The initial movement doesn’t move your center of mass, since there are no horizontal forces. Once the suspension is tilted, however, there is a horizontal force, and motion of the center of mass becomes possible.
My thoughts exactly, but they didn’t take me to the same endpoint as yours.
Very cool, and I agree that using only vertical forces, it’s not possible to start. I also agree as mentioned above, that you can’t displace your center of gravity simply by moving forward or back.
However, I suspect that when we do get started from a dead stop, it doesn’t rely on friction. This is based on how it feels, and how friction feels, so admittedly it’s acceptable as food for thought rather than evidence. My suspicion is that when we start from a dead stop, we’re using rotational inertia, as mentioned in the post above. Once we get going, we shift to the model shown in the flash (way cool), or a combination of the two.
Your optimum strategy assumes the vertical component dwarfs any component based on angular momentum about one’s center of gravity (including the seat).
I don’t follow; please explain. What bar? Do you mean the seat? If so, who cares where the seat is?
I was working off of moriah’s model there of a swing with rigid bars instead of chains, where the bending of the chains thus was removed as a factor.
To put it simply, when the swing is in its resting position, the chains (or bars or whatever) are vertical, and can exert no horizontal force. If, however, you displace them from vertical, then they can exert some amount of horizontal force.
The more I think about it, the more I’m convinced that when we start from a dead stop (as I’m sure we all have), we use angular momentum about our own center of gravity (plus seat and chains, but these could be zero and it would still work).
My thought is, if we’re sitting on the seat and not holding the chains, and have just one point of contact, we can’t get started. We have to be able to hold the chains to get two points of contact, to rotate ourselves about a lateral axis, to get started.
This is testable, but I don’t know of a convenient swing to test it. Any volunteers?
If we can start swinging while hanging from a motionless trapeze, that last bit would be wrong. Hmmm.
Ah I see. The main point of bars when originally raised was that with them you can go full circle, simply because you stay in the circle rather than falling in a parabola.
I don’t think I’ve ever swung on a swing with bars rather than chains, but I suspect I’d still be able to start it from nothing, and I just don’t buy the friction argument.
Also, I don’t see how bars would add any horizontal force to the overall picture. With chains or bars, you can’t move the center of gravity by mere horizontal movement.
The power of positive feedback…
You create (cyclical) oscillation in a (closed) system when F=-x (Force is opposite to displacement from equilibrium).
Pumping legs, leaning, etc. moves your center of mass/gravity away from directly under the pivot point, and the system moves to place your CoM under the pivot; the speed by which it moves is governed by gravity (and angle) so it’s not instantaneous. If you move the other way meanwhile, you are causing a force opposite to displacement.
As anyone who swings the right way knows 
the trick is to time things right.
How can you do this?
Above most say you can’t without an external force. My guess is you can by employing angular momentum, but I’m not sure about that. But I’m confident you can’t by simple horizontal motion.
You cannot move your center of gravity without an outside force. You cannot move your center of gravity horizontally without a horizontal outside force. The chains provide an outside force, and if the chain is tilted, they provide a horizontal outside force.
Not true at all. I can confirm that, sitting on the swing seat and not holding onto the chains (or bars), it is perfectly possible to start yourself swinging from a standstill.
As Tangent said upthread, all you have to do is shift your centre of gravity away from the plane of the swing supports (chains or bars). This will cause the swing seat to move such that your C of G (which is no longer directly above the centre of the seat) finds its lowest position. Momentum will then carry the C of G past the equilibrium point and up the other side, at which point you can shift the C of G in the opposite direction, and so on.
Of course, once you start swinging a bit higher, you have to hold onto the chains or risk sliding off and transferring your potential and kinetic energy to the ground via the medium of your backside, but it has nothing to do with the mechanics of swinging.
Don’t believe me? Are you sitting in a chair? OK - hold your arms and legs up so they are not touching anything. Now, can you shift your centre of gravity such that you fall out of the chair? Of course you can. If you were sitting on a swing seat, then rather than falling out of it, you would have just set up a swinging motion.
Edit: Chronos, your last post came after I wrote this. I disagree with you. You can easily move horizontally without touching the chains. Try it in your own chair now, if you don’t have a swing handy. Or a stool without a back, which is a closer match to a swing seat.
The horizontal force can be applied because there is friction between your buttocks and the swing seat.
Outside force? Muscle force, a big contraction, or lean back, is an outside force for COM, independent of the bars/chains. I’m trying to get your model definition squared away.
Also, from way upthread assumptions. When you start, or pump subsequently, you lean back but your butt/COM goes forward, not backward. Or what? Although the analyses would be the same, if I am right, I think.
Hummm
Sit in swing.butt & legs fwd, head shoulders lower.
