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Author Topic:   The Pumping of a Swing (Conservation of Angular Momentum)
JustinC
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Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 1 of 16 (551169)
03-21-2010 4:05 PM


I'm having trouble understanding how a child can seemingly increase the angular momentum of a swing (i.e, swing higher and higher). You can visualize the swing as a pendulum. The pumping would be the changing of the position of the bob.
There are two ways to "pump up a swing."
1.) Stand on the swing in a crouching position and start off with a little push. As you rotate through the lowest point (directly underneath the pivot) you stand up. This changest your center of gravity (the bob), and therefore you and swing move faster and therefore higher. At the apex, you crouch back down. Do this enough times and you'll increase the amplitude significantly.
2.) Sit in the swing. At the forward peak, swing your legs forward and your upperbody backwards. I think this works because your adding momentum to the bottom of the pendulum, i.e., your feet. Your upper body gets thrusted back in the process, so this would decrease your momentum. But since your feet are further away from the pivot, this change in momentum would increase the angular momentum more than the decrease in angular momentum caused by the head moving backwards.
I'm not sure this is exactly right, but that's my understanding of the process. If its not, then I would gladly be corrected.
Assuming this is right, it would seem that the angular momentum of the system has changed without any outside force. How is this possible.
Any help would be greatly appreciated.
Justin

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Message 2 of 16 (551243)
03-22-2010 2:37 AM


Thread Copied from Proposed New Topics Forum
Thread copied here from the The Pumping of a Swing (Conservation of Angular Momentum) thread in the Proposed New Topics forum.

  
Dr Jack
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Message 3 of 16 (551259)
03-22-2010 5:53 AM
Reply to: Message 1 by JustinC
03-21-2010 4:05 PM


I'm not sure why you feel it has to be an outside force? The energy transfered into the system comes from your muscles. Adding energy to angular systems can alter the angular velocity.

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nwr
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From: Geneva, Illinois
Joined: 08-08-2005
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Message 4 of 16 (551277)
03-22-2010 8:26 AM
Reply to: Message 1 by JustinC
03-21-2010 4:05 PM


JustinC writes:
Sit in the swing. At the forward peak, swing your legs forward and your upperbody backwards. I think this works because your adding momentum to the bottom of the pendulum, i.e., your feet.
While leaning backwards, you are holding the rope. This puts a bend in the rope, and shortens the swing. No additional angular momentum is required at that point. Because the swing is shortened, it moves faster and travels higher.
When it is near the high point, you release this force, unbending the rope and lengthening back to the original length. But now you are higher than you would otherwise have been, so the force of gravity will add more angular momentum on the next downward swing.
At least, I think that is how it works.

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Dr Jack
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Posts: 3514
From: Immigrant in the land of Deutsch
Joined: 07-14-2003
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Message 5 of 16 (551279)
03-22-2010 8:41 AM
Reply to: Message 4 by nwr
03-22-2010 8:26 AM


While leaning backwards, you are holding the rope. This puts a bend in the rope, and shortens the swing. No additional angular momentum is required at that point. Because the swing is shortened, it moves faster and travels higher.
But it works on swings with rigid 'ropes' too so this can't be right.
I believe it works because you use your muscles to alter your centre of gravity, converting the chemical energy in ATP to kinetic energy in muscles to potential energy in your body which then converts into the kinetic energy of the swing and increases angular momentum.

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nwr
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Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
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Message 6 of 16 (551290)
03-22-2010 9:16 AM
Reply to: Message 5 by Dr Jack
03-22-2010 8:41 AM


Dr Jack writes:
But it works on swings with rigid 'ropes' too so this can't be right.
It does not work nearly as well.
By raising your legs, you are also shortening the length. As you put it, this raises the center of gravity, and therefore reduces the average length (the length from swivel point to the center of mass). Or, equivalently, it reduces the moment of inertia.
Gravity removes angular momentum on the upswing, and adds angular momentum on the downswing. By reducing the length for the upswing, you reduce the amount of angular momentum removed. By increasing the length for the downswing, you increase the amount of angular momentum added.
As long as more angular momentum is added in the downswing than is removed in the upswing, the speed and height will increase. This ignores friction, wind resistance, etc., so in practice you need to add enough additional angular momentum to compensate for loss due to friction, air resistance, etc, and then add a little more if you want to increase speed and height.
You are correct about the conversion from chemical energy to kinetic energy. However, JustinC is correct that, since you are part of the system you cannot directly alter its angular momentum. You can redistribute mass so that gravity adds more angular momentum on the downswing than it removes on the upswing.

