# Conservation of momentum on a swing

• Monocles
In summary, the conversation discusses the conservation of momentum in a closed system consisting of a child, a swing, and gravity. It is explained that the child starts moving on the swing by transferring momentum from their muscles to the swing through leg and arm movements. The effect of air is negligible and the motion is possible because the child changes shape. The conversation also touches on the conservation of momentum in the human body and how it relates to lifting a finger. It is stated that momentum is always balanced and the law does not say that motion is conserved. The concept of converting gravitational force into linear force on a swing is also discussed.

#### Monocles

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.

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 don't 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.

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:

similar but longer videos:
http://jeffareid.net/real/gym1.wmv
http://jeffareid.net/real/gym2.wmv

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The only meaningful answer above is given by Jeff Reid. What you are doing on a swing is converting gravitational (downward) force to linear (circular) force. When you lean back in the swing, you are transferring part of the downward gravitational force into horizontal motion because of the swing chain. (You have to work out the force diagram -- physics 101.)

## 1. How does conservation of momentum apply to a swing?

Conservation of momentum states that the total momentum of a closed system remains constant. In the context of a swing, this means that the momentum of the person and the swing combined remains constant throughout the swinging motion.

## 2. Why does a swing slow down over time?

A swing slows down over time due to the force of friction acting on the swing. As the swing moves back and forth, the air resistance and the friction between the chain and the swing's attachment points gradually decrease the swing's momentum.

## 3. Can a person change the conservation of momentum on a swing?

Yes, a person can change the conservation of momentum on a swing by using their body to push and pull on the chains or ropes of the swing. This can add or subtract momentum from the system and change the swinging motion.

## 4. How does the length of the swing affect conservation of momentum?

The length of the swing affects conservation of momentum by changing the time it takes for the swing to complete one full cycle. A longer swing will take longer to complete a cycle, which can impact the momentum and speed of the swing.

## 5. What other factors can affect conservation of momentum on a swing?

Other factors that can affect conservation of momentum on a swing include the weight of the person on the swing, the angle at which the swing is released, and the surface on which the swing is located. These factors can alter the amount of force and friction acting on the swing, thus impacting the conservation of momentum.