I Dropping an extended Slinky -- Why does the bottom of the Slinky not fall?

[A.T.]

When we consider the physics of toppling dominoes we clearly see a set of dead times which are basically those intervals between the beginning of the fall and the instant of collision with the next piece.

Yes, for dominoes the finitness of the propagation speed is somewhat simpler to understand, than for a linear mass-spring system. There is no "dead times", here but instead a double integration at each finite element: the position of the element n-1 determines the acceleration of element n (along with two constants).

 

[DaTario]

Unlike the longitudinal waves, the twist mode speed visibly outruns the shock wave.

So if we filmed the slinky from below from the moment it was released with its lower metal end painted green as in the picture below, we would see this end rotate as it descends, is that it?

fig.: Slinky seen from below.

 

[Orodruin]

So if we filmed the slinky from below from the moment it was released with its lower metal end painted green as in the picture below, we would see this end rotate as it descends, is that it?

View attachment 343044
fig.: Slinky seen from below.

Not very much. It is a twist wave signal. This signal will also take some time to reach the bottom, but it will be faster than the longitudinal shock wave. As the twist signal reaches the bottom, it will reflect off the end of the spring. This will result in some twisting motion and typically also excite some longitudinal signal from the bottom up. If you look closely you will see the reflected twist signal as well as the lower end actually falling a little bit as the twist signal reaches it.

 

[DaTario]

Yes, I saw a subtle longitudinal wave rising from the lower end.

It seems to behave as Wilberforce pendulum with almost zero moment of inertia.

 

[AlexisBlackwell]

A falling spring, like an ordinary object, is subject to gravity. However, due to its structure and elasticity, the bottom of the spring is pulled upward, following the center of mass. This happens because when the top part of the spring falls, it pulls the bottom part with it, creating a balance between the force of gravity and the elasticity of the spring. The lower part appears to be "hovering" in the air, although in fact it is supported by the elastic force of the spring.

 

[Orodruin]

A falling spring, like an ordinary object, is subject to gravity. However, due to its structure and elasticity, the bottom of the spring is pulled upward, following the center of mass. This happens because when the top part of the spring falls, it pulls the bottom part with it, creating a balance between the force of gravity and the elasticity of the spring. The lower part appears to be "hovering" in the air, although in fact it is supported by the elastic force of the spring.

This has already been discussed extensively in this thread. What is your point?