# Swings and inertia

1. Dec 10, 2004

### T@P

as a child i remember swinging in the playground, and i knew somehow that keeping your legs straight on the way up, and tucked in on the way down would make you go higher. I was wondering exactly why this is true, is it something to do with the moment of inertia? just a thought

2. Dec 10, 2004

### Tide

This is an example of a parametric oscillator. The swing has a natural frequency (it's just a pendulum) and by raising and lowering your legs in synchrony with the natural oscillation you cause the amplitude of oscillation to grow. The pendulum's length is being varied periodically and resonantly.

3. Dec 10, 2004

### Integral

Staff Emeritus
Haven't you neglected a key companion to the leg motion? As you straighten your legs you lean back, as you curl your legs you lean forward. The combination of these motions results in a vertical shift of your center of mass. It is this change in potential energy which must be synchronized with the natural frequency of the swing.

There is another little factor, notice what happens to the swing when you are getting started from a dead stop (no push off from the ground) As you lean back you create a bend in the support lines at your hands. This action tends to lift the seat a bit, giving you a small potential energy change which converts to a small bit of rotational kinetic energy. Thus starting the motion.

4. Dec 10, 2004

### Cyrus

Thats such an interesting problem. It seems that you have started motion with no external forces, since you are part of the system itself!

5. Dec 10, 2004

### Ivan Seeking

Staff Emeritus
You are pulling against the swing supports through the chains or rope and doing work by lifting yourself; really pivoting about the point where you hold the chains.

6. Dec 10, 2004

### Integral

Staff Emeritus
Cyrus,
The shift in your CM is a change in PE. Your body does work when you change your position. It is this work that changes the PE that is converted to KE.

I think a key factor in starting from a stop, is the ability to create a shorter pendulum between your hands and the bottom of the swing. When observing this shorter pendulum the change in height of your body is clear, this change in height is constrained to a rotation around your hands, the resulting horizontal motion is then fed to the larger pendulum and the oscillations begin.

It would be interesting to see if you can self start a swing with rigid supports.

7. Dec 10, 2004

### Tide

Integral,

I suspect that would not be possible if you started with absolutely no displacement or speed for your initial condition. However, in the physical world there will always be some fluctuation, no matter how small, and the parametric oscillator will eventually amplify those fluctuations.

8. Dec 10, 2004

### Cyrus

you say you change your PE relative to your center of mass. Do you mean that you simply raise your body up, or does there have to be a side component as well? It seems that changing your PE is not enough to start motion, becuase you could sit there lifting your body up. I would think you have to move both forward/orbackwards and up at the same time.

9. Dec 10, 2004

### Tide

Cyrus,

See my previous post! :-)

10. Dec 10, 2004

### Cyrus

:surprised :surprised :surprised your post is eye opening tide! :rofl: But I do remember being able to start a swing moving from a dead stop when I was a little kid. It involved leaning way back until your whole body was nearly horizontal and then going back to an upright position. I see what you mean by not being perfect though. Gotcha

11. Dec 11, 2004

### Cyrus

Hmm i have anothere question tide. Are you sure its not possible to start from a dead stop? Suppose you lift yourself up with your arms on the ropes. (your arms are bent in the process.) Now while in the air and holding on, you unbend your arms. Now you are pushing out, but the swing reacts and moves away. So you are now in mid air, holding yourself up, leaning back, while the swing is leaning forwards. Your not swinging, but your just sitting in mid air like that. Then you bring your arms back in and bend them. Wont this induce swinging from a dead stop?

12. Dec 12, 2004

### Tide

Cyrus,

My comments on whether you could build amplitude from a dead stop were in reference to the RIGID structure Integral mentioned. I don't think there is any question about being able to pump up in the case of flexible ropes or chains.

