How do cats defy physics with their perfect landings?

[Archosaur]

Yes, "cats", the animal. Not some jargon or acronym you haven't heard of. I have a question about angular momentum and cats.

Cats are pretty famous for always landing on their feet. I imagined that they accomplished this by manipulating their angular velocity by distorting their body in response to their angular momentum (which cannot change over the course of the fall). If that were so, and if a cat were held upside down and dropped with no angular momentum, then it should not land on its feet.

So, I did what any questionably ethical empiricist would do in the situation. I picked up my roommate's cat, held it upside down (over the couch. It's a very soft couch. Calm down) and dropped it with as little angular momentum as I could humanly manage. She landed on all four feet (and, being a mellow cat, didn't run off, but instead looked at me as if to say "I'm sorry, were you expecting something reasonable?"). So, myself being more curious than empathetic, I repeated this experiment... let's just say several times, until she finally ran off.

Each time, without exception...

• She left my hands upside down and with very very little angular momentum.
• Something wonderful happened about half way through the fall, which, in retrospect, I should have filmed. This event is the source of my confusion.
• She landed squarely on all four feet.

Initially, I thought "She could orient her front half in any way she wanted, so long as her back half compensated, then, landing with her front feet, she could quickly bring her back feet around," but, I reiterate, she always landed on all four feet.

My question for you, Physics Forums, is "How do you think cats manage this?"

My question for you, cats, is "Who the f@$% do you think you are?"

 

[LostConjugate]

Well they have muscles so they can move their limbs and create torque in a gravitational field.

 

[jtbell]

You can do something similar when sitting on a stool on a turntable. You can start from rest, rotate 180 degrees, and come to rest again, by waving your arms around in a suitable way. Or you can hold a bicycle wheel horizontally and spin it.

 

[Oldfart]

Cats are very flexible. They can twist enough to get one foreleg on the ground, then untwist quickly while the foreleg is anchored, and land on all four feet. It wouldn't work if the cat were dropped upon a hard, slippery surface.

 

[Drakkith]

Cats are very flexible. They can twist enough to get one foreleg on the ground, then untwist quickly while the foreleg is anchored, and land on all four feet. It wouldn't work if the cat were dropped upon a hard, slippery surface.

You sure this is right?

 

[Q_Goest]

[*]Something wonderful happened about half way through the fall, which, in retrospect, I should have filmed.

Too late... there's been a few folks that beat you to it.
http://news.nationalgeographic.com/news/2006/09/060928-cats-land-video.html
http://techtv.mit.edu/videos/949-a-cat-always-lands-on-its-feet
http://dsc.discovery.com/videos/time-warp-slow-motion-clips-cat-landing.html

 

[Curl]

Looks like they use that tail. Still seems like they violate angular momentum conservation.

They need to cut a cat's tail off then repeat experiment to see what happens. Or at least tie the tail to the body.

 

[Drakkith]

Looks like they use that tail. Still seems like they violate angular momentum conservation.

They need to cut a cat's tail off then repeat experiment to see what happens. Or at least tie the tail to the body.

Lol, I hope all that was a joke. =)

 

[Curl]

Not a joke, its a logical experiment to see what the effect of a cat's tail is while falling.

If the cat falls on its face and bites the dust while the tail is duct-taped to the body, then we know how cats do it.

Give it a try if you got a cat, I don't so I can't do it.

 

[Drakkith]

I already know how cats do it. A combination of tail and body movements. Rotate the tail one way and the cat turns the other way. Without a tail it can still right itself. Maybe not as easy or as fast, but it can. I can do twists underwater using the same methods.

 

[Oldfart]

You sure this is right?

I saw this happen in some internet clip long ago. As I recall, the cat was dropped from a lower height than is shown in the above links.

 

[Phrak]

It's not the tail that accomplishes the inversion to much effect. It doesn't have enough mass. There's no need to be chopping off cat tails in experimental glee unless you include four limbs as well, but they aren't a requisite either.

