# Conservation of momentum on a swing

## Main Question or Discussion Point

I was thinking the other day about how conservation of momentum works in terms of a closed system consisting of a child and a swing and gravity. How does the child start moving on the swing? Does he need to push against the air to start going? Where does he extract the momentum from? If he does push against the air, does that mean that a child cannot start swinging from rest in a vacuum? This has been in the back of my mind for a couple of days, but nothing good has popped into my head.

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This also got me thinking about conservation of momentum in terms of the human body in general. For example, when I lift my finger, where am I taking momentum from? And where is it going once I stop moving my finger?

to answer your first question, the momentum comes from your muscles; when someone swings it has little to do with the air; the swinger moves his or her legs and or arms and the momentum is transferred to the swing; for your second answer you have to look at each individual muscle contraction and it's very complicated and i dont understand it well enough to explain it but here's a link that explains it well http://cstl-csm.semo.edu/trautwein/BS113Fall2003/Sliding Filament.ppt

I believe the effect of the air is negligible. (A swing would work on the Moon.) The motion is possible because the child is changing shape. When you move your finger, the whole Earth moves the other way to compensate. Of course, your finger is a tiny fraction of the mass of the Earth, so it moves much much farther. It's safe to say that the motion of the planet would not be measurable.

On a swing, it's trivial to start moving: if you start to lean your body then your centre of mass goes in one direction and the swing pivots in the other. More importantly, by shifting your mass (relative to the seat) at the right time, that acceleration can change the tension through the swing chain (think of lowering your effective weight as you swing up, and increasing it as you swing down).

As for the second Q: pick up a brick, go stand on a scale, then jerk the brick up and down.

I think you're misunderstanding: momentum is always balanced, the law does not say motion is conserved.

Getting momentum from your muscles makes no sense. Your muscles themselves are also gaining momentum, which means you'd be getting momentum out of nothing, thus violating conservation of momentum.

Taking momentum from the Earth makes sense in my head though. The brick analogy helped a lot.

cesiumfrog: I don't know what you mean by motion is conserved. I was only thinking of this problem in terms of conservation of momentum and closed systems.

rcgldr
Homework Helper
On a swing, the initial linear force is generated indirectly by exerting a torque. For example, leaning back and pulling on the chain creates a "backwards" torque (back on chain forwards on seat), which momentarily diverts the chain backwards at an angle from the support bar and raises the center of mass somewhat. This results in a forward linear force, sin(angle) times tension (weight). This can be repeated until the point where shifting mass towards and away from the support bar will also work (via angular momentum) due to the swining motion.

For a good example of the radial shifting of mass once swining here is a video of swinging rings where the guys can reach bar level in about 3 swings from back in the 1970's: