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 10th September 2006, 08:06 PM #1 ttch Scholar   Join Date: Aug 2006 Posts: 51 Conservation of Angular Momentum (again) Okay, another stupid post on a possible violation of the conservation of angular momentum in an isolated system. Imagine a cylinder that is rotating at a high rate in free space. This cylinder consists of a rod surrounded by a close-fitting tube. For convenience, the rod and tube each has the same amount of angular momentum. If desired, you can consider the two parts to be mechanically joined when the cylinder was spun up and then mechanically separated just before we begin. (1) The rod is removed from the tube at a low energy cost. You slide it out. (2) The rod is then reversed in orientation relative to the tube at another low energy cost (this does not have to be done quickly). You turn it around. (3) The rod is then reinserted into the tube at another low energy cost. You slide it back in. The two parts of the original cylinder are back together but are now rotating in opposite directions. (4) The rod and tube are each equipped with electrical windings, etc. such that in conjunction they may act as an electrical generator (as in a regenerative braking system) and this feature is now used to slow the total system finally to a non-rotating state, while generating electricity. The result is that we have converted a fair portion of the original angular momentum of the cylinder into usable energy, thereby violating the conservation of angular momentum in an isolated system. QED If you want, you can reverse this process to create angular momentum out of electricity. I realize that the three "low cost" operations may have a larger energy cost than I anticipate (particularly no. 2), but these should still be but a fraction of the rotational energy recovered. Again, the operations do not have to happen quickly. I'm going to be away from the net until late Wednesday. I would appreciate comments and refutations as they occur to you. Thanks to all interested JREF forum posters. P.S. Keep your mind out of the gutter.
 10th September 2006, 08:57 PM #2 bjb Graduate Poster     Join Date: Jan 2005 Posts: 1,079 You can't change the direction of a rotating tube in step two without performing work and expending energy. This violates the 'closed' nature of the system. You also violated the closed system by removing electrical energy from it. Of course, it is going to be very, very difficult to get a tube and cylinder to have the same rotational inertia when the tube fits inside the cylinder. The tube is going to have much less inertia than the cylinder. You can spin the tube faster to match the angular momentum of the cylinder, but then other conditions in the problem are violated. I'm really not sure what the point of the question is, but it seems like you're describing a flywheel energy storage system. Electrical energy is converted to rotational energy for storage, then released back as electrical energy. No laws of motion or thermodynamics are violated in the process.
 10th September 2006, 09:01 PM #3 Dr Adequate Banned   Join Date: Aug 2004 Location: Waiting Long Enough By The River Posts: 17,897 "Conservation of angular momentum" doesn't mean that angular momentum can't be turned into other forms of energy, otherwise a spinning-top would never stop spinning. Angular momentum is conserved only if there is no external torque.
 10th September 2006, 09:03 PM #4 Walter Wayne Wayne's Words     Join Date: Jul 2002 Location: Ottawa, ON Posts: 2,451 Originally Posted by ttch The result is that we have converted a fair portion of the original angular momentum of the cylinder into usable energy, thereby violating the conservation of angular momentum in an isolated system. QED But momentum and energy are not the same thing. Angular momentum is a vector. Angular momentum = Moment of Intertia x Angular Velocity However, the kinetic energy isn't a vector. Kinetic Energy = 1/2 x Moment of Inertia x Angular Velocity Squared If you want to think of the same situation in linear kinetics, think of a system of two identical cars travelling towards eachother at identical velocity. The momentum of the two will sum to zero. Their energy won't though, and this will mean we have lots of energy availabe to bend the cars around eachother. Walt
 10th September 2006, 09:04 PM #5 Pidge Thinker     Join Date: Mar 2003 Location: Watching the sunset from Mt Ruapehu Posts: 223 Originally Posted by ttch (2) The rod is then reversed in orientation relative to the tube at another low energy cost (this does not have to be done quickly). You turn it around. Originally Posted by ttch I realize that the three "low cost" operations may have a larger energy cost than I anticipate (particularly no. 2), but these should still be but a fraction of the rotational energy recovered. Again, the operations do not have to happen quickly. When you turn the rod around, the angular momentum - which is a vector quantity, a value and a direction, not a scalar quantity (value only) - of the rod must be conserved. Any change in the angular momentum requires work to be done on the rod. Back in Stage 1 Physics, I very enthusiastically (OOO!! OOOO!!! PICK ME!!!) (anyone in Phys104 at Canterbury University in 1990 might remember that...) volunteered to be the subject who sat belted into a chair that could spin freely about a vertical access (e.g. beefed up office chair with a car racing harness) The lecturer had a flywheel which freely spun on a axle, which he had spun up to a few tens of RPM. I'm sitting in the chair, not rotating. The Lecturer hands the fly wheel to me, with the fly wheel axle vertical. I turn the flywheel upside down. Guess what happens to conserve angular momentum? I start spinning in the direction that the fly wheel was originally spinning in. The angular momentum has been conserved, but energy hasn't - the fly wheel is still going at about the same speed, and I'm spinning in the opposite direction too. Remember how I turned the flywheel over? That wasn't exactly easy to do... I had to do go to some effort to do that. __________________ "Never argue with an idiot. They'll pull you down to their level and then beat you with experience." - Unknown
