This page discusses the February 15, 2011 Fun Physics Facts for the Family Demonstration...
Perhaps what is the longest delay for a retraction by the New York Times (49 years) was published on July 17, 1969. What other event happened around this date? These two events, the original 1920 editorial and the July 1969 retraction are obviously related (see the following footnote for an accounting of this retraction).
It is quite intriguing to note that an editorial published in the New York Times on January 13, 1920 made fun of the idea of rockets in space, claiming that Dr. Robert Goddard (1882-1945), the inventor of the liquid fuel rocket and father of American rocketry, was wrong and that rockets would not work in space since there was nothing to push against in the vacuum of outer space. You see, Robert Goddard wrote an article entitled "A Method of Reaching Extreme Altitudes" that was published by the Smithsonian in late 1919. The Jan. 13, 1920 Times editorial chided Goddard for his article, "That Professor Goddard, with his 'chair' in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react --- to say that would be absurd. Of course, he [Goddard] only seems to lack the knowledge ladled out daily in high schools." And years later, on July 17, 1969 just days before the first human was to walk on the Moon, the Times published a retraction on page 43 stating that they had obviously made a mistake about rockets in space in their earlier 1920 editorial, stating, "Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th century, and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error." Of course, Conservation of Linear Momentum requires the space vehicle to be propelled forward when its rocket engine expels combustion gases rearward, even without anything for those gases to push against.
A problem related to this is the following ...
For all of you budding astronauts, can an astronaut on a space walk, who can't physically reach her spaceship, turn around and face the opposite direction without using her thrusters? If so, how?
Perhaps she is on a space walk attaching some instrument to a special port on the side of the International Space Station (ISS). She has maneuvered herself into position, and has carried out the preliminary preparations of the port. Now she needs to turn around to "pick up" the instrument, and then turn back around while holding the instrument in order to be positioned to attach it. If she uses her thrusters to accomplish this maneuver, she knows that the rather crude nature of the thrusters means that she will be pushed out of position and then will have to use the thrusters to reposition herself. This takes both time and nitrogen (for the thrusters), two resources that are in limited supply. So she would like to accomplish her task without employing the thrusters, is this possible?
If your immediate response is "Of course!", then think about the following for a moment. What is the astronaut's angular momentum right before she wishes to turn around? Yup, it's zero since she has no angular velocity. Since she cannot reach out and touch anything in space, by the Conservation of Total Angular Momentum Law her angular momentum must be conserved, and thus it remains zero. Therefore, since her angular momemtum is zero, and obviously if she is spinning her angular momentum would be non-zero, she cannot spin around. Well, what do you think about this argument, is it a valid one?
Let's first do a simple experiment. Sit in a swivel chair that is well-oiled so that it spins easily (the left diagram: you, sitting on the swivel chair, are represented in an overhead view by the blond head on blue shoulders at the bottom of this drawing, the table is the smaller gold circle labeled m_p at the top, your right arm is the line and arrow pushing the table to the left). Without touching anything but the chair seat, spin around ... Oh, so you can't do it, huh! Next move closer to a table so that you can reach out in front of you and just touch the table. Now push in a left direction against the table with your right hand. What happens? That's right, you begin to spin in a clockwise direction, as shown in the left-hand schematic drawing.
So, just maybe the astronaut can't turn around! Maybe she does require something that she can push against in order to give herself a non-zero angular momentum? But wait, can she push against herself? What if she reaches around with her right arm and grabs her left shoulder and gives it a tug? Will this turn her around? No, since by conserving angular momentum means that her right shoulder must move in the opposite direction as her left shoulder. Okay, I'm convinced, the astronaut cannot turn around in outer space...
Here Sandy is attempting to turn around on a "lazy susan" platform by swinging her arms back and forth...her arms go one direction and her body goes in the opposite direction - she does not get anywhere. Sandy's angular momentum is zero before she moves, and it remains zero during her arm swinging.
Pushing against a chair, on the other hand, does allow Sandy to spin around. Now her angular momentum is not conserved since an outside force (torque from the chair) alters her angular momentum. (See the text for further explanation.)
Two people, initially having a net zero angular momentum, pushed off against each other, maintaining their net zero angular momentum...
Let's next extend this experiment. Say we have two swivel chairs and a buddy. You and your buddy sit facing each other in the swivel chairs. You are just close enough that if both of you stretch your arms out you can reach each other's hands. Now how can you turn around? Yup, you push against your buddy's outstretched hand. What happens? You turn around just as when you pushed against the table, but now your buddy also spins around so that you both are initially going in opposite directions! In fact, since angular momentum has a direction, you and your buddy have opposite angular momenta. [If you pay close attention, you will notice that you and your buddy are both revolving in the same direction. Does this not mean that you both have the same angular momentum? Here is where we have to be careful, for we must be measuring the angular momentum about the same axis, not two different axes. Thus we must measure the angular momentum of your buddy about your axis, not his. To better understand this point, the details of this calculation are performed in the following solution for this Example.] If we sum both of your angular momenta, we would find a value of zero. Before you guys pushed against each other you were sitting still with zero angular momentum, and after pushing against one another your combined angular momentum is still zero (you have +L and your buddy has -L angular momenta for a total of +L-L=0). So the total angular momentum appears not to have changed, it appears that it is conserved, in other words.
