# Explain the kinematics of a playground swing. **URL:** \ **Category:** Factual Questions\ **Created:** [May 28, 2013, 4:44pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554 "2013-05-28T16:44:00Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [May 30, 2013, 12:42am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/41 "2013-05-30T00:42:01Z")
Eh, stick out your arms and make circles, or swing them as pendulums. That’ll get the swing going. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [May 30, 2013, 12:42am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/42 "2013-05-30T00:42:30Z")
> [@Irishman](#): > > That is a very nice page with good text and pretty pictures. Unfortunately, I think it is wrong. > > If you look at Figure 4 of that page, it shows the person on the swing at the top of the backswing, as they lean back to start the swing pump forward. If you look at the line of the chain, it bends at the hands. I agree this happens. However, I believe he has the bend backwards. > > When one leans back on the swing, one is **not** pushing the chains to allow you to lean. Instead, one _pulls_ on the chains to keep from falling out the back of the swing. The rider is changing position at that point. While ending the backswing, the rider goes from a tight position to an arms-locked position, bending the chains On the downswing, they switch to pulling the chains, which are retreating from him. > [@Machine\_Elf](#): > > The simulator also suggests that most people’s leg action is counterproductive: when people lean back (spine perpendicular to chains), they tend to swing their legs up. If the purpose of leaning back is to move your COM away from the pivot point (and if the purpose of sitting up is to move your COM toward the pivot point), then leg action should be the other way around: > > -when you are sitting up, your knees should be straight, getting your leg mass as close as possible to the pivot point. > > -when you are leaning back, your knees should be bent, getting your leg mass as far as possible from the pivot point. That’s not the point of the leg swing. People do that so they save a little bit of ab workout. It’s identical to kicking out when doing a situp. It’s just making it easier/faster to sit up. Pulling the legs in uses angular momentum and leg muscle to throw your upper body, the part that counts, forward. What you’re suggesting is like telling a pitcher to kick is leg at the same time he throws the ball. No, no, no, the point is to throw the ball/torso, not the legs! > [@Machine\_Elf](#): > > 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. What? No. That’s what abs are for. You can put your hands under the seat for all it matters. You can even do this on the carpet right now. Put your hands under you and lean back. Did you fall over? > [@Kevbo](#): > > 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. Not really. Your head would just move backward. The air gets all Newtown’s third on your [del]ass[/del] throat. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [May 30, 2013, 12:49am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/43 "2013-05-30T00:49:11Z")
Even if you can’t move your center of mass horizontally, you can move the chains relative to the center of mass. If you push the chains forward with your hands and the seat back with your butt, they’ll be angled backwards at your hands. Pull them backwards, and they’ll be angled forwards at your hands. There are only two possibilities here. Either the long chain above your hands remains vertical the whole time, or it’s swinging back and forth with your hands. It won’t be vertical the whole time (that’s just silly), but if it were, that would mean you were swinging with the pivot at your hands. Instead, your center of mass stays put, at least approximately, so the long top part of the chain is not vertical, and alternates whether it’s angled forwards or backwards. A chain only transmits force directly along it’s length, so since it’s at an angle, there’s a horizontal component of force, which enables you to start swinging. For best results, alternate pushing and pulling with your hands at the natural period of the swing. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [May 30, 2013, 11:35am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/44 "2013-05-30T11:35:04Z")
> [@Chessic\_Sense](#): > > What? No. That’s what abs are for. You can put your hands under the seat for all it matters. You can even do this on the carpet right now. Put your hands under you and lean back. Did you fall over? If I don’t fall backward in the butt-on-the-carpet scenario, it’s because my COM did not move to the rear of the support point (i.e. my butt on the carpet). Likewise, if your hands are not on the chains, and you lean back AND swing your legs up/forward to act as a counterweight (this is what your abs would be pulling against), your COM hasn’t moved to the rear very far at all; it will still be positioned directly over the seat of the swing. If your hands are not on the chains a few feet up from the seat, it will not be possible to move your COM to a position rearward of the rearmost edge of the seat without tumbling backwards off of the swing. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [May 30, 2013, 11:52am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/45 "2013-05-30T11:52:24Z")
