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Moving your weight back is equivalent to moving the pivot forward, like having a ball on a string and moving your hand forward, then, when it moves forward, moving your hand back. What I don't understand is how you can propel it forward by only moving your legs forward, which should propel it back.

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You are not actually propelling it forward as such. What you are doing is that each time you swing you raise your legs at the top of each swing. This moves your bodies centre-of-mass to a greater height creating more potential energy. This potential energy is in turn transferred into kinetic energy, meaning after each swing you will go faster and higher and so on. EDIT Added: Note that you are swinging your feet in phase with the swing to make it go higher, making this a resonance effect. (added edit thanks to David white' comment below - thanks David)

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  • $\begingroup$ Dr jh, you could also add that you swing your feet in phase with the swing to make it go higher, making this a resonance effect. $\endgroup$ Sep 19, 2020 at 13:41
  • $\begingroup$ @DavidWhite Thanks David. Good point and I added it as you asked. $\endgroup$
    – joseph h
    Sep 19, 2020 at 22:38
  • $\begingroup$ Thanks Dr dj & Dave. Since I posed the question, I worked out how moving your legs forward shifts your centre of gravity back, It is because your legs are further from the fulcrum (pivots), and have more leverage than your upper body, so the "mass x displacement" is greater for it, like somebody about to fall off a cliff leaning over it to regain their balance. Also, I noticed that your legs and/or body are rotating, which tries to rotate the swing and push the pivots forward, pushing you back. I wrote an explanation & sent to 1 of 4 of us trying to work it out. I'll show it below. $\endgroup$ Sep 23, 2020 at 23:53
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It seems counterintuitive, somebody moving a swing forward by only swinging their legs forward: If somebody is standing on a frictionless base on a level surface and they thrust something forward without letting go of it, the combined centre of gravity remains the same. Mass times displacement is the same. But, when one object is above the other on a pivoting lever, the object furthest from the fulcrum has the most leverage, so, if they are the same size, the object nearer the fulcrum will move further back, shifting the centre of gravity back. Regardless of the size, the mass times displacement is greater for the object nearest the fulcrum. So when somebody on a swing swings their legs forward, because their legs are below the rest of their body, they actually shift their centre of gravity back slightly. It is the same as somebody about to fall over a cliff leaning over it to regain their balance.

Because their legs rotate forward and/or body rotates back, there is also a moment of rotational inertia which rotates the swing back slightly more, by trying to push the pivots forward as you press on the chains. When you lean back and swing your legs forward, everything except the bit on the seat rotates backwards, giving you maximum forward propulsion, both from rotational inertia, and shift of centre of gravity which is equivalent to moving the pivot forward. enter image description here

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    $\begingroup$ I strongly suspect that these answers about center of gravity are in fact wrong. If they were correct then one would expect that the part of the body to get exhausted first would be the legs or the back, when it is in fact the arms. And it seems to continue even when you are doing whatever you are doing on the upswing, kids do not tilt forwards until the apex. It seems to me like one must ultimately describe the action as a very surprising act of “pulling yourself forwards with your arms” but it is not clear to me how this manifests in the actual operation of the swing. $\endgroup$
    – CR Drost
    Sep 24, 2020 at 0:51
  • $\begingroup$ It is your arms that are doing most of the work moving your back. How it moves the swing is all to do with the weight distribution along the lever formed by the swing. Along the path round the circle you are essentially weightless, like an object thrown into the air. If the object extended part of itself without releasing it, there would be no effect on its motion (like the girl). But if the object is on a pivoting lever and the outer part moves, the mass x displacement of the inner part, which has less leverage will be more. U R also pushing on the pivot via the chain to rotate yourself. $\endgroup$ Sep 24, 2020 at 6:34

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