 10th September 2006, 09:12 PM #6 Zombified Back From The Dead     Join Date: Aug 2002 Location: Inside my brain Posts: 1,373 Originally Posted by ttch Okay, another stupid post on a possible violation of the conservation of angular momentum in an isolated system. Reminder: violation of momentum == check your work! Quote: Imagine a cylinder that is rotating at a high rate in free space. This cylinder consists of a rod surrounded by a close-fitting tube. For convenience, the rod and tube each has the same amount of angular momentum. If desired, you can consider the two parts to be mechanically joined when the cylinder was spun up and then mechanically separated just before we begin. Technically, they have the same angular velocity, not angular momentum. Angular momentum also depends on the rod and tube's angular inertia, which is analogous to mass for angular stuff. Quote: (2) The rod is then reversed in orientation relative to the tube at another low energy cost (this does not have to be done quickly). You turn it around. This operation completely reverses the angular momentum of the rod. It is not free. You have to apply an external torque to do it. Also note that time here does not affect the total energy, though it does affect how much torque you have to apply. But the total torque times time has to equal twice the initial angular momentum of the rod. Quote: (4) The rod and tube are each equipped with electrical windings, etc. such that in conjunction they may act as an electrical generator (as in a regenerative braking system) and this feature is now used to slow the total system finally to a non-rotating state, while generating electricity. Ok, but you get out no more than the energy you put in. Quote: The result is that we have converted a fair portion of the original angular momentum of the cylinder into usable energy, thereby violating the conservation of angular momentum in an isolated system. QED Nope. You ignored the fact that you started out with lots of kinetic energy, and then performed an operation that involved an external torque. You really ought to take a basic physics course. That's not a criticism, it's just that if you're genuinely interested in this stuff, you really owe it to yourself to learn it properly and get it figured out for yourself.
 10th September 2006, 09:17 PM #7 boooeee Dart Fener     Join Date: Aug 2002 Location: The Lando System Posts: 2,403 Actually, if I'm thinking about this correctly, the last step is superfluous if you're trying to demonstrate the non-conservation of angular momentum. After you flip the rod and place it back in the cyllinder, the net angular momentum of the cyllinder-rod system is now zero. This is because the rod's angular momentum vector is now pointing in the opposite direction of the cyllinder, cancelling it exactly. So, prior to hooking up your cyllinder-rod combo to a generator, you've already destroyed all of the angular momentum of the system. Hooking up the system to a generator is just plain vanilla kinetic-to-electric field energy conversion. The reason that you have not demonstrated the non-conservation of angular momentum is that it requires something extrnal to flip your rod. The change in the rod's angular momentum is transferred to whatever system flipped the rod. Also, the point has already been made by prior posters, but it's an important one: Do not confuse angular momentum with energy. __________________ my nerdy sports blog: betting market analytics
 11th September 2006, 12:25 AM #8 Art Vandelay Illuminator     Join Date: May 2004 Posts: 4,790 Originally Posted by Dr Adequate "Conservation of angular momentum" doesn't mean that angular momentum can't be turned into other forms of energy, otherwise a spinning-top would never stop spinning. Angular momentum is conserved only if there is no external torque. Going around gratuitiously insulting people is bad enough when you're right, but when one not only knows as little as you do, but so freely pontificates on the subjects one does not understand, one has no business criticizing anyone else. Angular momentum can NOT be turned into energy. Angular momentum is not, as you imply, a form of energy; it is a completely different property (note that energy and and angular momentum aren't even in the same category, let alone the same thing; energy is a scalar, while angular momentum is a vector). A spinning top transfers its angular momentum to the earth. It does not, as you imply, transform it into energy. Originally Posted by Pidge Any change in the angular momentum requires work to be done on the rod. Well, that's not quite true. Any operation that changes angular momentum and does work can be cancelled out with one that does negative work and doesn't change angular momentum. Quote: The angular momentum has been conserved, but energy hasn't - the fly wheel is still going at about the same speed, and I'm spinning in the opposite direction too. Wel, of course energy overall is conserved. You had to do work to turn the fly wheel.
