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Whatever happened to angular momentum??! [Feb. 19th, 2006|08:50 pm]
Arvind Narayanan
 [ Tags | physics, puzzle ] [ Current Mood | melancholy ]

The roomie was watching NBA all stars on ESPN yesterday and I wandered into part of the dunk contest. There was one that caught my attention — this guy runs toward the basket, jumps, grabs the ball, turns in the air, and dunks with his back to the basket. You'd think he generated the turning impulse with his feet at the point that he jumped, but it didn't look like that -- he didn't start to turn until he caught the ball.

To confirm that this is not an illusion, I had someone call out "left" or "right" after I jump, and then I turned in mid air. It really works. I can land with my feet turned around 90 degrees and my torso almost 180 degrees in the stipulated direction.

How the heck is this possible?? How can angular momentum fail to be conserved?

As a kid I once asked myself how I could sit on a chair with no part of my body in contact with anything except the chair, and yet manage to move myself and the chair. If you don't believe it is possible, try it; it's fairly easy (on the right surface). I figured out the answer after some thought, and over the years I have posed this puzzle to the number of people. Some were stumped, and some couldn't understand what the apparent contradiction was. One person, however, shot the answer back almost before the words were out of my mouth. Assuming she hadn't seen the puzzle before, she's a fricking genius.

But the turning-in-the-air conundrum really has me in a knot. I'm losing my faith in logic and science :) I particularly hate it when I can learn a skill but cannot explain how I do it. Any help? Any at all? Please?

 From: 2006-02-19 09:37 pm (UTC) (Link)
How is this so confusing? Your muscles do work, which causes acceleration.
 From: 2006-02-20 06:11 am (UTC) (Link)
Dude, I don't mean to be a prick, but you might want to take a look at the law of conservation of angular momentum. It states that for any system of particles, the rate of change of angular momentum equals the torque. When executing a mid-air turn, there is clearly no torque but angular momentum changes (or at least appears to change).

Physics 101: force == external force. Muscles don't count. If it were otherwise, you could fly by repeatedly jumping in mid-air.
 From: 2006-02-20 09:18 am (UTC) (Link)
Imagine that you're on a frictionless turn-table in a vacuum, and I give you a bicycle tire. Using your muscles, you can hold the tire perpendicular to the ground and begin to accelerate its spin until it has a high speed. Then again using your muscles, tilt the wheel to one side. You now have angular momentum in the opposite direction of the tilt, despite the fact that no external force has been applied to the Arvind+turn-table+bicycle-wheel system.

Now imagine that you're in a swivel chair that has some friction in the swivel mechanism. Hold your arms out, and move them to the left slowly enough that you do not overcome the friction and rotate to the right. Then suddenly rotate your arms to the right. You will overcome the friction and rotate slightly to the left. If you repeat this process several times, you can rotate all the way around. I'm not sure whether your angular momentum is non-zero though; all you've done here is conserved momentum by having your arms and body rotate in different directions.

Maybe one of these is relevant...
 From: 2006-02-19 11:23 pm (UTC) (Link)
I'll explain it with as much patience as I can muster- and the answer is fairly obvious (but I'm open to other ideas!)Here goes:
The ball's velocity would be the sum of the speed of the player AND that of the ball- so that's basically why a slam dunk is done, in order to maximise the possibility of a basket while minimising the work required. This can be attributed to the fact that it's mighty difficult to shoot while running (focussing on the basket which happens to be a smaller target, than passing to say, another player!)- so a good player goes through the process of moving his entire body when really close to the basket, protecting the ball all the while and then just nudges the ball into the basket.
As regards your particular query- angular momnetum IS conserved!Here's why- when the player jumps for the shoot(dunk, whatever!), he's opposing the force of gravity, using "muscle power" to provide the necessary acceleration against the fall, and inorder to extend his "stay" up there, he twists his body (again using muscles- and you might have noticed that players raise their hands when jumping, it's not just to catch, but to prolong the jump, as well!), and hell, they must have had loads of practice!;P
Anyway, IF the impulse had been generated during the jump, it still wouldn't be a bad dunk, but he will not have the advantage of the additional seconds for the shoot!
Here's an analogy- imagine there's a spaceship taking off, and suppose it needs to rotate in order to achieve a gravitational field (using the centripetal force- which in this case will provide the necessary gravity, towards the centra of the ship-a la Arthur.C.Clarke!)It's not necessary the the ship must rotate right from take-off, it could start the process say, only when it's escaping the atmosphere (for say conserving fuel, and so on!), momentum is still conserved!
It's the same for bb- except muscular work is done, in this case!
*And yeah!I used to play basketball in school!:D*
 From: 2006-02-24 03:25 am (UTC) (Link)
Does it make sense now?;P
*I tried, I really did, I really did try!*
 From: 2006-02-24 05:35 am (UTC) (Link)
What's different now?

Your spaceship analogy in particular is flawed, since a spaceship works on the rocket principle. The only way a basketball player can do that is by... farting massively to one side.