If this is the case, then what happened when you pushed against the table? In this case the table was attached to the floor (through friction supplied by the force of gravity), and the floor was attached to the Earth. Indeed, the entire Earth changed its angular momentum by an amount opposite to the change in your angular momentum, it is just that the Earth is so large and so massive that we could not see this change in the Earth's angular momentum. However, it was there and the total angular momentum of you spinning in the chair and the entire Earth was still conserved!
Here is a video (Astronaut-Turn_Around_Cons_L-1080p.mov) demonstrating these issues surrounding conservation of angular momentum.
Click on the following link to watch the video on YouTube: http://youtu.be/VUueiewb-b8
(YouTube offers multiple alternative video resolutions, so download the highest resolution that you can reasonably download.)
Description of the video: This video first shows Sandy attempting to spin around while seated on a turntable by swinging her arms. Her arms go one way while her torso goes the other way -- her net zero angular momentum is conserved. Secondly, Sandy pushed off against a chair, now she can change her angular momentum through the action of the external force. And lastly, if two individuals, both on turntables, push off against one another then their net angular momentum remains zero.
Note: Don't be confused by the rotations of the two swivel chairs in the above video. In a cursory viewing, it appears that the two chairs are rotating oppositely while in fact they are rotating in the same direction. But the momentum is still zero around one of the rotation axes...see the PDF solution file below for this calculation.
So, just maybe the astronaut can't turn around! Maybe she does require something that she can push against in order to give herself a non-zero angular momentum? But wait, can she push against herself? What if she reaches around with her right arm and grabs her left shoulder and gives it a tug? Will this turn her around? No, since by conserving angular momentum means that her right shoulder must move in the opposite direction as her left shoulder. Okay, I'm convinced, the astronaut cannot turn around in outer space...
On the other hand, cats are remarkable animals, so agile and flexible. A cat dropped from a height of a few feet with its back facing the ground will somehow right itself and land on its feet. In light of the above Conservation of Angular Momentum argument, how is this possible?
So, which is it?
An astronaut who cannot reach out and push against anything, can she turn around in outer space or not? Explain.
So, since there are two seemingly reasonable arguments that yield opposite answers, you must analyze this problem using what you know about rotation and angular momentum. Actually carry out a mathematical analysis to see if it is possible.
Solution:
First of all, let's modify the swivel chair experiment for a moment. Let's say that a flexible tether of length r_o attaches you to the mass m_p (see the Figure above). And let's say that the mass m_p is much greater than your mass. Initially, the combined angular momentum of you and m_p is zero. But what happens if you push sideways against m_p. Since m_p is so large, it will hardly move but you will begin to rotate. Right? Right! But shouldn't the angular momentum be zero still? Yes it should. And since you indeed do rotate and thus have a non-zero angular momentum, the mass m_p must rotate in the opposite direction so that its angular momentum can cancel yours. Let's calculate the details of how this is possible, shall we?
Click for full-size image
The Angular Momentum of the astronaut and mass m_p is initially zero. When the astronaut swings the mass around her head in one direction, the astronaut must rotate in the opposite direction to conserve the zero angular momentum.
In fact, if we calculate the angular velocity, \omega_o, of the astronaut and compare it with the angular velocity, \omega_p, of the mass, then we find that they have opposite signs (constant K>0):This means that if the astronaut swings the mass counterclockwise, then she will rotate clockwise, as shown in the above Figure.For those wishing to see the details of the mathematical derivation, they are included in the PDF file:The following video (Astronaut-Turn_Around_Rope-1080p.mov) shows this scheme where m_p is simply a knot at the end of a rope.
Click on this link to watch the video on YouTube: http://youtu.be/yI5RuUUOoPE
(YouTube offers multiple alternative video resolutions.)Description of the video's experiments: This video demonstrates the above method for an astronaut to turn around by swinging a rope above her head. When the rope is revolved in one direction, the body must rotate in the opposite direction in order to conserve angular momentum.
Click for full-size image
The mass m_p does not have to make a full orbital motion in order to still have a non-zero angular momentum. For instance, along the path drawn at the left, the angular momenta are zero along the two radii labeled 2 and 4. Along the segment 1 the angular momentum is positive (counterclockwise) while along segment 3 it is negative (clockwise). But because of the differences in the radius of 3 versus 1, the momentum along 1 is greater in magnitude that the opposite momentum along 3. Hence the momenta along 1 and 3 do not cancel and there is a net positive (counterclockwise) angular momentum of the mass m_p following the path shown. This means that the astronaut must have an opposite angular momentum in order to conserve the zero momentum, thus she rotates clockwise.
Similarly, if we compute the angular velocity of the astronaut in the above situation, we find (constant K'>0):which means, once again, that if the mass is rotated counterclockwise the astronaut will rotate clockwise in order to compensate.