 11th September 2006, 12:36 AM #9 Zombified Back From The Dead     Join Date: Aug 2002 Location: Inside my brain Posts: 1,373 The kinetic energy associated with a rotating object as a function of its angular momentum is T = L2/2I, where L is the magnitude of the angular momentum vector (L2 = L . L - i.e. dot product) and I is the angular moment of inertia. This is analogous to the linear formula T = p2/2m.
 11th September 2006, 12:45 AM #10 Art Vandelay Illuminator     Join Date: May 2004 Posts: 4,790 Yes, but it is that kinetic energy associated with L that is converted, not L itself.
 11th September 2006, 08:37 AM #11 Soapy Sam NLH   Join Date: Oct 2002 Posts: 25,929 What if the cylinder and rod are made of neutronium, several million miles long and have relativistic surface velocities? Just asking.
 11th September 2006, 10:14 AM #12 Walter Wayne Wayne's Words     Join Date: Jul 2002 Location: Ottawa, ON Posts: 2,451 Originally Posted by Soapy Sam What if the cylinder and rod are made of neutronium, several million miles long and have relativistic surface velocities? Just asking. Have you tried calculating the Moment of Inertia for a cylinder taking relativity into account? Not fun. Plus I find mithral has much better tensile properties for the stresses encountered in such a system. Walt
 11th September 2006, 10:18 AM #13 ponderingturtle Orthogonal Vector     Join Date: Jul 2006 Location: Tarrytown, NY Posts: 26,558 Originally Posted by ttch Okay, another stupid post on a possible violation of the conservation of angular momentum in an isolated system. Imagine a cylinder that is rotating at a high rate in free space. This cylinder consists of a rod surrounded by a close-fitting tube. For convenience, the rod and tube each has the same amount of angular momentum. If desired, you can consider the two parts to be mechanically joined when the cylinder was spun up and then mechanically separated just before we begin. (1) The rod is removed from the tube at a low energy cost. You slide it out. (2) The rod is then reversed in orientation relative to the tube at another low energy cost (this does not have to be done quickly). You turn it around. You seem to be totaly ignoreing gyroscopic effects here Quote: (3) The rod is then reinserted into the tube at another low energy cost. You slide it back in. The two parts of the original cylinder are back together but are now rotating in opposite directions. (4) The rod and tube are each equipped with electrical windings, etc. such that in conjunction they may act as an electrical generator (as in a regenerative braking system) and this feature is now used to slow the total system finally to a non-rotating state, while generating electricity. The result is that we have converted a fair portion of the original angular momentum of the cylinder into usable energy, thereby violating the conservation of angular momentum in an isolated system. QED Error, you can not turn a rotating object like that for trivial energy cost so you need to reconstuct the arugement with out that error in it.(hint you can't)
 11th September 2006, 10:38 AM #14 boooeee Dart Fener     Join Date: Aug 2002 Location: The Lando System Posts: 2,403 Originally Posted by ponderingturtle Error, you can not turn a rotating object like that for trivial energy cost so you need to reconstuct the arugement with out that error in it.(hint you can't) Actually, I think you can. You can make the energy cost as low as you want by increasing the moment of inertia of the system that is flipping the rod. What you can't do is flip the rod without changing the angular momentum of the system that is flipping the rod. The angular momentum of the system flipping the rod must by twice the original angular momentum of the rod. There is no way around that. The energy required to flip the rod can be made as low as you want. What the original poster has described is two separate processes: 1. Exchange of angular momentum between the rod and the system flipping the rod. 2. Conversion of the kinetic energy of the spinning system into electrical energy. Apples <> Oranges Angular Momentum <> Energy __________________ my nerdy sports blog: betting market analytics
