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 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: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.
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.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.
This would work regardless of friction at the pivot, wouldn't it?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.
From: http://en.allexperts.com/q/Physics-1358/2008/5/Physics-swing-motion.htm [Broken]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.
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: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.
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.
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.Is it possible to initiate swing motion on a frictionless swing with internal motion only?
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.It is possible, but I think the real reason is conservation of angular momentum.