- slight movement of chains fwd .
Sit up & swing legs rear at the same time.
Both movements cause some movement of total mass.
With timed input of the these small movements of mass, the build up of kinetic energy + gravity will compound the movement & you will be swinging.
Every child knows that it works without knowing any physics. Making impossible changes to the system (frictionless ??? ) to prove that it does or does not work then is silly.
So why does it work?
Because you can not take the imperfections out of the system.
Pure physics will work also if you add the power of human muscles and that power must be constantly imputed or the system slows to a stop … eventually.
Throw in impossible conditions and you can make it do impossible things but IMO, you have learned nothing.
I dc not see why their is any disagreement about how swinging works. Both kinds. <veg>
When you lean back, you shift your COM backwards (out of the plane of the chains/bars). It is now no longer in its lowest potential position (which is when the COM is lowest, i.e. in the plane of the chains, with the seat at the bottom of its arc). So the seat moves forwards, and overshoots. Then, while your COM is in front of the plane, you shift it even further forwards, by extending your legs forwards. Now the COM has even further to fall to regain equilibrium, and so it will overshoot even further on the other side. And so on…
You lean back, or swing your legs out. The swing angle (the angle of the rope or chain) moves to compensate. But - it only does so as fast as the force of gravity at that angle lets it.
In a perfect world, let’s say you standing on a skateboard, as you move one way, the skateboard moves the other and eventually you land on your butt on about the same point you started from, minus the skateboard zipping away. However, on a pendulumnar (?) construction, as the swing moves to compensate, the rope constrains it to also move upward against gravity. Gravity is now trying to return it to center when you readjust yourself. That little bit of up/down differential is what gets the cyclical motion going.
If you lean back - that is, if you shift your COM to the rear away from the swing seat - the only way to avoid tumbling out of the swing is to have your hands on the chains a few feet above the seat. When you do this, the portion of chain below your hands will shift forward (along with the seat), and your head/torso will shift to the rear, but:
-the portion of chain above your hands will remain vertical, and
-your COM will still be positioned directly below the pivot point.
Agreed. On a swing, the chains will only be vertical if your centre of mass is directly in line with the chains. That is, assuming the chains are attached to the centre point of the seat, the chains will only be vertical if your CoM is also directly centred above the seat.
It is trivially easy to shift your CoM relative to the seat. Even just leaning backwards so that it is over the back edge of the seat will put the chains out of the vertical plane by a small angle, and therefore also raise the seat by a small amount compared to its rest position.
Only if you do it slowly.
Yes it would. I’ve seen experiments done that demonstrate it. When Mythbusters did the birds in a truck thing, the scales fluctuated (but always netting out to zero).
You’re just making part of the system act on another part of the system - action and reaction. - another demonstration of this kind of effect is the use of flywheels to orient satellites in space - the flywheel spins one way and by reaction, everything that isn’t the flywheel spins the other way.
That is an Awesome simulator. I was playing with it, and encountered the same observations about pumping the action by shifting the pivot length during the translation, not just at the end points.
I was thinking about this. It is worth trying, but I suspect the principle may be that the leg motion is tied to torso motion to offset your balance shift to help you stay on the seat, and the weight differential between legs and torso makes it work.
Also, thinking about the start from rest case, I agree angular momentum plays a roll. When you shift your weight backwards, the seat shifts forwards to keep cg under the line of motion, but angular momentum continues the rotation beyond that stop point. Then a rapid shift of cg forward will turn put a torque in the other direction, and angular momentum will carry past the vertical point. Repeat.
Ultimately, you can’t say that it’s due to angular momentum vs. linear momentum, since they’re really both just manifestations of the same underlying phenomena.
The starting bit is tricky for me. I think it requires some friction at the upper pivot points for you to initially push off against. Kids usually push off against the ground to get started, even if only in the act of climbing on to the seat.
Without friction I can’t see how it is possible to shift the body’s center of mass except toward or away from the upper pivot. With friction you can lean back and “bend” the chains causing a small torque to get you started. Alternatively, by just kicking your legs, you can exploit the friction as it resists the motion that would be required for your center of mass not to move.
Even though you couldn’t get your center or mass to move without friction, you could still start by blowing, and timing your breath. Probably can’t get enough force to overcome real friction that way, but it would work if you ever found yourself stuck in a physics text book.
Once established, even a small swinging can be amplified by pumping. Pumping is just moving part of the bodies weight (legs mostly) closer and farther from the pivot, changing the moment of inertia of the system and working against gravity to add energy to the system. I think incensors are sometimes driven this way by pulling on a rope that shortens and lengthens the pendulum. I have only seen this in movies…seems like something only done in big catholic cathedrals.