Okay, even though my book is now out in the world and I spent years working on it, I still manage to come across new things that surprise me about the problem of the falling cat! A good example of this came across my twitter feed the other day: a video of a cat doing some pretty incredible acrobatics. I include a gif of the relevant action, which includes a slower-motion version of the flip, below.
The cat, and the people, are startled by the sound of a passing car. The cat almost instantly does a complicated maneuver that results in it turning to cat the possible threat.
What surprised me about this: assuming that this video has not been altered, and I have no reason to think that it has, we have a cat that is using the cat-righting reflex to do something quite distinct from making sure it lands on its feet! In particular, it is using the “cat flip” to change its horizontal orientation, rather than its vertical orientation.
Being that I am now evidently the world cat flip expert by default, I thought I would take a closer look at this video to see if I can analyze the motion being done.
Okay, first of all here’s a shorter clip that shows only the slowed section of the video.
My take on this video is that the cat is basically combining two motions — a front flip, which gets its head pointed towards the threat, but upside down, and then a “bend and twist” cat flip, which puts it right-side up.
So what is the “bend and twist?” In my book, I describe how cats likely use a combination of several maneuvers to help right themselves, as anything that speeds up the process reduces the chance that the cat will land poorly and get injured. But the “bend and twist” is probably the most important of these maneuvers.
Newton’s third law of motion is often stated that, “for every action, there is an equal and opposite reaction.” This is really a statement of conservation of momentum: if you push on something, that something pushes back on you! It is not possible for something to spontaneously gain momentum; something else must get equal and opposite momentum to balance. Some years after Newton, it was discovered that nature also obeys a law of conservation of angular momentum, or “momentum of rotation.” We might state this as “for every twist, there is an equal and opposite counter-twist.”
If you sit in a spinning office chair, you can experience this yourself — if you twist your upper body to the left, the chair will rotate a little to the right, and vice-versa. The motion isn’t perfect, because there is friction in the chair, and air resistance, so a little bit of your twist will always be transferred to the Earth, unnoticed.
When the first high-speed photos of a falling cat were presented to the French Academy of Sciences, the audience was stunned to find that a cat seems to spontaneously flip over, even though it started with zero angular momentum! Their naive early understanding of angular momentum was that an object can only rotate if it has angular momentum, and only an object with angular momentum can rotate.
However, this only applies to rigid spinning bodies, like a bicycle wheel, whereas any cat parent will tell you that cats are very much not rigid bodies!
The essence of the “bend and twist” maneuver is that a cat can bend at the waist, and then twist the upper and lower halves of its body in opposite directions. The conservation of angular momentum is achieved by the counter-rotation of the two halves of the cat’s body!
A simplified picture of this process is shown below, treating the upper and lower halves of the cat’s body as cylinders.
The exact process is, of course, a bit more involved, but this is the basic idea: the cat uses the two parts of its body to counterbalance its own rotation!
To understand the flip of the cat in the video above, we only have to add one step: a forward somersault that puts it more or less upside down. Here’s a depiction of the modified maneuver.
Here’s the video of the cat again, slowed down and zoomed in.
Hopefully you can see the bendy-twisty action that the cat takes once it is more or less standing on its head!
There are a couple of caveats to my simple argument. First, it is to be noted that the cat looks like it almost does a cartwheel, rather than a simple front flip, in turning around. This would make sense, as the cat would already be facing partly sideways, meaning it needs to do less twist to complete its motion. Second, I drew the flip and the B&T as separate, distinct motions, though it looks like the cat really overlaps the two motions. Again, nature tends to do things the most efficient way, not the way that is simplest to visualize!
As I said, I find this video fascinating because it shows a cat using its turning reflex for something other than surviving a fall. Researchers have shown (again discussed in my book) that the cat-turning reflex requires conscious brain activity to function, which makes it distinct from simple reflexes like the knee jerk reflex. It appears that cats have some conscious control over this reflex and can use it in surprising ways! Is this 180° twist also a natural behavior that all cats can do, or is it something that only some cats have figured out in the course of their lives? It is an intriguing mystery to me.
Let me end by showing another interesting variation on the cat-turning reflex that I encountered online some time ago. A cat, chasing a toy, leaps up and back, making it rotate backwards end over end. In order to land, it does two distinct bend and twist maneuvers! The first one turns it upright, but then it continues rotating upside down again, and so it does a second B&T to finally land on its feet.
Though the falling cat problem has been investigated for over 300 years, it turns out that cats can still surprise us with some of their tricks.