The physics of the "hardest move" in ballet - Arleen Sugano

翻译人员: Yolanda Zhang 校对人员: Chen Zou

In the third act of "Swan Lake,"

在《天鹅湖》的第三幕中

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

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

用单脚足尖交替支撑，放平

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

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,

而且在那大约30秒的时间内

she's like a human top in perpetual motion.

她像是只陀螺，无限地转下去

Those spectacular turns are called fouettés,

这些精彩的旋转 叫做fouettés

which means "whipped" in French,

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,

在她旋转的过程中

friction between her pointe shoe and the floor,

脚尖和地板的摩擦力

and somewhat between her body and the air,

和她的身体所受到的空气阻力

reduces her momentum.

会减少她的动量

So how does she keep turning?

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,

她会放下支撑脚

and then twists as it rises back onto pointe,

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

展开的双臂和 不断产生扭转力的足尖

both help drive the fouetté.

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

但真正的秘诀以及 你几乎没察觉到停顿的原因

is that her other leg never stops moving.

在于她的另一条腿从没有停止转动

During her momentary pause,

在她短暂的暂停之时

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

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,

当腿向着身体方向缩回之时

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

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,

动量在下肢与身体之间 来回转移

keeping her in motion.

使她保持持续转动

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

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

in one of two ways.

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

那么当下肢缩回之时 更多的动量可以回到舞者的身体

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

更多的角动量意味着 她可以完成更多圈

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

The other option is for the dancer

另一个选择是

to bring her arms or leg in closer to her body

当舞者再次踮脚时 将她的手臂或者腿

缩得离身体更近些

once she returns to pointe.

Why does this work?

这为什么有效呢？

就如其它芭蕾舞旋转动作一样

Like every other turn in ballet,

the fouetté is governed by angular momentum,

挥鞭转由角动量（L）控制

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

它等于角速度(ω)乘以旋转惯性（I）

And except for what's lost to friction,

除了摩擦损耗的动量之外

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

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

现在，旋转惯性可以被当做

as a body's resistance to rotational motion.

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,

所以当舞者的手臂更靠近身体的时候

her rotational inertia shrinks.

她的旋转惯性减小

为了保持角动量

In order to conserve angular momentum,

her angular velocity, the speed of her turn,

她的角速度 也就是旋转的速度

has to increase,

需要增加

allowing the same amount of stored momentum

从而保存相同的动量

to carry her through multiple turns.

让她实现多次的连续旋转

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

你可能见过滑冰的人 做过相同的动作

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

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,

在柴可夫斯基的芭蕾舞剧中 黑天鹅是女巫

and her 32 captivating fouettés do seem almost supernatural.

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.

但不是魔法 让这一切发生

It's physics.

是物理学