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

2,540,118 views ・ 2016-03-22

TED-Ed


Please double-click on the English subtitles below to play the video.

00:06
In the third act of "Swan Lake,"
0
6779
2315
00:09
the Black Swan pulls off a seemingly endless series of turns,
1
9094
4927
00:14
bobbing up and down on one pointed foot
2
14021
2864
00:16
and spinning around, and around, and around 32 times.
3
16885
5987
00:22
It's one of the toughest sequences in ballet,
4
22872
2572
00:25
and for those thirty seconds or so,
5
25444
1773
00:27
she's like a human top in perpetual motion.
6
27217
3925
00:31
Those spectacular turns are called fouettés,
7
31142
3248
00:34
which means "whipped" in French,
8
34390
1713
00:36
describing the dancer's incredible ability to whip around without stopping.
9
36103
4245
00:40
But while we're marveling at the fouetté, can we unravel its physics?
10
40348
4089
00:44
The dancer starts the fouetté by pushing off with her foot to generate torque.
11
44437
4444
00:48
But the hard part is maintaining the rotation.
12
48881
3283
00:52
As she turns,
13
52164
870
00:53
friction between her pointe shoe and the floor,
14
53034
2507
00:55
and somewhat between her body and the air,
15
55541
2928
00:58
reduces her momentum.
16
58469
1712
01:00
So how does she keep turning?
17
60181
1996
01:02
Between each turn, the dancer pauses for a split second and faces the audience.
18
62177
5248
01:07
Her supporting foot flattens,
19
67425
1541
01:08
and then twists as it rises back onto pointe,
20
68966
3409
01:12
pushing against the floor to generate a tiny amount of new torque.
21
72375
4413
01:16
At the same time, her arms sweep open to help her keep her balance.
22
76788
4569
01:21
The turns are most effective if her center of gravity stays constant,
23
81357
4151
01:25
and a skilled dancer will be able to keep her turning axis vertical.
24
85508
4800
01:30
The extended arms and torque-generating foot
25
90308
2730
01:33
both help drive the fouetté.
26
93038
2321
01:35
But the real secret and the reason you hardly notice the pause
27
95359
3342
01:38
is that her other leg never stops moving.
28
98701
3220
01:41
During her momentary pause,
29
101921
1806
01:43
the dancer's elevated leg straightens and moves from the front to the side,
30
103727
4536
01:48
before it folds back into her knee.
31
108263
2585
01:50
By staying in motion, that leg is storing some of the momentum of the turn.
32
110848
5434
01:56
When the leg comes back in towards the body,
33
116282
2320
01:58
that stored momentum gets transferred back to the dancer's body,
34
118602
3663
02:02
propelling her around as she rises back onto pointe.
35
122265
3995
02:06
As the ballerina extends and retracts her leg with each turn,
36
126260
3378
02:09
momentum travels back and forth between leg and body,
37
129638
4545
02:14
keeping her in motion.
38
134183
2150
02:16
A really good ballerina can get more than one turn out of every leg extension
39
136333
4184
02:20
in one of two ways.
40
140517
1741
02:22
First, she can extend her leg sooner.
41
142258
2313
02:24
The longer the leg is extended, the more momentum it stores,
42
144571
3735
02:28
and the more momentum it can return to the body when it's pulled back in.
43
148306
4249
02:32
More angular momentum means she can make more turns
44
152555
2674
02:35
before needing to replenish what was lost to friction.
45
155229
3678
02:38
The other option is for the dancer
46
158907
1696
02:40
to bring her arms or leg in closer to her body
47
160603
3451
02:44
once she returns to pointe.
48
164054
1765
02:45
Why does this work?
49
165819
1221
02:47
Like every other turn in ballet,
50
167040
1679
02:48
the fouetté is governed by angular momentum,
51
168719
2708
02:51
which is equal to the dancer's angular velocity times her rotational inertia.
52
171427
5079
02:56
And except for what's lost to friction,
53
176506
2156
02:58
that angular momentum has to stay constant while the dancer is on pointe.
54
178662
4802
03:03
That's called conservation of angular momentum.
55
183464
3386
03:06
Now, rotational inertia can be thought of
56
186850
2533
03:09
as a body's resistance to rotational motion.
57
189383
3416
03:12
It increases when more mass is distributed further from the axis of rotation,
58
192799
4989
03:17
and decreases when the mass is distributed closer to the axis of rotation.
59
197788
4760
03:22
So as she brings her arms closer to her body,
60
202548
2481
03:25
her rotational inertia shrinks.
61
205029
3059
03:28
In order to conserve angular momentum,
62
208088
1900
03:29
her angular velocity, the speed of her turn,
63
209988
2701
03:32
has to increase,
64
212689
1286
03:33
allowing the same amount of stored momentum
65
213975
2317
03:36
to carry her through multiple turns.
66
216292
3002
03:39
You've probably seen ice skaters do the same thing,
67
219294
2858
03:42
spinning faster and faster by drawing in their arms and legs.
68
222152
3862
03:46
In Tchaikovsky's ballet, the Black Swan is a sorceress,
69
226014
3799
03:49
and her 32 captivating fouettés do seem almost supernatural.
70
229813
5223
03:55
But it's not magic that makes them possible.
71
235036
2469
03:57
It's physics.
72
237505
1218
About this website

This site will introduce you to YouTube videos that are useful for learning English. You will see English lessons taught by top-notch teachers from around the world. Double-click on the English subtitles displayed on each video page to play the video from there. The subtitles scroll in sync with the video playback. If you have any comments or requests, please contact us using this contact form.

https://forms.gle/WvT1wiN1qDtmnspy7