The question is this: You have a solid flexible object with initially zero angular momentum about its center of mass. It is dropped. manipulate it's shape so that it is inverted, and has reacquired it's initial shape on landing--still with zero angular momentum. How do you distort the shape to accomplish this? I think the best object to consider is a cylinder in the proportions of a cat to keep in the spirit of the question, but a hotdog would do just as well.

 

[Buckleymanor]

Not a joke, its a logical experiment to see what the effect of a cat's tail is while falling.

If the cat falls on its face and bites the dust while the tail is duct-taped to the body, then we know how cats do it.

Give it a try if you got a cat, I don't so I can't do it.

You just need the right type of cat.

http://en.wikipedia.org/wiki/Manx_(cat )

 

[Archosaur]

You can do something similar when sitting on a stool on a turntable. You can start from rest, rotate 180 degrees, and come to rest again, by waving your arms around in a suitable way...

This is certainly not what is happening when cats flip over. You would not be able to have any net change in the position of the office chair (or stool or whatever) if it weren't for static friction, which is decidedly missing from the mid-air environment.

Similarly...

I can do twists underwater using the same methods.

Though I don't have the heart to drop a cat in a vacuum, I suspect it would still land on it's feet. When you do twists, you are pushing off of the water. I don't think cats do anything like this, especially in a less viscous medium like air.

The question is this: You have a solid flexible object with initially zero angular momentum about its center of mass. It is dropped. manipulate it's shape so that it is inverted, and has reacquired it's initial shape on landing--still with zero angular momentum. How do you distort the shape to accomplish this? I think the best object to consider is a cylinder in the proportions of a cat to keep in the spirit of the question, but a hotdog would do just as well.

Yes. This is the question.Also, thanks for the links, Q_Goest!

 

[rcgldr]

The tail effect is not that signifcant. The cat whirls it's hind quarter in a circular motion, which causes it to rotate in the opposite direction (conserving angular momentum).

If a person is in a pool floating in an intertube, the person can bend at the waist and rotate his legs, which ends up rotating the persons upper body with the legs barely moving. If the same movement were done in air while in zero-g, there would be similar but diminshed effect, circular and rotational motion. On a trampoline, it's fairly easy to do a 1/2 twist going into a pike (bent at the waist) position and trying to rotate the legs while unpiking.

 

[Drakkith]

Rcgldr, you just reminded me of a good example. I have a trampoline and I can twist in midair whenever I want during a flip or jump. I forgot about that...

 

[rcgldr]

Rcgldr, you just reminded me of a good example. I have a trampoline and I can twist in midair whenever I want during a flip or jump. I forgot about that...

The principle for doing a twist while doing a front flip or back flip is a bit different, since you can effectively "tuck" on one side (usually arm movement) to generate a rotation while flipping, as well as the pike and "move" legs method.

To create the "cat" scenario, you need to jump straight up without a flip, then get into a pike position and try to move your legs to one side or the other. Your legs will move a bit, but you'll also rotate. A 1/2 twist isn't too difficult to do.

 

[Drakkith]

Sorry, that's pretty much what I meant. Jumping up straight with no twisting, and I can rotate to land on my stomach or back or whatever I want. I'm assuming its the same principles for a cat.

 

[Phrak]

The flexibility of a cats spine enables it to bend in all directions much more than our own.

The tail effect is not that signifcant. The cat whirls it's hind quarter in a circular motion, which causes it to rotate in the opposite direction (conserving angular momentum).

That's pretty much half of it. If it were only the hind quarters the maneuver would take longer to accomplish. The entire arch of the spin has both the head and hindquarters gyrating about the mid-quarters, offset in generally the same direction.

 

[ashishsinghal]

So Drakkith, now I suppose we shift are attention from cats to you. How can you twist in mid air without any sufficient external torque?

 

[Archosaur]

Right. In order to do something like a flip, you start with angular momentum and tuck your legs so your angular velocity increases. You can't jump straight up and then do a flip, or even land on your stomach.

