We all know that Slinkys walk down stairs, alone or in pairs. What this video presupposes is, maybe that’s not the best way to play with them? Who knew that you could treat a Slinky kind of like a yo-yo or juggling ball? Here’s a slightly shorter video of equally impressive tricks.
The explanation that “it takes time for the bottom of the slinky to feel the change” might work ok, but it isn’t the best.
Then why doesn’t the bottom of the slinky fall as the top is let go? I think the best thing is to think of the slinky as a system. When it is let get, the center of mass certainly accelerates downward (like any falling object). However, at the same time, the slinky (spring) is compressing to its relaxed length. This means that top and bottom are accelerating towards the center of mass of the slinky at the same time the center of mass is accelerating downward.