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 Message 9 by JustinC, posted 03-22-2010 3:20 PM nwr has replied

  
Dr Jack
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From: Immigrant in the land of Deutsch
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Message 7 of 16 (551293)
03-22-2010 9:23 AM
Reply to: Message 6 by nwr
03-22-2010 9:16 AM


You are correct about the conversion from chemical energy to kinetic energy. However, JustinC is correct that, since you are part of the system you cannot directly alter its angular momentum. You can redistribute mass so that gravity adds more angular momentum on the downswing than it removes on the upswing.
Yes, that's what I'm saying.

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slevesque
Member (Idle past 4641 days)
Posts: 1456
Joined: 05-14-2009


Message 8 of 16 (551370)
03-22-2010 3:00 PM
Reply to: Message 7 by Dr Jack
03-22-2010 9:23 AM


Nwr explanation is much more complete because it says how the engery you are spending transfers to the system and increases the angular momentum.
Your explanation with energy is right, but it's form of ''you are spending energy and this energy goes to the system'' does not explain how it goes to the system.
As for the OP, I'll just add (since I agree with nwr) that saying there is no outside force is incorrect, since the force of gravity is correct. And it is the force of gravity that adds angular momentum when you change the position of the center of mass.
Remove the force of gravity, and you are correct that you will never be able to add angular momentum (you won't have an oscillatory system at all in fact)
Edited by slevesque, : No reason given.

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JustinC
Member (Idle past 4844 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 9 of 16 (551371)
03-22-2010 3:20 PM
Reply to: Message 6 by nwr
03-22-2010 9:16 AM


Thanks for the replies.
By raising your legs, you are also shortening the length. As you put it, this raises the center of gravity, and therefore reduces the average length (the length from swivel point to the center of mass). Or, equivalently, it reduces the moment of inertia.
I can't tell if this is equivalent to another explanation I've read. It goes like this.
The person rotates their body in the opposite direction as the swing is rotating at the peak of the upswing.
So say that the upswing is counterclockwise. As the child approaches this apex, she swings her legs forward and head backward, effectively rotating her body clockwise.
Due to the conservation of angular momentum, this would add a little momentum to the swingset and therefore cause it to go a little higher.
This seems like it would work with rigid or flexible 'ropes'.
Another question: if we included the earth in our system, would the rotation of the earth have to change slightly to compensate for the increase in angular momentum of the child?
Thanks
Edited by JustinC, : No reason given.

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nwr
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From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 10 of 16 (551378)
03-22-2010 3:41 PM
Reply to: Message 9 by JustinC
03-22-2010 3:20 PM


JustinC writes:
The person rotates their body in the opposite direction as the swing is rotating at the peak of the upswing.
So say that the upswing is counterclockwise. As the child approaches this apex, she swings her legs forward and head backward, effectively rotating her body clockwise.
Due to the conservation of angular momentum, this would add a little momentum to the swingset and therefore cause it to go a little higher.
No, that does not seem to explain the pumping. The swing set goes higher at the expense of the child not going as high. So nothing is accomplished since the aim is for the child to also go higher.
It really is the redistribution of mass, the moving of the center of mass of the child/swing system closer to the pivot, that matters. The effect of gravity on angular momentum depends on the force and the distance from the pivot at which the force is applied. If the mass is closer to the pivot on the upswing than on the downswing, then the angular momentum removed by gravity on the upswing will be less than the angular momentum added by gravity on the downswing. And that achieves what you want.
Incidentally, you can do a "reverse" pumping to slow the swing down more rapidly.
JustinC writes:
Another question: if we included the earth in our system, would the rotation of the earth have to change slightly to compensate for the increase in angular momentum of the child?
Yes, although the effect would be imperceptible. For that matter, driving your car also affects the earths rotation, and by a lot more than pumping up that swing (though still imperceptible).