 

[rcgldr]

Right. In order to do something like a flip, you start with angular momentum and tuck your legs so your angular velocity increases. You can't jump straight up and then do a flip, or even land on your stomach.

This wouldn't be possible on a trampoline, but if hovering in a space station, you could wind mill your arms one way to cause your body to flip the other way, even if there was no atmospheric drag. As soon as your arms stopped moving, you would stop rotating.

On a trampoline, you can pike (bend at the hips), and try to swivel your legs in a circle, which will offset them a bit and also rotate you about 1/2 twist. This is similar to what cat does. Although it's probably thinking that it's swirling it's hindquarters, it's actually swirling both ends.

 

[sophiecentaur]

I have a feeling that, if you let the cat fall a very long way there would be no permanent spin generated because its total angular momentum would have to remain at zero and it has no 'rotating parts' (such as a flywheel) with which to 'dump' angular momentum. The cat's secret (amongst others) is to time its twisting so that it has the correct orientation when it's landed.

 

[cepheid]

I have sort of vaguely followed this thread. I came across this:

http://www.physics.utoronto.ca/dept-items/colloquium/physics-colloquium-for-march-10-2011

It seems like a bit of a coincidence. I wonder if the speaker is involved here in some way?

 

[m.e.t.a.]

In this http://www.youtube.com/watch?v=RHhXbOhK_hs", a falling cat appears to go through the following motions:

1. Arch back. (Actually, its back is already arched at the start of the fall.) The cat is now bent nearly in half.

2. Rotate front and rear of body in opposite directions. By "opposite" I mean that both fore and rear portions of the cat rotate in the same direction (CW or ACW) w.r.t. the "axis" of the cat, but rotate in partly opposite directions w.r.t. each other in space. Torques partly cancel each other, making rotation possible without the need to push against the air etc.

3. Straighten back.

There is also some motion of the tail, and other motions of the legs etc. which are hard to keep track of. I am not considering these other motions here—just the motion of the body axis.

I have drawn a diagram to try to show what I mean. Does this make physical sense?

http://img11.imageshack.us/img11/1778/physicsforumscatflipang.png

 

[rcgldr]

1. Arch back. (Actually, its back is already arched at the start of the fall.) The cat is now bent nearly in half.

At the start of the video, the cat is bent forward at the stomach, not arched. It mostly maintains the bend angle while rotating and trasitioning into an arched position.

The key is the fact that it's bent nearly in half, same as my trampoline anology if a person bends at the hips 90 degrees and tries to move his/her legs to one side. When bent nearly in half, each half of the body has more angular inertia than the "other half"s angular intertia about the "other half"'s central axis (axis of rotation). This allows internal torques from whirling each half to generate a rotation on both halfs.

The rotation will continue as long as each half continues to be whirled around in a circle. Once the whirling stops, so does the rotation, but the orientation has now been changed.

 

[Drakkith]

So Drakkith, now I suppose we shift are attention from cats to you. How can you twist in mid air without any sufficient external torque?

I'll have to remember to go out tonight or tomorrow and try it, but I think it has to do with different movements of my arms and such. Extending, twisting, etc.

I think most people aren't thinking about something that can move its own parts, which your standard physics class probably doesn't go over when they talk about angular momentum.

 

[rcgldr]

So Drakkith ... how can you twist in mid air without any sufficient external torque?

I'll have to remember to go out tonight or tomorrow and try it, but I think it has to do with different movements of my arms and such. Extending, twisting, etc.

Twisting is possible, by bending at the hips and trying to move (whirl) the legs to one side, similar to the cat. Flipping rotation would be minimal, whirling your arms around vertically and bicycling your legs would produce only a small rotation along a horizontal axis, although if hovering in a space station and given sufficient time it would work (even without the effects of atmospheric drag).

To make this a true test, you'd need a second person observing and randomly calling out when to attempt the twist so that the person bouncing on the trampoline doesn't know until mid-air to attempt the twist or not.

 

[m.e.t.a.]

At the start of the video, the cat is bent forward at the stomach, not arched. It mostly maintains the bend angle while rotating and trasitioning into an arched position.

