# How does a swing work?

As I'm swinging, I gradually increase the amplitude of my motion, and thereby increase my angular momentum (about the pivot). But where does the torque come from?

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mathman
I presume your legs are moving in and out - that's where it comes from.

That can't be it because what you really need is an external torque.

rcgldr
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Starting from a rest position, if you lean forward or backwards while holding the chains or ropes that support the swing, the center of mass initially doesn't move, but the chains or ropes are displaced in the direction of upper body lean, producing a horizontal component of tension in the chains or ropes, and this produces the torque. Repeatedly cycling through a forwards and backwards lean if timed correctly, will increase the amplitude of the swing.

My teacher told me, that they studied this extensively at one time at his university. The conclusion was that the torque must come from friction at the point, where the chains were attached but that it was hard to see how.

This has to do with the fact that total energy is not conserved in a pendulum with varying length (time dependent Hamiltonian).

Intuitively, the fixing of the pendulum to a point is what allows you to move faster. Let's imagine that instead of a person swinging his/her legs, you are a simple point mass that moves up and down with your center of gravity. Let's say that you do the following:
as you move down (from either direction), you gradually pull your feet towards you until you start moving up, at which point you stop and hold your feet. You can choose a trajectory so that the tension from your legs is aligned with your trajectory and therefore gives you more energy. Gravity will only do work to counter the change in height. The work from your legs then gets transferred to gravitational potential energy, so you get to a height that is greater than your starting point and on a tighter circle too, so that when you shoot your legs out at the top you'll be starting from a larger angle from the vertical than you were to begin with.

rcgldr
Homework Helper
Intuitively, the fixing of the pendulum to a point is what allows you to move faster. Let's imagine that instead of a person swinging his/her legs, you are a simple point mass that moves up and down with your center of gravity.
That method only works once a swinging motion is established. The swinging motion can be initiated from a stationary position by leaning forwards and backwards producing a horiztonal component of tension in the supporting chains or ropes. Leaning forwards and backwards can also be used to increase the swinging motion. It's difficult to move the center of mass "up" and "down" very much unless a person squats and stands on the swing, and this only works if the swing is already in motion. As an extreme example of moving mass "up" and "down", there was an old gymnastics event called swinging rings, where the person hangs onto the rings by hand and either runs up or gets pushed to start the initial swing, then somewhat somersaults while holding the rings to move mass inwards and outwards realtive to the support. Link to video:

I don't know if one can easily say that just a horizontal component to tension is what lets you start swinging, but (theoretically) you can easily initiate swinging just by moving your arms (or legs) forward very fast, so that you displace your COM from equilibrium. The OP seemed to have questions about where all the torque comes from, and so I gave as simple a case-in-point answer as I could without considering how the swinging motion is established (I don't know about you, but when I use a swing I never start from a stationary hang unless I have to).
As for the change in center of mass location, I believe that the mass contribution of legs is more than sufficient to have a meaningful contribution to swinging motion: remember that although the effective distance over which the tension is acting on your legs is "small", the tension is also a force that is on the same order as your weight, which is pretty big (1g is a very fast acceleration). Nice video!

rcgldr
Homework Helper
I don't know if one can easily say that just a horizontal component to tension is what lets you start swinging, but (theoretically) you can easily initiate swinging just by moving your arms (or legs) forward very fast, so that you displace your COM from equilibrium.
Internal forces can't move COM, it's the horizontal component of tension in the supporting chains or ropes (caused by leaning and pulling or pushing horizontally on the chains or ropes (while pushing or pulling on the swing itself, also creating a somewhat internal torque)) that allows the initial motion from a rest position. The COM isn't immediately displaced, it takes a bit of time for the horizontal component of tension to accelerate the COM.

Whoops. I guess I should have thought about my answer more carefully. I think it should work if you initiate motion (of the swing/legs--not COM) by moving some part of your mass back and forth (so that your legs are still parallel to the swing), and then start moving your legs up and down as described before. That way you're doing work by moving your legs closer to the axle, while you can choose the trajectory of the "other" mass (with some constraints) so that you are not doing any counter work. I know that leaning against the chain would lead to different horizontal components in the tension in parts of the rope, but how specifically does this component of the tension do work if the length of the chain is constant?

Khashishi
The friction at the top of the chain of the swing provides the torque. This friction is insensitive to the angular velocity of the swing, so if there is a different angular velocity going forward and going backward, then there can be a net torque.

There is a different velocity going forward and backward because the person modifies the moment of inertia of system using hir body.

A.T.
Starting from a rest position, if you lean forward or backwards while holding the chains or ropes that support the swing, the center of mass initially doesn't move, but the chains or ropes are displaced in the direction of upper body lean, producing a horizontal component of tension in the chains or ropes, and this produces the torque.
This would work regardless of friction at the pivot, wouldn't it?

Kevin Johnson said:
If a swing had a frictionless pivot and the swing plus passenger were in perfect equilibrium (hanging motionlessly right under the hinge), then it would be indeed impossible for the passenger to set the swing in motion.
From: http://en.allexperts.com/q/Physics-1358/2008/5/Physics-swing-motion.htm [Broken]

So what is true here? Is it possible to initiate swing motion on a frictionless swing with internal motion only?

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A.T.
dEdt said:
As I'm swinging, I gradually increase the amplitude of my motion, and thereby increase my angular momentum (about the pivot). But where does the torque come from?

That can't be it because what you really need is an external torque.
If you are already swinging, the external torque around the pivot comes from gravity, all the time when your center of mass is not exactly under the pivot. A simple pendulum changes its angular momentum continuously due to that external torque. By changing the distance between pivot and your center of mass you change your moment of inertia which, given the right timing can accelerates your swing. See chapter 2.1:
http://staff.kfupm.edu.sa/phys/tahmed/How to pump a swing.pdf

However, this method cannot start the swing from rest. But the one described by rcgldr apparently can, see chapter 2.3 in the above article.

rcgldr
Homework Helper
Starting from a rest position, if you lean forward or backwards while holding the chains or ropes that support the swing, the center of mass initially doesn't move, but the chains or ropes are displaced in the direction of upper body lean, producing a horizontal component of tension in the chains or ropes, and this produces the torque.
Is it possible to initiate swing motion on a frictionless swing with internal motion only?
I would say yes. Say the system is at rest and the person pushes on the chain to lean backwards (this produces a torque opposed by angular inertia of the person). The chain supplies an opposing force since a "bent" chain raises the COM which is opposed by gravity, so it is gravity (and angular momentum) that is allowing this method to work, and not friction at the pivot point.

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It is possible, but I think the real reason is conservation of angular momentum. If you model a human being as a dumbbell, then if the dumbbell starts to rotate, (instantaneous) conservation of angular momentum about the axis of the swing implies that the rotating mass will be displaced from its equilibrium position, putting the mass into motion. From then on, the mass can increase the amplitude of its oscillations by a combination of increasing/decreasing its length and by rotating in different directions.

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rcgldr
Homework Helper
It is possible, but I think the real reason is conservation of angular momentum.
Assuming chain is not rigid, then I think the other factor is gravity (as explained in my previous post), which allows a person to push or pull on the chain and/or swing to generate a local torque.