Anyway players raising their arms (not hands. Even though arm and hand both map to kai in Tamil. I used to have trouble with that as well.) increases their radius of gyration and decreases angular velocity. That effect is more relevant to the question of mid air turns than gaining extra time.
 From: (Anonymous)2006-02-24 05:59 am (UTC) (Link)
Off-topic : This reply made me look at dictionaries and realise that the hand consisted of only the palm and the fingers ( and possibly the wrist too, depending on dictionary ). Even more shocking to me was that "kai" could mean this ( so that should be true with malayALam as well ); in malayALam I had always thought of "kai" as arm, "mun-kai" as forearm \$\cup\$ palm \$\cup\$ fingers, and "kaippatti" and palm \$\cup\$ fingers.
Sandeep

P. S. : Oxford dictionary seems to also give "The whole arm" as a meaning for hand; so in this respect english may not be different from tamizh in theory - in practice do you use any word to distinguish the two?
 From: 2006-02-24 06:08 am (UTC) (Link)
I don't really care what the dictionary says - language is defined by usage. I have never heard a native speaker use hand to mean arm. And I don't think I've heard a Tamil speaker use anything other than kai to mean either hand or arm.
 From: 2006-02-24 07:53 pm (UTC) (Link)
Your spaceship analogy in particular is flawed, since a spaceship works on the rocket principle. The only way a basketball player can do that is by... farting massively to one side.

Be banal, dude- that analogy wasn't for the energy involved but to stress on the "turning in mid-air routine".

Anyway players raising their arms (not hands. Even though arm and hand both map to kai in Tamil. I used to have trouble with that as well.) increases their radius of gyration and decreases angular velocity. That effect is more relevant to the question of mid air turns than gaining extra time.

That's exactly what I was implying by the term "muscle action"- but I concede I should've used the "arms" when talking about the way players rise when jumping.

 From: 2006-02-24 06:00 am (UTC) (Link)
And a couple more things:

You use way too many exclamation points. Unless you were actually jumping up and down while posting :)

When you use a whole paragraph to belabor a simple point, it not only decreases comprehensibility, you also come off as smug.
 From: 2006-02-20 01:04 pm (UTC) (Link)
Does this help?

http://www.exploratorium.edu/skateboarding/trick03.html

 From: 2006-02-20 01:23 pm (UTC) (Link)
Wow... exactly the experiment that I performed, and the answer sounds believable. I hadn't realized I was moving my arms in the other direction, but I must have been. Thanks!
 From: (Anonymous)2006-02-20 10:49 pm (UTC) (Link)

But the turning-in-the-air conundrum really has me in a knot. I'm losing my faith in logic and science :) I particularly hate it when I can learn a skill but cannot explain how I do it. Any help? Any at all? Please?

Hi,
Have you ever read "The Tao of Physics" by Fritjof Capra. Please take a look. It is an eye opener just in case you have not read it before. It was an eye opener for me.

Ah.. Yes I am Saura, from Chennai. Was taking a look on Gtkboard and reached here. email: rsaura@gmail.com
 From: 2006-02-21 07:47 am (UTC) (Link)
Thanks... I'll take a look.
 From: 2006-02-21 11:46 am (UTC) (Link)
Hmm.. it appears to be something that attempts to draw a parallel between physics and mysticism. As a skeptic and unbeliever, I don't find that sort of thing worth reading, to put it mildly.

You probably interpreted my statement "I'm losing my faith in logic and science" literally. It was a JOKE. That's why there's a smiley right after it.
 From: (Anonymous)2006-02-21 09:45 pm (UTC) (Link)
As a skeptic and unbeliever, I don't find that sort of thing worth reading, to put it mildly.

Hmm.. exactly the same mindset I had. He is saying only science and he is not asking us to believe in God. He is a theoretical physicist. So if you like reading physics or maths I suggest you to take a look.

PS: Could I know your email id?
 From: 2006-02-23 05:41 am (UTC) (Link)
I was going to reply with a long harangue, but realized I didn't have the energy. Look, I understand what the book is about. It is one of the viewpionts that I viciously hate. It is what the RSS monkeys do. Unfortunately you can be a reputed academic and still be a complete nut.

My email address is on my LJ profile page.
 From: 2006-02-24 03:23 am (UTC) (Link)
I completely agree!
And, coincidences galore- I was reading it only last week (and was gonna post on it but couldn't due to interference from Mr.Ill-Health!), and its analogies and parallels aren't worth talking about (hell, that's an understatement- they suck!), but I guess the descriptions of mysticism as such (inclusive of Hinduist, Buddhist, Taoist and Zen forms) were pretty tolerable!
My suggestion-nothing's worth not reading, but I don't vouch for reader-satisfaction, no matter how popular the book/author is(and I was suggested this book by umpteen trusted sources!)
 From: 2006-02-24 05:26 am (UTC) (Link)