Physics · One slow-motion trick
Hold a Slinky by its top coil and let the rest hang down, stretched long. Now let go. The top coils rush downward. The bottom coil does something that looks wrong: nothing. It hovers in mid-air, as if gravity had not heard about the drop yet, until the falling coils finally crash into it.
Before the release, the bottom coil has two forces on it that cancel. Gravity pulls it down, and the stretched spring above it pulls it up by exactly the same amount. That upward pull depends on one thing only: how far apart the bottom coil and its neighbour above it are. As long as that gap stays the same, the pull stays the same, and the bottom coil stays where it is.
So the real question is how the bottom coil could ever find out that someone let go of the top. The answer is that it can only find out from its neighbour, and the neighbour only from its neighbour, and so on up the whole spring. The news of the release has to travel coil by coil. Nothing in the Slinky is rigid enough to deliver it instantly.
When the top is released, the top coil is pulled down by everything stretched beneath it, so it accelerates hard. It slams into the coil below, which is still hanging, and the two stick together and move on to hit the next one. A growing stack of bunched-up coils races down the spring, and the front of that stack is the news. Below the front, every coil is still hanging exactly as it was. Above it, they have all collapsed and are on their way down together.
In a 2012 analysis of a real Slinky, Cross and Wheatland at the University of Sydney found that the bottom does not start to fall until the top section has collapsed onto it, and that for real Slinkies this takes typically about 0.3 seconds. That is why slow-motion footage shows such a clean pause: for a few tenths of a second, the bottom coil has simply not been told.
Here is the part that makes the whole thing make sense. After the release, the only outside force on the Slinky is gravity. So its centre of mass, the average position of all the coils, falls exactly like a ball you dropped from the same spot: distance = ½ × g × time², from the very first instant. No pause, no delay.
That is not a contradiction with the hovering bottom. The average of a still bottom and a top racing down is something in between, and the top rushes down fast enough to make the average fall right on schedule. When the front finally reaches the bottom, the whole squashed stack carries on down together, moving at the speed the centre of mass has reached by then.
This is a simple model: 40 equal coils joined by springs, with sticky collisions when they meet. Press Release, then drag the time slider to go through the fall frame by frame. Watch the blue bottom coil against its dashed starting line, and watch the ring that marks the centre of mass stay level with the ball.
Tap Release, or tap the picture.
Drag the time slider slowly across the moment the bottom coil leaves its dashed line. In this model the bottom starts moving at about 0.26 seconds for a one-metre hang, close to the real figure above. Then change how far the Slinky hangs. A longer spring takes longer to deliver the news, and the delay grows roughly with the square root of the length: a spring half a metre long delivers it in about 0.19 seconds, one 1.2 metres long in about 0.29.
Whatever length you pick, compare the two readouts for the centre of mass and the ball. They match to within a few millimetres, and the small gap is only the model's time-step.
The coils are held apart by a stretched spring, which stores energy. When the coils crash together and stick, that energy does not come back as motion. In the standard model it ends up as heat, because the collisions are inelastic. This is why a collapsed Slinky does not bounce back up when it lands: most of the energy that mattered has already been spent in the collapse.
Any object that can be stretched or squeezed passes a change along as a wave. Let go of one end of a rope, a rod or a steel beam, and the other end learns about it only when a wave arrives; in steel that wave moves at roughly 5,000 metres per second, so it is over before you can see it. A Slinky is a nearly perfect teaching tool because its wave is slow and its coils are big. It stretches the same idea out until you can watch it cross the spring.
Sources: Cross & Wheatland, “Modeling a falling slinky”, American Journal of Physics (2012); arXiv 1208.4629. The simulation here is a simplified chain-of-beads model, not a fit to a particular Slinky.