 11th September 2006, 11:11 AM #15 69dodge Illuminator   Join Date: Nov 2002 Posts: 3,607 Originally Posted by ttch Okay, another stupid post on a possible violation of the conservation of angular momentum in an isolated system. You say it's isolated, but as we'll see, actually it's not. Originally Posted by ttch Imagine a cylinder that is rotating at a high rate in free space. This cylinder consists of a rod surrounded by a close-fitting tube. For convenience, the rod and tube each has the same amount of angular momentum. If desired, you can consider the two parts to be mechanically joined when the cylinder was spun up and then mechanically separated just before we begin. How was it spun up? Spinning it up requires an input of energy from somewhere. That's why you can get energy out at the end: it was put in at the beginning. Originally Posted by ttch (1) The rod is removed from the tube at a low energy cost. You slide it out. (2) The rod is then reversed in orientation relative to the tube at another low energy cost (this does not have to be done quickly). You turn it around. Reversing the rod can be done with no input of energy, but it does require the application of a torque: something has to twist the rod. What do you imagine is twisting it? It won't turn around all by itself. Whatever applies a torque to the rod, changing the rod's angular momentum, will in turn have an opposite torque applied to itself by the rod, in accordance with Newton's law of action-reaction, and therefore its own angular momentum will be changed by the same amount in the opposite direction. So the total angular momentum is in fact conserved, when you take into account this other object, as you must. Originally Posted by ttch (3) The rod is then reinserted into the tube at another low energy cost. You slide it back in. The two parts of the original cylinder are back together but are now rotating in opposite directions. (4) The rod and tube are each equipped with electrical windings, etc. such that in conjunction they may act as an electrical generator (as in a regenerative braking system) and this feature is now used to slow the total system finally to a non-rotating state, while generating electricity. The result is that we have converted a fair portion of the original angular momentum of the cylinder into usable energy, thereby violating the conservation of angular momentum in an isolated system. QED No. You've converted the original rotational energy into electrical energy, and you've transferred the original angular momentum to whatever reversed the rod's orientation. [edit: Hmph. I see boooeee just posted basically the same thing, while I was typing this up.] Last edited by 69dodge; 11th September 2006 at 11:15 AM.
 11th September 2006, 12:01 PM #16 RenaissanceBiker Eats shoots and leaves.     Join Date: Aug 2006 Location: South Carolina Posts: 6,869 I'm not trying to sound elitist or insulting, but why don't you just go take a college physics class or two? It really isn't that hard and you can learn a lot. Posting these kind of questions to a message board just seems kind of lazy to me. "I can't be bothered to look this up myself. Can someone explain it to me in a way I can easily understand?" Sorry if that sounds mean, but cheese and rice! Assume step 2 uses very little energy because you do it slowly? You need to learn more about energy and momentum. __________________ "Truth does not contradict truth." - St. Augustine "Faith often contradicts faith. Therefore faith is not an indication of truth." - RenaissanceBiker
 11th September 2006, 12:17 PM #17 kalen Your Daddy     Join Date: Mar 2004 Location: Classified Posts: 933 Originally Posted by ttch I'm going to be away from the net until late Wednesday. I would appreciate comments and refutations as they occur to you. I hope you're not away because you're standing in line at the patent office. __________________ No way! Yahweh!
