Puzzle 4

[zekeman]

Defyiing law of angular momentum?

Here is a fun puzzle for you purists.

How is it that a kid sitting on a swing starting at rest can, without any help, always cause the swing to oscillate?

Please explain.

 

[berkshire]

Kid sitting, swing still, kid extends legs, changes CG Pendulum ( swing ) moves to compensate. Kid retracts legs, CG shifts back You know the rest.
B.E.

 

[SNORGY]

If I was sitting on a swing with my wife, I am not sure about the swing, but I imagine I could cause her to osculate.

Regards,

SNORGY.

 

[berkshire]

So would that produce an osculating orbit?
B.E.

 

[SNORGY]

As long as it's not relative, it works for me.

Regards,

SNORGY.

 

[IDS]

Starting from complete rest it's not that easy to start swinging. Once there is a small oscillation it is easy to increase the momentum of the swing by transferring momentum from the rest of the planet, by moving the position of your centre of gravity with respect to the swing pivot point.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[GregLocock]

Not too sure which bit is the puzzle. If you think a linear force can't produce rotational acceleration then tie a large rocket horizontally to the swing seat and fire it.

If you think there are no torques then try swinging in a swing that hasn't been firmly staked to the ground.




Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[FeX32]

Defying law of angular momentum?
Be careful.
The moment of inertia changes. Abiding by the conservation of the moment of momentum.


Fe

 

[IDS]

If you think a linear force can't produce rotational acceleration then tie a large rocket horizontally to the swing seat and fire it.

In the absence of a rocket, and starting from rest, where does the linear horizontal force come from?

The moment of inertia changes. Abiding by the conservation of the moment of momentum.

If there is no angular momentum to start with changing the moment of inertia will make no difference.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[FeX32]

"moment" of momentum, so the person can translate linear to rotational as Greg suggests as well, to get it started. After that, it can be thought of in many ways, one is mostly "I" manipulation.


Fe

 

[IDS]

so the person can translate linear to rotational as Greg suggests as well, to get it started.

Where does the linear momentum come from?

Once the swing is started there is no problem magnifying it, but the mechanism for starting the swing is not that obvious. I'm not saying that it's impossible, obviously it isn't, but so far no-one has given an adequate explanation of how to start a swing from complete rest with no direct contact with the ground.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[tygerdawg]

Gosh, awfully early / not enough coffee yet to retrieve Sophomore Dynamics knowledge from the 70's, but here goes:

1. Assign a coord sys on center of mass CM, somewhere near the kid's belly button. +X = forward, +Y = aligned with gravity field.
2. Kid leans back and kicks legs forward. CM is now (??) slightly rearward of chains by virtue of pivot point where kid is holding chains. This is change in momentum dM/dt = accel & applied at CM. Causing a -RZ rotation moment. Resolve forces in X,Y, kid moves slightly forward.
3. Repeat opposite in rearward direction -X.
4. Repeat in something near natural oscillation frequency of swing/pendulum to amplify motion.

Can it be done by kid sitting still? I don't see how. I would think replacing kid with a static mass would prove this. Kid would always be making small balance corrections and thus impart momentum change. However, a static weight would also start to oscillate due to (?) force imparted by action of Earth's rotation. Check out "Foucault Pendulum" for this effect, I think it may apply to the swing with static mass.

TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering

http://www.bluetechnik.com

 

[ivymike]

perhaps the premise is bad. I don't think I've ever seen a kid start a swing from "rest" at the bottom of the arc. They always back up with their feet until letting go makes them swing forward. As noted above, it's easy from then on. Starting from rest all you can do is fidget, and your cg stays pretty well directly beneath the pivot.

 

[EspElement]

Well, when you put your legs out doesnt it shift your center of gravity and thus the swing wants to level out, so about the time that you get centered again, you shift your center back to the other side by pulling your legs in.. as you back you shift it again and it continues to grow

 

[FeX32]

I think of the starting mechanism, in simple terms, as the same mechanism that can move you in your "rolly" chair like the one im sitting on right now. If you impose a dynamic force utilizing the inertia say in a body part (or whole body), you can impose a reaction force that can propel yourself forward, without touching the ground. Abiding by:
d(p)/dt=F, where p=m*v {ie. adding a force changes momentum}



Fe

 

[SomptingGuy]

I think part of this is the ability of the swinger to move his/her COG more quickly than the swing can restore it. At least that's what I told the cops when they turfed me out of the kids' park today.

- Steve

 

[ivymike]

Well, when you put your legs out doesnt it shift your center of gravity and thus the swing wants to level out, so about the time that you get centered again, you shift your center back to the other side by pulling your legs in.. as you back you shift it again and it continues to grow

so, could a shuttle propel itself through space by this method?

 

[zeusfaber]

So who has kids who can be bothered to sit perfectly still long enough for all the oscillations caused when they climbed onto the swing to damp out completely (*) before they attempt to get the thing moving again?

In a vacuum chamber, so gusts of wind don't acidentally get them started and convection currents set up by their body heat don't accidentally trigger micro-oscillations? Suppose that might also help with the "sitting perfectly still long enough" problem - even if it does put a bit of a mocker on the subsequent "get it going" attempts.

* Assuming an exponential decay, I guess this would take for ever - it would certainly feel that way to a hyperactive toddler.

A.

 

[FeX32]

I should have said "without directly touching the ground". If you don't indirectly use the ground then you aren't going anywhere (the same way you can indirectly use the swings supports to "gain access" to the ground)
Lets put a toddler in space and let him/her kick like crazy and see if he/she moves at all


Fe

 

[GregLocock]

Stand up, move body forward

sit down move body back.

You have just created a (time separated) torque, equal to the difference in CG height times the acceleration times the mass/2.

My rocket example was solely to demonstrate that an indisputably linear force can create a torque.



Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight