<jmfbahciv@aol.com> wrote in message
news:e63u43$8ss_003@s941.apx1.sbo.ma.dialup.rcn.com...

I've never gone through the exercise of understanding how it is
possible for a person dangling in the seat to pump it up in the first
place.

It's the same as the falling cat problem. How can a cat dropped upside down
turn himself the right way up.

<jmfbahciv@aol.com> wrote:

I've never gone through the exercise of understanding how it is
possible for a person dangling in the seat to pump it up in the first
place.

It's the same as the falling cat problem. How can a cat dropped upside down
turn himself the right way up.

On Tue, 6 Jun 2006,

"Edward Green" <spamspamspam3@netzero.com> wrote:

Related playground question: how can a child standing in the middle of
a turntable, not touching anything else, make it rotate?

He turns his head, triangulating the point where his mother
called so he can run the other way.

The trick is to not stand in the middle. Gate-pumping was an occasional
fun distraction - stand on a gate, and make it open or close without
contact with the ground. Friction can be useful! I've not done the maths
for it, but I think one could use it to find the coefficient of friction
for the gate hinges.

Swing-pumping is more mysterious than gate-pumping. Perhaps a nice
discussion topic for students.

Scripsit

"Edward Green" <spamspamspam3@netzero.com> wrote:

It's amazing how children can pump swings, while drawing a force
diagram explaining how they do it might challenge bright freshman
physicists. Of course the Earth and gravity are the other side of the
equation for conserving angular momentum, just as for a pendulum. But
I've never gone through the exercise of understanding how it is
possible for a person dangling in the seat to pump it up in the first
place.

I was never able to do that; I always needed a jump start.

But you were able to pump up the oscillation once it got started,
right?

That's an interesting observation. I had tried (and failed) to
construct a good explanation based on moving one's center of mass
_perpendicular_ to the rope. But once the oscillation has been set up
here is a possible model for pumping by movement _along_ the rope's
direction:

At the bottom of each swing you pull up your legs, doing work against
gravity *plus* work against the centrifugal force; the latter
component will increase your angular velocity by preservation of
angular momentum. At each dead-point let the legs fall down; this only
returns energy from gravity.

As far as I remember, what I actually did back when I was a
kid-on-a-swing was that during the (last half of the) forward swing I
would have my legs stretched out in front of me. At the front deadpoint
I would *begin* bending the knees such that my heels hit the underside
of the seat at the bottom of the back swing, and at the back deadpoint
I would similarly *begin* streching my legs again.

I always thought that this technique worked by moving my
center-of-mass backwards and forwards,

but that can't really be true -
in the direction perpendicular to the rope all I should be able to do
was to change the _distribution_ of my mass around a smoothly
oscillating center, which would have no effect.

What the technique _did_ achieve was to _lower_ my center of mass
briefly during the downward half of each half-swing. Since the angular
velocity was lower during the lowrering of the feet than during the
raising, energy would be pumped into the oscillation.

Henning Makholm wrote:

Scripsit "Edward Green" <spamspamspam3@netzero.com>

Related playground question: how can a child standing in the middle of
a turntable, not touching anything else, make it rotate?

Friction in the bearing allows it to transmit a small torque to the
turntable. The child starts turning her torso with a torque that it
small enough to be countered by the turntable, then suddenly reverses
her rotation with a large torque in the opposite direction. The large
torque overcomes the friction and the turntable begins to rotate.

I don't think that the trick will work a second time once the
turntable does rotate. It depends on non-linearity of the friction.

Thank you for the answer, but not the answer I was looking for.

The child can make the turntable rotate even assuming a frictionless
bearing, even have a time averaged non-zero rate of rotation, although
he cannot put it into a steady state rotation. He does this by first
twisting one way then twisting back, having altered his moment of
inertia in the interim by extending or dropping his arms. The net
result will be a repeatable re-orientation of turntable + child. Of
course the net angular momentum, if zero at the first, must remain
zero: the point is, deformable bodies can reorient in the absence of
external torques.