 11th September 2006, 12:51 PM #18 boooeee Dart Fener     Join Date: Aug 2002 Location: The Lando System Posts: 2,403 Originally Posted by RenaissanceBiker I'm not trying to sound elitist or insulting, but why don't you just go take a college physics class or two? It really isn't that hard and you can learn a lot. Posting these kind of questions to a message board just seems kind of lazy to me. "I can't be bothered to look this up myself. Can someone explain it to me in a way I can easily understand?" Sorry if that sounds mean, but cheese and rice! Assume step 2 uses very little energy because you do it slowly? You need to learn more about energy and momentum. So, what's the point of having this sub-forum if the response to any question is "Why don't you just take a college course on microbiology/basic physics/string theory/etc.?". Sometimes asking a basic question can result in an interesting discussion in which a casual reader could learn a thing or two. So, I'm willing to cut ttch a break on this. However, if he starts 7 more threads about how this time his new scenario truly demonstrates non-conservation of angular momentum, then, by all means, let him have it. __________________ my nerdy sports blog: betting market analytics
 11th September 2006, 01:58 PM #19 Zombified Back From The Dead     Join Date: Aug 2002 Location: Inside my brain Posts: 1,373 Biker and I both made this suggestion, and its a sincere one. It wasn't meant to be "GTFO the forums" (well, at least in my case). But if ttch is really interested in physics, he may very well enjoy it and get a lot out of it, and it would really help him if he spends much time thinking about these sorts of things. Maybe he's not that interested, who knows. Towards an actual proponent of PM machines, though, the suggestion would be more pointed; conservation rules in mechanics are pretty basic, freshman stuff.
 11th September 2006, 02:53 PM #20 boooeee Dart Fener     Join Date: Aug 2002 Location: The Lando System Posts: 2,403 Understood. I agree that if ttch really wants to understand these issues, taking college physics would be the best approach. The vibe I was getting from Biker was that college physics was the only approach and that posting a question to a message board was a waste of everyone's time. My apologies if I misunderstood. __________________ my nerdy sports blog: betting market analytics
 12th September 2006, 05:11 AM #21 RenaissanceBiker Eats shoots and leaves.     Join Date: Aug 2006 Location: South Carolina Posts: 6,869 If anyone owes anyone an apology, I owe one to ttch. I really hope he (she?) is interested in physics and pursues a study of the subject, in a manner that best suits him (her?). Knowledge is power. __________________ "Truth does not contradict truth." - St. Augustine "Faith often contradicts faith. Therefore faith is not an indication of truth." - RenaissanceBiker
 12th September 2006, 08:02 AM #22 bjb Graduate Poster     Join Date: Jan 2005 Posts: 1,079 This was a perfectly good thread until know-it-all-know-nothing Art came along.
 20th September 2006, 01:23 AM #24 Beausoleil Thinker   Join Date: Mar 2003 Posts: 237 Originally Posted by ttch First the mistake: Obviously the 2nd operation (turnaround) is not low-cost. Not in free space, my stupid mistake, obvious to me the next morning. However, supported in an acceleration field like a gravity well (like on the surface of the Earth, say) it can be made very low-cost: Assume both tube and rod are horizontal. Just support the now-separate but still-rotating rod by an extension of its axis, let the other side go, and the rod will precess to any degree you want, including a simple turnaround. (If a rod doesn't exactly work here we can find some alternative geometry like originally-linked gyroscopes.) Gravity does the work. Et voila! Violation! Somebody will probably correct me to the effect that gyroscopic precession in a gravitational field alters the angular momentum of the (principal) gravitating body. If you know this to be true, please post a reference and ignore the rest of this blathering. (But if it's true then it does indeed appear that you can get something for nothing...) As far as energy generation goes, I don't see the point. You could hook up your generator to the original spinning system and generate energy that way. Using gravity to do the work doesn't alter the fact that, if that part of the process is taken into account, there is no violation. Gyroscopes precess because there is a torque exerted by the Earth's gravitational field - the line joining the centres of mass of the gyroscope and the Earth does not pass through the pivot. Gravitational attraction acts on both bodies along this line, so both bodies experience a torque about the pivot and both have their angular momentum changed to equal and opposite extents. If your proposed violation of conservation of angular momentum involves transforming it into energy, you can be certain that you've misunderstood both concepts.
