After recently seeing a video of a man doing a loop on a swing, it occurred to me that swinging in that manner is pretty counterintuitive to the things I learned in physics class.
Basically, how do we make it go higher without an external force to push us, and without pushing ourselves off of anything? I’m stuck thinking that you can’t lift a chair that you’re sitting on, so a swing should work the same.
My first thought was it must be something to do with how you generally swing your legs, but in the video I saw, the guy on the swing didnt use his legs in that way at all as he was standing on the seat of the swing.
So, in simple terms what actually is happening there, and where does that momentum come from?
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Momentum cones from your movement. You’re actually adding momentum by moving your muscles, which in turn gets energy from biological sources (ATP). So you are actually using energy from your cells to gain momentum.
When you change your position and more importantly, the length of your body by extending your legs and torso, then pulling them in, you’re changing your center of mass.
While you’re correct in that you’re not going to go higher without an external force to push you, that external force can be generated by you pushing against the shifting center of mass by changing your body position.
Basically, you’re adding energy to the cycle by shifting your own mass. If you didn’t move, you’d just stay still.
*You* are the “external” force. Even standing on the swing, you are throwing your weight against the swing, leaning forward or backward. This shifts the center of gravity of the swing so that gravity will cause it to shift. Once the swing becomes balanced again, you shift your weight the other direction so that gravity is pulling the swing in the other direction.
Because of the mass of the swing and you on it, the swing has some momentum. It doesn’t immediately stop when it should be balanced: it will move a little bit past the balance point and *then* slow down, and then stop. If you weren’t shifting your balance each time, you would slow down from energy lost due to friction and things. Eventually you would come to a full stop.
The other important thing is the *resonant frequency* of the swing. The length of the ropes/chains and the mass determine the period of the swing – how often it naturally wants to go back and forth. No matter how high the swing goes, the period stays the same. When you swing your mass properly, you’re matching the period so that the frequency of the swing moving and the frequency of you shifting your weight *constructively interfere*. That preserves the energy of the swinging motion and adds to it so that you keep swinging higher.
But again to be clear: *you* are adding energy into the system by shifting your weight against the natural swing, which would otherwise destructively interfere with the swing and slow you down.
You’re right you need to be pushing off something, but it’s just counterintuitive as to what you are pushing off. You are essentially pushing of the bar of the swing using the chain.
It’s easier to visualize when you are already at a bit of altitude. Say at 45 degrees. If you raise your center of gravity a bit you push of the seat. You are accelerating your body toward the bar. Some of that works against gravity, the rest accelerated you sideways.
Then at the dip when the swing is vertical you can reset your center of gravity. Since the swing is straight up and down you resetting your center of gravity doesn’t change the forward and back motion.
It’s also why it’s really hard to start swinging from a dead stop. You need at least a bit of an angle to be transferring force forward or back.
So as long as you can direct force against the seat you can go higher. You legs do this by trying to raise your center of gravity when pulled in, and when standing you can do the same with a bit of a couch, or pulling on the chains with your hands.
To ass to it,
When you swing to go forward, you are tilting your upper body back as well as pulling on the rope, when swining back, you push on the ropes creating a Mini swing effect(ex: the rope is 3 meters long but with you arms, you a pulling at 0.75 meters from the seat.) Its easier to create a self swinging momentum shift with 1/4th of the rope than with the whole rope.
What you’re looking at is not momentum (at least not in the physics sense of the word). Gravity act on you all the time, so your momentum keep changing. Your momentum are never preserved.
The word you are looking for is energy. Essentially, your body+swing system keep exchanging between kinetic energy and potential energy. Total energy is loss through friction, and max potential energy determine the highest point you can reach. With that argument it looks like you shouldn’t be able to swing higher than when you start….but that’s wrong, because energy can come from many sources. In particular, chemical energy from within your body get converted into kinetic energy, so you can actually add energy to this kinetic+potential total energy.
So that should explain your misconception away. Momentum is not preserved, energy is also not preserved either. Both of them can increase.
So, the next question, is how to actually do it?
When you move your body on the swing without pushing on anything, you can’t change the angular momentum of the entire body+swing system. However, what you can change is your mass distribution, which change your center of mass. Because the angular momentum does not change (as a result of center of mass change), changing the center of mass can increase or decrease your speed: the closer the center of mass from the pivot (ie. your center of mass is raised), the faster your speed. And increase speed means increase kinetic energy, and hence total energy. For maximum gain, raise your center of mass at maximum angular momentum.
Of course, just raise your center of mass won’t be a sustainable method, because you can’t raise forever. So you do need to move the center of mass back. So what happened when you do so? Well, the extra energy can’t just go back into your body, so you just need to ensure it does not go to the wrong place to keep all that extra energy to yourself. When you raise your center of mass, you also done work against gravity, so your potential energy increase too. This gain in potential energy pay back the loss of potential energy when you lower your center of mass. To avoid huge loss of kinetic energy, lower your center of mass at minimum angular momentum.
In summary, you use gravity to increase your maximum angular momentum, and you use your body’s chemical energy to increase your maximum kinetic+potential energy, so neither of these can limit you.
You dont need work from an external force to go higher. The work of internal forces isn’t necessary 0. By changing your center of gravity you can make the swing oscillate.
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