The mathematical details are included in the PDF:
And the path for the mass m_p does not even have to be the special one analyzed above, it can be circular and still yield a net positive angular momentum. Once again the astronaut must therefore have a negative angular momentum in order to cancel the positive momentum of the mass.
And, finally, if we compute the angular velocity of the astronaut in the above case where the mass spins, we find (constant K">0):which again means that a counterclockwise rotating mass produces a clockwise rotation of the astronaut.
The derivation is likewise given in the PDF:Following is a video (Astronaut-Turn_Around_Jug_NoGershwin-1080p.mov) demonstrating this method for an astronaut to turn herself around.
Click on this link to watch the video on YouTube: http://youtu.be/sXe2AO4JKxs
(YouTube offers multiple alternative video resolutions.)Description of the video's experiments: This video shows a water jug being revolved in front of the body. In order to conserve angular momentum, the body must then rotate in the opposite direction.
And the answer is: Yes!
From a Conservation of Angular Momentum point of view, if the astronaut, whose initial angular momentum is zero, swings a heavy object on a rope causing it to orbit around her then while the object is in orbit the total momentum must remain zero. This means that the astronaut must turn around in the opposite direction to conserve this zero angular momentum (see the top diagram above). Employing the middle diagram, we argue that the object does not actually have to orbit the astronaut to have a non-zero angular momentum all by itself thereby necessitating that she have an opposite momentum in order to conserve the zero total. Finally, we show in the bottom diagram that the object does not even have to follow the special trajectory used for the argument presented in the middle drawing. The above PDF file, CM-AstronautTurnAround.pdf, makes these physical arguments mathematically quantitative by calculating the actual angular momentum for the object and for the astronaut for each of these situations.
Here Steve is performing the astronaut turn around strategy with a 1.5 gallon jug of Clorox bleach.
There is an alternative strategy for an astronaut to turn herself around, and that entails the use of a gyroscope. Below the method is demonstrated in the video, but here we give just a cursory introduction since this concept is very closely related to the topic of the third FPF demonstration entitled "The Most Magnificient Mechanical Machine" (link: FPF-03 The Most Marvelous Mechanical Machine ).
There is an even more clever solution to the astronaut turn around problem that relies on an old favorite, the gyroscope. (See the above PDF file for a full description of this alternative.)
Sandy is performing the astronaut turn around technique using a gyroscope.
Following is a video (Astronaut-Turn_Around_Rotor-1080p.mov) demonstrating this method for an astronaut to turn herself around.
Click on this link to watch the video on YouTube: http://youtu.be/O1JbldH_ADs(YouTube offers multiple alternative video resolutions.)Description of the video's experiments: This video shows a different type of astronaut turn around methodology employing a gyroscope. The angular momentum vector of the gyroscope is constant (conserved) unless acted upon by a net torque. The torque changes the angular momentum. Thus, the astronaut may turn around by applying a torque to the axle of the rotating rotor, as demonstrated in this video.
Note: For at least the last 30 years, new mathematics based upon differential geometry, differential forms, and gauge symmetries, have been making inroads into a number of fields of physics besides particle physics. For old codgers like me, it has meant having to learn the new mathematics on our own, and the result has been that the old way (vector calculus, divergence, gradient, curl, stokes) is still more intuitive than the new way. The new way, however, is better in the sense that it can represent the symmetries inherent in the physical world better than the old way. Some might even argue that the right-hand bias of the old way delayed the discovery of electromagnetics which is not biased to either right-hand or left-hand symmetry. While somewhat dated, I would still recommend Misner, Thorne, and Wheeler's Gravitation as a great introduction to the modern differential geometry approach that helps us regain, or retain, some of our insights into the physics. I mention all of this because there is a 1993 "Falling Cat Theorem" by Richard Montgomery employing Gauge Theory and Differential Forms to describe the process whereby a cat can right itself as it free falls with zero angular momentum.Supplementary Material:
- Here is the Bibliography for the references contained in the solution PDF file (CM-AstronautTurnAround_pw04.pdf):
- If you would like to understand angular momentum at a little deeper level, then the following PDF file
provides a geometric interpretation of angular momentum and its relationship to linear momentum:
- Conservation of Angular Momentum is derived in the PDF file:
- Conservation of Angular Momentum for multiple particle systems is derived in the following PDF file:
- And for those wishing to understand, really understand, at a very deep level why angular momentum is conserved, then the following PDF derives Noether's Theorem and shows how symmetries of the Universe yield the various laws of physics, and, in particular, we apply Noether's Theorem to rotational symmetry in order to derive the Conservation of Angular Momentum Law (This is an Advanced Topic requiring Lagrangian Mechanics):
[Emmy Noether (1882-1935), by the way, was one of the first female professors, and a short snippet of her fight for an academic career is given.]
Summary Concepts:
- Torque changes the angular momentum.
- If there is no torque, then the angular momentum is constant.
The following link goes to a page containing all FPF Demonstration video YouTube links: FPF Videos
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