13. Dec 13, 2004

### Cyrus

Hey Tide,

But even for a RIGID structure, could the same argument not apply? We are now on a rigid swing. You grab each bar of the rigid swing and lift yourself up so you are suspended. Push with your arms until they are locked. Wont this force the rigid swing to pivot forward as you push on it. Either that or it will remain in place and you will move back depending on how heavy it is. I guess if it were heavier than you are, then you could never get it to swing no matter how hard you tried, because you would just move back and it would sit there. Anyways, lets assume its much lighter than you are and it does move forward. Then cant you simply relax your arms and it will swing back to its origonal position, but now with speed since you raised its potential energy. You can then let go and fall onto the chair when its beneath you and thus induce swinging even on a rigid body? Once you fall onto the chair it should continue moving but with less speed, becaus that is simply an inelastic collision, and if you time it right so that the chair is passing exactly below you when its at an angle of 90 with the horizon, then momentum is conserved in only the x direction at that instant of impact. And that would just be: m1v1 = (m1+m2)v2, with v2 now being smaller than v1 because the mass increased?

14. Dec 13, 2004

### Cyrus

Another point i forgot to add. Lets say this swing is RIGID. We start off in equilibrium. Then the child holds him/herself up in the air by grabing onto the columns, and then pushes out with his/her arms. Now there is a force produced by the child that will produce a torque. If the colums and seat are not to heavy, then the swing should start to pivot. I would guess that it did not pivot all the way, because the girl my move backwards as well, but it might be some combination of the two occurances. Now its bed time, I look forward to your post in the morning on how im all wrong :-) Good night.

15. Dec 13, 2004

### Tide

Cyrus,

That sounds a little like the "cat always lands on its feet" argument which seems to defy conservation of angular momentum - but it works (provided the cat has enough initial height!) and angular momentum conservation is safe!

Your proposal may work. Maybe we can get some grad students to do an experiment ...! ;-)

16. Dec 13, 2004

### KingNothing

Grad students my butt. Give me a week to make a rigid swing. On the other hand, I don't know anything about parametric oscillators or pendulums or frequencies, or waves, although I would like to learn about it, because it sounds very interesting.

On another note, what would be the best way to go through with an experiment like this? I was thinking about taking some 8 foot long metal rods and sticing them throught the chains on a playground set and using some wire to make sure the chains stay rigid to it. Then just take a strong piece of 2x4 and duck tape it onto the seat real good and try it. Would that accurately reconstruct the scenario?

17. Dec 13, 2004

### krab

You don't need to actually build one, since the physics is so simple. You can build a virtual swing using sodaplay (www.sodaplay.com[/URL]). I simulated a child on swing as an equilateral triangle, with one of the sides as a muscle, and the top vertex fixed in space. The muscle oscillates sinusoidally, and so if this frequency matches the natural frequency of the triangle as a whole (acting like a pendulum), the whole thing begins to swing back and forth. To look at it, go to

[URL]http://sodaplay.com/constructor/?getmodel=krab+swing[/URL]

The controls at the side allow you to change gravity, frequency, friction, and the rigidity of the other two bars of the triangle. The upshot is that if starting from a dead stop, it does begin to swing. The best technique is to first set the frequency to zero (the control is the thingy on the left edge at the top), and then slowly pull it down until it is in resonance, which will be at about a quarter of the way down. Have fun. (BTW, you need Java.)

Last edited by a moderator: Apr 21, 2017
18. Dec 13, 2004

### T@P

wow krab that model is very interesting, thanks alot! thanks to everyone else that posted too, your thoughts were very usefull :)

19. Dec 13, 2004

### T@P

actually i was playing with krabs model and i noticed that when i turned off gravity, it always made i way up to a certain height and stayed there, regardless of where i started "stopped" gravity. can anyone explain that?

20. Dec 13, 2004

### Cyrus

krab can you explain how your model works. Im a little confused in understanding how it works. You seem to have made a triangle. It looks as if the right side of the triangle is the rigid pole of the swing. The left side is a little confusing though. It seems to be oscillating, but it is also attached to the pivot point. Shouldent it be attached only at the very button where the person would sit? Thanks,