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On a playground swing, children quickly learn how to swing higher and higher by timing their body motions with the resonant frequency of the swingset. But it occurs to me that it seems you're making something out of nothing, creating motion without anything to push against.

It can't be the air, because if you assume a swinging speed of 10kph (~6mph), and that the final speed of the air is limited by that of the "swinger" imparting the momentum, for a 50kg (110lb) child to reach 10kph she'd have to move at least 50kg of air to that speed, which is over 40,000 liters for dry air at STP. Moreover, it's hard to imagine it's anything at the end of the swing because intuitively (I know, not the best model to use) tension can only pull, not push, so the idea of the swinger applying a reactionary force through the rope seems counter to the model of tension in a rope (or chain, as swings tend to be).

What's going on here?

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  • $\begingroup$ I don't know which specific movement you are mentioning, but I used to bring my legs closer to increase speed. Later, I realized this was due to the conservation of angular momentum. $\endgroup$
    – PNS
    Jul 17, 2020 at 6:53

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That's a great question! The link here indicates that you give yourself a little potential energy shift at the top of the swings through your body motions, which then results in increased kinetic energy at the bottom of the swing. Seems reasonable and from what I remember swinging on a swing, I do lift myself slightly at the end of each upward trajectory.

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