

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  • March 3, 2019 at 5:05 pm
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    The only thing I could think about is how he’s saying fouetté wrong

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  • March 4, 2019 at 5:29 pm
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    There really not the hardest move

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  • March 27, 2019 at 5:11 pm
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    moment değil momentum olucaktı kardeşim ama neyse

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  • April 3, 2019 at 1:27 pm
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    Ballet is the most serious thing more than you think it is.

    Meh.. it s probably not

    NO! It's the hardest thing you will done in your life. Dancers just make it look easy but they die inside

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  • April 16, 2019 at 2:52 am
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    My high score is 16 wish me luck on getting more!

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  • April 18, 2019 at 6:53 pm
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    its not physics that makes it possible its practice the ballerinas are glued to…physics is just explanation..

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  • April 23, 2019 at 2:22 pm
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    i can only do seven

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  • April 25, 2019 at 4:05 pm
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    Ok my head started to spinning 😣

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  • May 5, 2019 at 2:29 pm
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    Without Pointe I do 7
    With Pointe 1 :c

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  • May 11, 2019 at 2:22 am
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    hearing this guy say "foo-eh-tay" makes me want to die. it's "fweh-tay"

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  • June 1, 2019 at 8:57 pm
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    i knew that one day im gonna understand this video. it tooks me a year but im here as a little bit more cultured

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  • June 14, 2019 at 12:21 pm
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    😱 I am so glad that I am not a ballerina!

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  • July 9, 2019 at 10:48 am
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    Everyone, stop touched about spotting, expertise, how he prounounce it and just – for once, sit back and enjoy the science of the hardest ballet move!😶😶😶😶😑😶😶🐦🐟

    Reply
  • July 13, 2019 at 10:35 pm
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    Loved this. As an engineering physiscist, I so appreciated the scientific understanding of the art form I have always loved.

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  • July 20, 2019 at 8:46 pm
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    Foo-ette-ayez. AHH that made me cringe so bad😭

    Reply

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