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JustinC
Member (Idle past 4844 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 11 of 16 (552112)
03-26-2010 3:41 PM
Reply to: Message 10 by nwr
03-22-2010 3:41 PM


No, that does not seem to explain the pumping. The swing set goes higher at the expense of the child not going as high. So nothing is accomplished since the aim is for the child to also go higher.
Thanks for engaging me. I think this topic should be wrapped up soon.
Just a few more questions. I understand the explanation that explains the increase in momentum by the changing the moment of inertia.
The other explanation I proposed I got from Page Not Found | Grinnell College
For the driven oscillator one must think of the angular motion, or more precisely, the angular momentum. As we picture the swing this is made up of two parts; the motion of the swing as it moves back and forth and the rotation of the swinger as he rotates about the seat of the swing. This is probably clearer for someone seated on the swing. If the swinger rotates suddenly the sum of these two motions is unchanged. But by rotating about the seat in one direction one can impart a rotation of the swing about the support at the top of the swing in the opposite direction. This allows the swinger to give a kick to the motion of the swing about the support and thus drive the swing higher. This is the mechanism of the driver oscillator.
I'm not sure I understand it fully, so I may have not explained it accurately in the previous post. I seems, though, that the swinger is rotating in the opposite direction as the swing and this imparts some momentum to the swing without changing the center of mass.
Clip 5 on the website has a wheel attached to a rigid arm and increases the amplitude by rotating the wheel.

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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 12 of 16 (552125)
03-26-2010 5:18 PM
Reply to: Message 11 by JustinC
03-26-2010 3:41 PM


I still don't think I fully agree with that explanation. But I do see where my earlier explanation was incomplete. So I'll try again.
Note that I uninstalled quicktime a few years ago, and I don't feel like reinstalling. So I was unable to watch those movie clips. I did find another site with diagrams, which I think covers the same thing.
The explanation given seems to be that you rotate, and transfer angular momentum to the system. Then when the swing is rotating the other way (on the return) you rotate the other way. So that you are adding each time with no net change in your own angular momentum. And I guess that works to an extent, but I think the effect would be small.
However, what I do see happening, is that this strategic motion (or rotation) of the person's body, if done with the right timing, has the effect of lengthening the down motion period and shortening the up motion period. And then reversing that motion for the swing return again lengthens the down swing in the other direction and shortens the upswing in the other direction.
Since the amount of angular momentum change caused by gravity depends on how long the gravitational force is applied, lengthening the down swing and shortening the upswing will increase the amount of angular momentum added in the downswing and reduce the amount of angular momentum removed in the upswing.
I'll still think about that some more.
Thanks for persisting with this. I did learn some more about it as a result.
----------
As indicated, I was not able to watch those clips. But let's talk about the theory they give of transferring angular momentum by rotating that wheel.
It seems to me that if that wheel rotation were done only when the swing is near the bottom, you would get the effect of transferring angular momentum. If the rotation is done near the top, you also get the effect of lengthening the down swing and shortening the upswing, which I think is the more important part. If I had the equipment, I would want to experiment with that to see if my analysis is correct.

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xongsmith
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From: massachusetts US
Joined: 01-01-2009
Member Rating: 6.8


Message 13 of 16 (552139)
03-26-2010 7:31 PM
Reply to: Message 12 by nwr
03-26-2010 5:18 PM


It's all about incrementally transferring momentum from the earth. If you watch an adult on a child's swing, you will see the 4 legs dig into the earth on each pumping motion. You have to add the earth into the system to observe conservation of angular momentum.

- xongsmith, 5.7d

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slevesque
Member (Idle past 4641 days)
Posts: 1456
Joined: 05-14-2009


Message 14 of 16 (552264)
03-27-2010 9:36 PM
Reply to: Message 13 by xongsmith
03-26-2010 7:31 PM


we are talking about the situation where the kid by itself pumps his own momentum. Of course he someone is pushing him it is pretty straightforward and easy, but your explanation doesn't explain why a kid, byt itself, without touching the ground, can swing.
Just including the earth into the system doesn't necessarily do it, since the kid goes back and forth.

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xongsmith
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Posts: 2578
From: massachusetts US
Joined: 01-01-2009
Member Rating: 6.8


Message 15 of 16 (552268)
03-27-2010 10:01 PM
Reply to: Message 14 by slevesque
03-27-2010 9:36 PM


your explanation doesn't explain why a kid, byt itself, without touching the ground, can swing.
Yes, it does.
The kid's pumping motion alternately makes the back legs of the swing set dig into the earth and then the front legs, increasing the pendulum's amplitude and gradually, bit by bit, adds to the swing set angular momentum in one rotational direction and the opposite rotational momentum to the earth for each direction of swinging, undetectable due to the huge mass of the earth in comparison. So instead of pushing back against his brother's pushing, he pushes back against the earth with the pumping motion, driving the legs into the ground. If the legs are encased in cement, as they often are on public playgrounds, then you wont see it except maybe by studying the cross beam holding up the swings and inferring the transmission of the force into the legs and cement.

- xongsmith, 5.7d

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