Re: What physical laws are used to keep button spinning on string?

It sounds like you created a pretty fun toy.  This works much like a fly wheel, better yet a yo-yo.   Conservation of energy is the key.

This process can be broken down into 2 phases:
 

1. Winding/Rewinding -- storing of kinetic energy as potential energy
2. Unwinding  -- expending kinetic energy

But, rotating your hands, you twist the string and store potential energy by converting the kinetic energy of your hands and the button into the twisted string.   When you pull the ends of the string loop, the string tries to unwind.   The unwinding of the string transfers kinetic energy back to the button.   However, the button is now confined to spin on the axis of the string instead of looping through the air as it did during the winding phase.  This can cause the button to spin very fast if you tug it correctly.   Once the string is fully unwound, it is very likely the button will continue to move, thus winding the string in the opposite direction.  The string will continue winding until the button stops moving.  Then if you pull the string loops again the button will rotate in the opposite direction from the first time.   This process of winding, unwinding, and rewinding can be carried on for a long time.   This works especially well with larger buttons because they have a larger moment of inertia and will overcome the friction that occurs at the rewinding stage of spinning.

As you indicated, you have to relax the tension in the string or the tension of the string rewinding will cause the button to slow back down.    If you time it correctly the button can be kept moving nearly continuously -- spinning forward, then back, then forward for as long as you wish.

 However,  there is energy loss in this system.  The sound you hear comes from work (energy) performed on the air around the button.  Sooner or later the button will stop unless you continue to add energy.   Fortunately, you are doing that every time you pull the string tight.

Here is a previous response explaining the physics of a yo-yo.

http://www.madsci.org/posts/archives/oct98/907781908.Ph.r.html

Sincerely,

Tom "Button Popper" Cull