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  • In the third act of "Swan Lake,"

    在「天鵝湖」第三幕,

  • the Black Swan pulls off a seemingly endless series of turns,

    黑天鵝成功完成 那似乎無止境的連續旋轉,

  • bobbing up and down on one pointed foot

    以一個腳尖上下移動,

  • and spinning around, and around, and around 32 times.

    不停不停地旋轉了 32 次。

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

    是芭蕾最難的一串動作之一,

  • and for those thirty seconds or so,

    在那大約三十秒裡,

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

    她像個陀螺人一樣不停歇地轉動。

  • Those spectacular turns are called fouettés,

    那驚人的旋轉叫做 單足趾尖旋轉/fouettés ,

  • which means "whipped" in French,

    法文是 快速攪拌/whipped ,

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

    描述舞者無間斷旋轉的非凡能力。

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

    但當我們對 fouetté 讚嘆之餘, 可否用物理解釋它?

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

    舞者開始做 fouetté 是用腳頂推地面製造扭轉力。

  • But the hard part is maintaining the rotation.

    但困難的部份是保持旋轉。

  • As she turns,

    當她旋轉時,

  • friction between her pointe shoe and the floor,

    摩擦力在尖頭鞋和地板之間,

  • and somewhat between her body and the air,

    以及有些在身體及空氣間,

  • reduces her momentum.

    降低了她的動量。

  • So how does she keep turning?

    所以她是如何保持旋轉?

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

    每個旋轉之間, 舞者會有一瞬間暫停且面對觀眾,

  • Her supporting foot flattens,

    她支撐的腳會放平,

  • and then twists as it rises back onto pointe,

    當又踮起腳尖時會再次旋轉,

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

    因為她頂推地板 再次產生少許的新扭轉力。

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

    同時,她的手臂迅速展開以保持平衡。

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

    如果她的重心保持穩定, 則旋轉最具效率,

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

    一位技術純熟的舞者 能保持旋轉軸垂直。

  • The extended arms and torque-generating foot

    展開的手臂和產生扭轉力的腳

  • both help drive the fouetté.

    共同協力推動 單足趾尖旋轉。

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

    但真正秘訣以及 你幾乎不覺得停頓的原因

  • is that her other leg never stops moving.

    是因為她的另一條腿永遠在動。

  • During her momentary pause,

    在動量暫停之際,

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

    舞者那隻抬起的腿打直, 並且從前面移到旁邊,

  • before it folds back into her knee.

    然後向後折回到膝蓋。

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

    藉著持續動作, 那下肢儲存了一些旋轉的動量,

  • When the leg comes back in towards the body,

    當下肢縮回靠近身體時,

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

    儲存的動量轉移到舞者身上,

  • propelling her around as she rises back onto pointe.

    當又踮起腳尖時,動量推動她旋轉。

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

    當芭蕾舞者每次旋轉, 伸直與縮回她的下肢,

  • momentum travels back and forth between leg and body,

    動量來回於下肢和身體之間,

  • keeping her in motion.

    讓她繼續轉動。

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

    一位非常好的芭蕾舞者 能每次下肢伸直時 旋轉多於一圈。

  • in one of two ways.

    就是用下列兩個方法之一。

  • First, she can extend her leg sooner.

    第一,她可提早伸直下肢。

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

    下肢伸直的時間越久, 所儲存的動量就越多,

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

    當下肢縮回時, 就有更多動量回到身體,

  • More angular momentum means she can make more turns

    更多的角動量意味著 她可轉更多圈 ──

  • before needing to replenish what was lost to friction.

    在因摩擦力損失動量,需再補充之前。

  • The other option is for the dancer

    另一個方法是

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

    當舞者又踮起腳尖時, 馬上將手臂和下肢縮得更靠近身體。

  • once she returns to pointe.

    這為什麼管用呢?

  • Why does this work?

    就像芭蕾其他每個旋轉一樣,

  • Like every other turn in ballet,

    單足趾尖旋轉 受角動量 (L) 的影響,

  • the fouetté is governed by angular momentum,

    舞者的 角動量 (L) = 角速度 (ω) * 轉動慣量 (I)

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

    除了摩擦力流失的動量外,

  • And except for what's lost to friction,

    當舞者踮腳尖時, 角動量 (L) 是維持恆定的,

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

    這稱為「角動量守恆定律」。

  • That's called conservation of angular momentum.

    現在,轉動慣量(I) 可想成是身體對旋轉的阻力,

  • Now, rotational inertia can be thought of

    當越多質量離旋轉軸越遠時, 轉動慣量(I)會增加;

  • as a body's resistance to rotational motion.

    當質量離旋轉軸越近時, 轉動慣量(I)會減少。

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

    所以當她把手臂縮更靠近身體時,

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

    轉動慣量(I)會變小,

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

    為了保持角動量 (L),

  • her rotational inertia shrinks.

    角速度(ω)── 即她的旋轉速度必須增加。

  • In order to conserve angular momentum,

    用相同的儲存動量,

  • her angular velocity, the speed of her turn,

    就能讓她旋轉許多圈。

  • has to increase,

    你可能看過溜冰者作過相同動作,

  • allowing the same amount of stored momentum

    旋轉得越來越快── 藉著縮回他們的手臂和下肢。

  • to carry her through multiple turns.

    在柴可夫斯基的芭蕾舞劇, 黑天鵝是位女巫,

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

    她迷人的 32 單足趾尖旋轉 真是神乎其神,

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

    但並不是魔術讓旋轉成為可能,

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

    是物理!

  • and her 32 captivating fouettés do seem almost supernatural.

    翻譯:Ann Chen

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

  • It's physics.

In the third act of "Swan Lake,"

在「天鵝湖」第三幕,

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B2 中高級 中文 美國腔 TED-Ed 動量 舞者 角動量 伸直 手臂

【TED-Ed】用物理解釋芭蕾舞中最難的旋轉動作 (The physics of the "hardest move" in ballet - Arleen Sugano)

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    Bruce Lan 發佈於 2016 年 04 月 02 日
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