 20th September 2006, 09:33 AM #25 RenaissanceBiker Eats shoots and leaves.     Join Date: Aug 2006 Location: South Carolina Posts: 6,869 Originally Posted by ttch First the mistake: Obviously the 2nd operation (turnaround) is not low-cost. Not in free space, my stupid mistake, obvious to me the next morning. However, supported in an acceleration field like a gravity well (like on the surface of the Earth, say) it can be made very low-cost: Assume both tube and rod are horizontal. Just support the now-separate but still-rotating rod by an extension of its axis, let the other side go, and the rod will precess to any degree you want, including a simple turnaround. (If a rod doesn't exactly work here we can find some alternative geometry like originally-linked gyroscopes.) Gravity does the work. Et voila! Violation! Here you are adding energy. There is no violation. __________________ "Truth does not contradict truth." - St. Augustine "Faith often contradicts faith. Therefore faith is not an indication of truth." - RenaissanceBiker
 20th September 2006, 11:40 AM #26 boooeee Dart Fener     Join Date: Aug 2002 Location: The Lando System Posts: 2,403 Originally Posted by ttch First the mistake: Obviously the 2nd operation (turnaround) is not low-cost. This is not the mistake. Changing the orientation of the rod in free space or on the surface of the Earth is as low cost as you want to make it. I know other posters have contradicted this, but they are not correct. 69dodge posted the same thing, and if you check his posting history, you'll find he knows his stuff (my track record is a bit more spotty). What you have described is converting the kinetic energy of the spinning rod into electrical energy. Originally Posted by ttch @boooeee reiterated etc., and noted that the total angular momentum prior step 4 was already zero. Yeah, but I'm trying to extract the original momentum into some useful form of energy. Also, again, "Do not confuse angular momentum with energy." If there isn't some sort of idealized conversion between the two then I guess I'm really confused. Is it possible to start something rotating without any application of energy whatsoever? Angular momentum and energy are just two different things. That's all there is to it. It is true that if you know an object's angular momentum and its moment of inertia, you can calculate its rotational energy. The formula is L^2/I where L is the square of the angular momentum vector and I is the moment of inertia. Don't think of your scenario as converting angular momentum into electrical energy. You are converting rotational energy into electrical energy. Since the rod was already spinning at the beginning of your scenario, that is where the electrical energy is coming from. Somebody had to do work to spin the rod in the first place. __________________ my nerdy sports blog: betting market analytics
 21st September 2006, 01:19 PM #27 Art Vandelay Illuminator     Join Date: May 2004 Posts: 4,790 Originally Posted by ttch @Art Vandelay was criticized by other posters so I don't have to respond to him at all. Yippee! Huh? Is "criticism" now a synonym for "refutation"?
 21st September 2006, 05:34 PM #28 davefoc Philosopher     Join Date: Jun 2002 Location: orange country, california Posts: 7,333 Originally Posted by Art Vandelay Huh? Is "criticism" now a synonym for "refutation"? I don't think you were wrong Art, but I did think you came across as a bit of a jerk. Not quite the same thing as a refutation I suppose, but it's the best I could do considering that I thought your assertions related to angular momentum and energy were correct. ttch wrote: Quote: @69dodge reiterates the conservation of angular momentum: "Whatever applies a torque to the rod, changing the rod's angular momentum, will in turn have an opposite torque applied to itself by the rod, in accordance with Newton's law of action-reaction, and therefore its own angular momentum will be changed by the same amount in the opposite direction. So the total angular momentum is in fact conserved, when you take into account this other object, as you must." Revised, I don't see this to be true. If the Earth gets angular momentum from gyroscopic precession (which doesn't slow gyroscopes) when all the energy from the original system is later recovered, it would seem we've gotten something for nothing. So I would have trouble believing that. I think boooeee has basically addressed this. But if you still disagree with his explanation reduce the situation to linear momentum and energy. If a brick is floating in space can you get it to change its momentum without changing the momentum of something else? if you put a little spring inside the brick and split it apart the sum of the momentum of the pieces of the brick before and after the spring is released will be the same. Momentum can't be turned into energy. When you throw a brick against the wall you change the momentum of the earth a little by bracing yourself against the earth when you throw the brick. The earth's momentum changes in the opposite direction when the brick hits the wall and the wall transfers its momentum to the earth. The energy situation is quite a bit different although it is conserved also, but the energy transitions from one form (chemical) to another form (heat) in the process of you throwing the brick against the wall.
 22nd September 2006, 03:21 AM #29 ttch Scholar   Join Date: Aug 2006 Posts: 51 To Art V.: I wasn't trying to criticize you so much as I was looking for any excuse to avoid responding in depth to each of 20+ posts. Please accept my apology. Thanks to all for your responses. You've given me a lot to chew on, and a good reason to hit the books.

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