> [@Machine\_Elf](#): > > If your hands are not on the chains a few feet up from the seat, it will not be possible to move your COM to a position rearward of the rearmost edge of the seat without tumbling backwards off of the swing. Are you sure? What if you grip the front of the seat with your hands? I think you could get your COM behind the back of the seat without falling off. The seat would tend to tip backwards, but as long as you held on and were able to keep your grip, you wouldn’t fall off. ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [May 30, 2013, 3:11pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/46 "2013-05-30T15:11:10Z")
There is also the “standing pump” on the swing, which is similar. If you dispace the chain/rope from vertical, it actaully moves upwards a bit. Now you dip and stand up in time with the swinging. What are you doing? You are moving your COM up and down, so the angular momentum takes you higher (high COM?) and lower when you squat a bit on the down swing. you are playing games with your angular momentum, same as the spinning skater who draws her arms in to spin faster. On the way up, move close to the pivor point, climb higher. On teh way down, move lower so gravity will increase the angular momentum. As you pass through vertical, stand up higher to make the swing go faster. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [May 30, 2013, 3:17pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/47 "2013-05-30T15:17:29Z")
> [@Colophon](#): > > Are you sure? What if you grip the front of the seat with your hands? I think you could get your COM behind the back of the seat without falling off. The seat would tend to tip backwards, but as long as you held on and were able to keep your grip, you wouldn’t fall off. If you grip the front of the seat wth your hands and then lean back, the seat will pivot on the first link of chain until a) your head hits the ground, or b) your COM ends up in a position colinear with the upper portion of chain - directly below the pivot point. If you grab the chains with your hands a few feet up, you avoid a) and ensure b). Seriously, go find a swing and try these while an observer standing to the side watches the chains. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [May 30, 2013, 3:25pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/48 "2013-05-30T15:25:36Z")
Just a minor point about the real physics demonstrator:- [http://www.sciences.univ-nantes.fr/s...tafumeiro.html](http://www.sciences.univ-nantes.fr/s...tafumeiro.html) It is possible to persuade the censer in the diagram to swing above the horizontal. In the real world, if that happened then the censer would fall straight down and not swing outwards. This is why you can’t swing a full circle on a chain swing. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [May 30, 2013, 4:59pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/49 "2013-05-30T16:59:33Z")
> [@bob\_2](#): > > Just a minor point about the real physics demonstrator:- [http://www.sciences.univ-nantes.fr/s...tafumeiro.html](http://www.sciences.univ-nantes.fr/s...tafumeiro.html) > > It is possible to persuade the censer in the diagram to swing above the horizontal. In the real world, if that happened then the censer would fall straight down and not swing outwards. This is why you can’t swing a full circle on a chain swing. For a chain swing, yes. But if [you’ve got solid steel bars instead,](http://en.wikipedia.org/wiki/Kiiking) things can get interesting. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [May 30, 2013, 5:23pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/50 "2013-05-30T17:23:41Z")
> [@Machine\_Elf](#): > > If you grip the front of the seat wth your hands and then lean back, the seat will pivot on the first link of chain until > > a) your head hits the ground, or > b) your COM ends up in a position colinear with the upper portion of chain - directly below the pivot point. Not if the swing has solid bars rather than chains, and the swing is rigidly attached to them. Not all swings have chains. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [May 30, 2013, 6:48pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/51 "2013-05-30T18:48:19Z")
> [@Chessic\_Sense](#): > > That’s not the point of the leg swing. People do that so they save a little bit of ab workout. It’s identical to kicking out when doing a situp. It’s just making it easier/faster to sit up. Pulling the legs in uses angular momentum and leg muscle to throw your upper body, the part that counts, forward. That makes sense. It fits with what I was trying to get to - the standard swing dynamic combines the shifting COM to increase momentum with the ease of movement of the human body. The legs are a compromise for body movement. > [@](#): > > What? No. That’s what abs are for. You can put your hands under the seat for all it matters. You can even do this on the carpet right now. Put your hands under you and lean back. Did you fall over? No, if you are using your abs, you have to counter with something, whether that is your legs sticking the other direction or hooking your feet under the couch. That’s why situps are harder if you don’t hold your feet. COM stays over the base, or you can’t hold yourself up. > [@](#): > > Not really. Your head would just move backward. The air gets all Newtown’s third on your [del]ass[/del] throat. So are you saying your neck is a limp rag? If you hold your neck reasonably stiff, then blowing out should provide a force. > [@Colophon](#): > > Are you sure? What