The people-spinners at Ibach Park
Paul shows how to get it started with maximum moment of intertia and high angular velocity.
Everybody staggers when they leave
The kids also try it...
...and Lillie watches.
Keturah demonstrates the high moment of inertia position: stretched far from the axis of rotation.  To make the experience most exciting, we want to maximize angular velocity while in this position.  That's what Paul is doing above. Then she draws herself toward the axis of rotation.  This can take surprisingly great force.  As her moment of inertia gets smaller, her angular momentum and angular velocity increases. The closer she gets to the axis of rotation, the greater becomes her angular velocity.  The great force required to get close in at higher speeds keeps it relatively safe for kids: it can be hundreds of pounds.  That force pulling us in is where the great energy of spinning comes from as we pull ourselves in. Her moment of inertia is at minimum here.  Her angular velocity is very, very high.  Most people's vestibular canals take this as an insult!  Try this, and you will greatly appreciate the vestibular training of figure skaters.
Angular momentum
a product of two parameters:

J = w ´  I

Everything has angular momentum, and the sum of all the angular momenta of all the things involved in any happening never changes.

w is spin velocity

 Not even if things slow down by friction, or by being pushed or pulled by something else, like Lillie pushing her daughter, or by being tugged on by the moon via gravity.

Angular momentum just gets "transferred" by those things.  The sum stays the same. 

That's a pretty powerful principle!

 By starting with big value of I, our angular momentum is big:  that's a good start for some exciting times to come.

We get spun incredibly fast when we pull ourselves in because that product w ´  I stays constant.  The value of  w  goes way up because the value of I goes way down.

There's very little friction in the bearings of these playground people-spinners.  So we don't transfer much of our angular momentum to the Earth through friciton in the bearings.  Friction from the air (viscosity) is pretty small too.  (But neither of these is negligible: both will  succeed in slowing us down after a while.)

 

 So what is I? 

For each and every tiny bit of Keturah, the I of the bit is the mass of the bit times the square of its distance to the axis of rotation.

Ibit = mbitd2bit

Her total I is the sum of the I's for all her parts.  Work it out like this:

Shoulder-bit distance is d1, knee-bit distance is d2. 

I of combination, shoulder-bit (sb) + knee-bit (kb) is:   msbd12 + mkbd22

Then, just add all the other little bits into the sum.

She will decrease all those values of "d" by a big fraction when she gets herself right into that axis.  A large fraction will be decreased by a factor of 1/10 or more.  The moment of inertia for those will be decreased by a factor of 1/100.  If that's the average decrease of I, her angular velocity will increase by a factor of 100.  Start at 1 rev per second; end at 6000 rpm.

Try this by getting on a Ibach people-spinner, and you will instantly understand why you won't get going that fast.  That's a lot of spin energy.  That energy comes from you, pulling yourself in.  (Energy goes as force times distance.)

However, consevation of energy is another physics topic--for another time.  Its another pretty powerful principle,

 
 
 
 
 

 
 
 
 
 
 
The five picture are adjacent frames in a video tape.  Lillie and her yellow twisted pole are spinning steadily.  Between frames she and pole have turned several degrees, and that's the same as though the camera had rotated around them.  So adjacent frames will appear stereoscopically if we fuse two different frames by crossing or spreading our eyes.  The above are arranged for eye-crossing.  Lillie's daughter is walking from left to right: she also appears stereoscopically.  Father, Paul, and the rest of the scene does not present us stereoscopic depth