Semantics. A cat bending forward at the stomach creates a $\cap$ shape, which I would call "arching the back", while bending in the opposite direction creates a $\cup$ shape. I suppose it depends on which way up your head is with respect to the cat.

The key is the fact that it's bent nearly in half, same as my trampoline anology if a person bends at the hips 90 degrees and tries to move his/her legs to one side. When bent nearly in half, each half of the body has more angular inertia than the "other half"s angular intertia about the "other half"'s central axis (axis of rotation). This allows internal torques from whirling each half to generate a rotation on both halfs.

The rotation will continue as long as each half continues to be whirled around in a circle. Once the whirling stops, so does the rotation, but the orientation has now been changed.

I think I see what you're saying, and I would agree. This seems the most plausible explanation of the twisting.

 

[cepheid]

I just realized that maybe nobody took a look at my link (post #24) because I didn't explain what it led to, so people reading my post might have thought I was just being off topic. Anyway it leads to the abstract for next week's physics colloquium at my university:

Rotation with zero angular momentum: Demonstrations of the falling cat phenomenon go sour

It is well known that a system with zero angular momentum can, by appropriate deformations, rotate while always maintaining the condition of zero angular momentum. This effect explains how a cat that is dropped while upside down can turn over and of how certain gymnastic maneuvers are performed. These rotations are taken as a demonstration of the "non-integrability" of a "non-holonomic" constraint. There is a simple demonstration of this rotation-with-zero-angular-momentum effect with a rotating platform. But the demonstration often doesn't work because most floors are not perfectly flat. I found a simple better demonstration experiment. Unfortunately, the experiment came out all wrong for different reasons. But I figured out why and did a second demonstration experiment. And that came out wrong exactly in the opposite way.

The talk presents the four puzzles: a) how can you turn while having zero angular momentum? b) Why does a rotating platform demonstration often not work. c) Why does a simple demonstration not work? d) Why does almost exactly the same demonstration not work in the opposite way?

I have no idea what the "non-integrability" of a "non-holonomic" constraint is. The only thing I got out of it was the first sentence, that it is apparently possible for something to rotate while maintaining zero angular momentum, by deforming.

EDIT: I should add that most physics colloquia abstracts that I've seen are far less silly-sounding than this one.

 

[Phrak]

I have no idea what the "non-integrability" of a "non-holonomic" constraint is. The only thing I got out of it was the first sentence, that it is apparently possible for something to rotate while maintaining zero angular momentum, by deforming.

And it is. A fairly easy thought experiment is to replace the cat with a rather plump and metamorphosing sausage. Draw a line down one side of the sausage then divide it into 4 equal sections, one through four. Think of this as a transformer sausage. The sections can move around as long as they only push and pull one one another. No outside agents are allowed to exert any forces on the sections in this experiment.

Displace section one radially from section two. Section two and three stay attached to each other. Section four is displaced in the same direction as segment one.

Now it's best to use the symmetry of the system and just look at two sections at a time. Sections one and two have their axis separated by some rigid rod. A chain drive or belt connects the two. Now a means can be supplied to spin the two with respect to the rod without external forces or energy.

To conserve angular momentum the two segments, or disks, will need to orbit about each other. Also, important to note, the angular displacements of the line drawn on the original sausage, and now appearing on each section remains the same on each section. We can't allow one segment to turn faster than the other.

As the sections are brought back into alignment, after some number of revolutions, the line drawn down the side is displaced.

So the cat thing is reduced to two sprockets and chain, a separating rod, and some means of propulsion.

 

[Phrak]

Come to think of it, it might be fairly easy to demonstrate in a classroom, properly suspended on a string with something available from Toys R Us.

 

[sophiecentaur]

I think most people aren't thinking about something that can move its own parts, which your standard physics class probably doesn't go over when they talk about angular momentum.

The nature of an object's construction doesn't determine whether or not angular momentum is conserved. No explanation of how a cat works can do without the basic conservation laws.