In the third act of 'Swan Lake,' the Black Swan pulls off a seemingly endless series of turns,
在《天鹅湖》的第三幕中，黑天鹅完成了一个似乎无止境的连续旋转，
bobbing up and down on one pointed foot and spinning around, and around, and around 32 times.
用单脚足尖交替支撑，放平，然后一直转啊转，一共32圈。
It's one of the toughest sequences in ballet,
这是芭蕾舞中最难的连续动作之一，
and for those thirty seconds or so, she's like a human top in perpetual motion.
而且在那大约30秒的时间内，她像是只陀螺，无限地转下去。
Those spectacular turns are called fouettés, which means 'whipped' in French,
这些精彩的旋转叫做fouettés，在法语中意思是“挥鞭转”，
describing the dancer's incredible ability to whip around without stopping.
描述了舞者连续转动的非凡能力。
But while we're marveling at the fouetté, can we unravel its physics?
但是在我们为此惊叹时，我们能否解释它的物理原理呢？
The dancer starts the fouetté by pushing off with her foot to generate torque.
舞者用脚尖蹬地获取扭转力来开始fouetté。
But the hard part is maintaining the rotation.
但是困难的部分是保持转动的连续。
As she turns, friction between her pointe shoe and the floor,
在她旋转的过程中，脚尖和地板的摩擦力
and somewhat between her body and the air, reduces her momentum. So how does she keep turning?
以及她的身体所受到的空气阻力，会减少她的动量。那么她是如何做到持续旋转的呢？
Between each turn, the dancer pauses for a split second and faces the audience.
在每个旋转之间，舞者会有一瞬间暂停并面向观众。
Her supporting foot flattens, and then twists as it rises back onto pointe,
她会放下支撑脚，再在踮起的过程中扭转，
pushing against the floor to generate a tiny amount of new torque.
蹬地以获取微量的新的旋转动力。
At the same time, her arms sweep open to help her keep her balance.
与此同时，她的双臂向外展开以保持平衡。
The turns are most effective if her center of gravity stays constant,
如果她的重心保持稳定，这些旋转最为流畅，
and a skilled dancer will be able to keep her turning axis vertical.
有经验的舞者能够保持她的旋转轴垂直。
The extended arms and torque-generating foot both help drive the fouetté.
展开的双臂和不断产生扭转力的足尖共同帮助完成这个“挥鞭转”的动作。
But the real secret and the reason you hardly notice the pause is that her other leg never stops moving.
但真正的秘诀以及你几乎没察觉到停顿的原因，在于她的另一条腿从没有停止转动。
During her momentary pause, the dancer's elevated leg straightens and moves from the front to the side,
在她短暂的暂停之时，舞者那只抬起的腿伸直，然后从前面转到旁边，
before it folds back into her knee.
然后折叠回到膝盖。
By staying in motion, that leg is storing some of the momentum of the turn.
通过持续动作，那条腿储存了一些旋转的动量。

When the leg comes back in towards the body, that stored momentum gets transferred back to the dancer's body,
当腿向着身体方向缩回之时，那些储存的动量被转移回到舞者身上，
propelling her around as she rises back onto pointe.
当她再次踮起脚尖时，动量推动她旋转。
As the ballerina extends and retracts her leg with each turn,
随着芭蕾舞者在每次旋转中伸缩她的腿，
momentum travels back and forth between leg and body, keeping her in motion.
动量在下肢与身体之间来回转移，使她保持持续转动。
A really good ballerina can get more than one turn out of every leg extension in one of two ways.
一个优秀的芭蕾舞者能够通过以下两种方式之一在每次下肢伸直时完成多于一圈的旋转。
First, she can extend her leg sooner.
第一，她可以提早伸直她的腿。
The longer the leg is extended, the more momentum it stores,
她伸展腿的时间越长，所储存的动量就越多，
and the more momentum it can return to the body when it's pulled back in.
那么当下肢缩回之时，更多的动量可以回到舞者的身体。
More angular momentum means she can make more turns before needing to replenish what was lost to friction.
在补充必要的因摩擦力损耗的动量之前，更多的角动量意味着她可以完成更多圈。
The other option is for the dancer to bring her arms or leg in closer to her body once she returns to pointe.
另一个选择是，当舞者再次踮脚时，将她的手臂或者腿缩得离身体更近些。
Why does this work? Like every other turn in ballet, the fouetté is governed by angular momentum,
这为什么有效呢？就如其它芭蕾舞旋转动作一样，挥鞭转由角动量控制，
which is equal to the dancer's angular velocity times her rotational inertia.
它等于角速度乘以旋转惯性。
And except for what's lost to friction, that angular momentum has to stay constant while the dancer is on pointe.
除了摩擦损耗的动量之外，当舞者踮起脚尖时，角动量必须保持不变。
That's called conservation of angular momentum.
这被称作“角动量守恒定律”。
Now, rotational inertia can be thought of as a body's resistance to rotational motion.
现在，旋转惯性可以被当做身体对旋转动作的抵制。
It increases when more mass is distributed further from the axis of rotation,
它在更多重量分布在远离旋转轴的位置时增加，
and decreases when the mass is distributed closer to the axis of rotation.
在更多重量分布在靠近旋转轴的位置时减少。
So as she brings her arms closer to her body, her rotational inertia shrinks.
所以当舞者的手臂更靠近身体的时候，她的旋转惯性减小。
In order to conserve angular momentum, her angular velocity, the speed of her turn, has to increase,
为了保持角动量，她的角速度，也就是旋转的速度，需要增加，
allowing the same amount of stored momentum to carry her through multiple turns.
从而保存相同的动量，让她实现多次的连续旋转。
You've probably seen ice skaters do the same thing, spinning faster and faster by drawing in their arms and legs.
你可能见过滑冰的人做过相同的动作，通过收缩手臂和腿来加速冰上的旋转。
In Tchaikovsky's ballet, the Black Swan is a sorceress, and her 32 captivating fouettés do seem almost supernatural.
在柴可夫斯基的芭蕾舞剧中，黑天鹅是女巫，她迷人的32次挥鞭转看起来就像是魔法。
But it's not magic that makes them possible. It's physics.
但不是魔法让这一切发生。是物理学。