if you grip the front of the seat with your hands? I think you could get your COM behind the back of the seat without falling off. The seat would tend to tip backwards, but as long as you held on and were able to keep your grip, you wouldn’t fall off. How many people do you know who swing holding on to the seat bottom? He was responding the the assertion that one could support oneself with abs without holding on. Holding on to the seat is holding on. However, he also points out the standard swing has a ring connection to the chain, so if you try to hold onto the seat, the seat will rotate about that bottom chain link and dump you upside down. Holding the chains provides a cantilever support. If you have a rigid “chain” and a welded seat, then sure, you can hold onto the seat to prevent falling out of the seat backwards. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [May 30, 2013, 11:46pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/52 "2013-05-30T23:46:34Z")
> [@md2000](#): > > 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. That’s an interesting possibility. If it’s true, it means that a short swing starts more easily than a long one, though, and that doesn’t jive with my memory. By this I’m talking about horizontal motion or speed, not angular speed, as the latter is clearly slower to build up with a very long swing. > [@Chronos](#): > > 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. I’m talking about the difference betwen angular momentum about your COM versus the angular momentum about the swing’s fulcrum. This was one of the explanations given in a cite above, and I think it’s still a possibility. I still say you can’t move your COM. All you can do is move the chain and seat, and doing so doesn’t change the equation significantly (except for the height bit, which bears more thought. But on second thought, it doesn’t shift the COM from the vertical, so gravity isn’t trying to do anything. I withdraw my support above. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 31, 2013, 12:48am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/53 "2013-05-31T00:48:24Z")
Oh, sure, you can describe the problem in terms of angular momentum if you’d like, and describing it that way might make it easier to understand (though “easier to understand” can be a matter of taste). I’m just saying that you can also describe the problem without use of angular momentum, too, and that should give you exactly the same answers. ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [May 31, 2013, 1:16pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/54 "2013-05-31T13:16:31Z")
A short swing starts easier than a long one, but if it’s too short, the childhood-learned procedure does not work well - you can’t move your center of masss easily in the appropriate envelope, and the pendulum swing period time is too short to make adjustments in time to match displacement. (Period is proportional to length of pendulum - and gravity) ---
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [May 31, 2013, 4:54pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/55 "2013-05-31T16:54:28Z")
Video: [http://youtu.be/tLIUjXnthqA?t=1m](http://www.youtube.com/watch?v=tLIUjXnthqA#t=0s1m) Jump to 1:00 if it doesn’t happen automatically. They’re purposely starting from zero swing (well, as close as they perceive). ---
**Author:** ![Isai](https://avatars.discourse-cdn.com/v4/letter/i/2acd7d/32.png) [@Isai](https://boards.straightdope.com/u/Isai)\ **Post date:** [November 7, 2013, 3:52pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/56 "2013-11-07T15:52:21Z")
The swing can move from rest. Take a similar example: a canoe at rest on a lake with Mary and George sitting at each end. When Mary throws a package to George, the boats moves in the opposite direction as long as the package is in the air, and then stops moving when George catches it. In this case the reason is the conservation of linear momentum. ---
**Author:** ![snailboy](https://avatars.discourse-cdn.com/v4/letter/s/97f17d/32.png) [@snailboy](https://boards.straightdope.com/u/snailboy)\ **Post date:** [November 8, 2013, 2:35am UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/57 "2013-11-08T02:35:26Z")
When you’re sitting in the swing motionless, your center of mass is directly below the swing pivot, but slightly behind the seat. You loosen your arms temporarily and start to fall backwards from the seat. The top of your body moves backwards while the bottom of your body and the seat move forwards. The seat is mostly pulling up on your butt causing a torque but as the seat goes forward, the chain becomes angled so it also pulls on you with a slight horizontal force, giving you linear momentum as well as angular momentum. Of course the pivot is effectively secured to the ground via the frame and the weight of the swing, so it’s not going anywhere (unless it’s a really light swing). If you were to just continue falling, you would fall down and backwards while the swing seat was slung forwards, but after a moment, you tense your arms again preventing the swing seat from exerting that force on you and causing the chains to pull you the other direction since your center of mass is behind the pivot. You pull yourself up as this is happening. Since you can’t hold on to the swing behind you, you can’t really boost yourself in the opposite direction so your next boost comes when your center of mass returns to the position behind the pivot. The process continues but as you build up momentum, it transitions into centrifugal force pulling you out of the seat rather than gravity. I think this may have been what a few others were alluding to, but I felt like my explanation was a little more thorough. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [November 8, 2013, 8:19pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/58 "2013-11-08T20:19:08Z")
