The Pumping of a Swing (Conservation of Angular Momentum)

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.

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.

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. 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).

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.