> [@snailboy](#): > > When you’re sitting in the swing motionless, your center of mass is directly below the swing pivot, but slightly behind the seat. You loosen your arms temporarily and start to fall backwards from the seat. The top of your body moves backwards while the bottom of your body and the seat move forwards. The seat is mostly pulling up on your butt causing a torque but as the seat goes forward, the chain becomes angled so it also pulls on you with a slight horizontal force, giving you linear momentum as well as angular momentum. Of course the pivot is effectively secured to the ground via the frame and the weight of the swing, so it’s not going anywhere (unless it’s a really light swing). Pretty good description so far. > [@](#): > > If you were to just continue falling, you would fall down and backwards while the swing seat was slung forwards, but after a moment, you tense your arms again preventing the swing seat from exerting that force on you and causing the chains to pull you the other direction since your center of mass is behind the pivot. Murky. You lean back as far as you can while securely holding on, the swing shifts forward to keep your center of gravity under the pivot. Any momentum generated by that motion slides you slightly further forward - from a stop that isn’t much. > [@](#): > > You pull yourself up as this is happening. Since you can’t hold on to the swing behind you, you can’t really boost yourself in the opposite direction so your next boost comes when your center of mass returns to the position behind the pivot. Not exactly. You can shift your weight forward - sit up, lean forward and grip the chains close to your shoulders. It isn’t as far a shift from the chain line, but it does move cg to the front of the seat, as far in front of the pivot line as possible. The combination of lean and gravity pull you back the other direction. This gets the motion flowing. > [@](#): > > The process continues but as you build up momentum, it transitions into centrifugal force pulling you out of the seat rather than gravity. As you get higher in the swing curve, inertia helps keep you pulled against the seat and does help you lean backwards. But gravity is still the key driver. I need to go find a swingset. I was thinking about testing the pendulum effect contribution by attempting to swing with the body movement plan described previously, rather than the traditional method. ---
**Author:** ![snailboy](https://avatars.discourse-cdn.com/v4/letter/s/97f17d/32.png) [@snailboy](https://boards.straightdope.com/u/snailboy)\ **Post date:** [November 8, 2013, 9:41pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/59 "2013-11-08T21:41:53Z")
> [@Irishman](#): > > Murky. You lean back as far as you can while securely holding on, the swing shifts forward to keep your center of gravity under the pivot. Any momentum generated by that motion slides you slightly further forward - from a stop that isn’t much. I think we’re saying the same thing here except I wouldn’t use the verb “keep” since your center of gravity isn’t under the pivot at all times. I’d say it pulls it back towards the pivot. > [@](#): > > Not exactly. You can shift your weight forward - sit up, lean forward and grip the chains close to your shoulders. It isn’t as far a shift from the chain line, but it does move cg to the front of the seat, as far in front of the pivot line as possible. The combination of lean and gravity pull you back the other direction. This gets the motion flowing. It’s been a long time since I was in a swing. I can’t imagine leaning forward while holding on to the chains, but maybe it’s possible. We can both agree that there isn’t nearly as much of a boost while going back as going forward. > [@](#): > > As you get higher in the swing curve, inertia helps keep you pulled against the seat and does help you lean backwards. But gravity is still the key driver. Well gravity still gives you the acceleration but centrifugal force / inertia allows you to adjust your center of mass to take advantage of gravity. That’s what I meant. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [November 8, 2013, 10:24pm UTC](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554/60 "2013-11-08T22:24:11Z")
> [@snailboy](#): > > It’s been a long time since I was in a swing. I can’t imagine leaning forward while holding on to the chains, but maybe it’s possible. We can both agree that there isn’t nearly as much of a boost while going back as going forward. “Forward” is a relative term. Sitting upright in the swing, one leans slightly forward while still gripping the chains. You’re not leaning way in front of the seat, but your weight is more to the front of the swing than the back of the swing. Watch kids when they really want to pump the swing. They will lay all the way flat for the forward stroke, and on the back swing their head will be even with if not in front of their knees. [Previous page](https://boards.straightdope.com/t/explain-the-kinematics-of-a-playground-swing/659554.md?page=2)