Possibly incorrect physics test question - Momentum

[stfz]

I was completing a chapter on momentum in my physics textbook.
I took the test, in which I encountered the following question:

Would a cat without a tail be able to right itself while falling so that it always landed on its feet?

Earlier in the chapter the author explained that cats were able to land on their feet almost all the time due to the fact that they had tails. While falling upside down, the cat would spin its tail in direction opposite to the direction it wanted to spin. Due to the law of momentum conservation (its application is approximated here), the cat's body will begin to spin the other way. Given enough time, the cat will be right side up for landing.

My answer to the question was that the cat would still be able to land upright, provided that it was able to spin or turn another one of its appendages, such as a leg.

My (rather drawn out) rationale is that the cat only spins less than 180 degrees in order to land upright. I assume cats can move their legs almost 180 degrees about their body, so it should be possible for the cat to land upright.

However, the textbook states that a cat with no tail will not be able to right itself.

Is there any logical or scientific explanation, or is it a perhaps badly put , ambiguous question?

 

[paisiello2]

You're right on this it looks like:
https://en.wikipedia.org/wiki/Cat_righting_reflex

 

[256bits]

A falling cat in action, slow motion,
http://www.richannel.org/the-physics-of-a-falling-cat

You should notice that the tail does rotate in the opposite direction of the cat body spin, helping to orient the rear half of the cat as it falls, into the feet down position for a landing, although tail rotation seems to be neglected in this video and in other descriptions of falling cats.

I would presume though that a cat without a tail would learn quickly how to right itself correctly, due to the other aspects of how it does right itself, such as tuck and extension of its feet, flexible spine, and angled body.

 

[paisiello2]

Too funny, especially the part about the Air Force experiments in zero g.

 

[Nugatory]

I would presume though that a cat without a tail would learn quickly how to right itself correctly, due to the other aspects of how it does right itself, such as tuck and extension of its feet, flexible spine, and angled body.

Manx cats have no tails, and they land on their feet just fine.

 

[BruceW]

yeah, in reality, even if a cat loses it's tail, it can still land on it's feet. possibly the tail helps. But I would guess the two most important things are the incredible flexibility of the cat as it twists it's body to land on its feet (you can see this in slow-motion videos), and the other thing is the cat seems to have this 'behaviour' of landing on it's feet. (compared to other similar animals that are not so bothered how they land).

 

[A.T.]

My answer to the question was that the cat would still be able to land upright, provided that it was able to spin or turn another one of its appendages, such as a leg.

Right. But the quickest way is actually to spin (or rather swing) the entire rear body half around, and that's what cats mainly do. In fact it is so quick that human vision cannot follow it, so the only thing we notice is the tail swinging around. That's why the importance of the tail is often overemphasized. Here is an animation of this basic mechanism:

https://www.youtube.com/watch?v=yGusK69XVlk

A real cat flip is not that symmetrical though, because the cat wants to turn around the front half faster to see where it is going. So the cat will modify the inertial moments of the body halves, by extending and retracting the legs. And cats with a tail will additionally swing it relative to the rear half, but that is not crucial.

 

[A.T.]

...the incredible flexibility of the cat as it twists it's body...

A cat is flexible, but it doesn't "twist" it's body in the sense of a torsion. That would be painful even for a cat. And the cat would have to untwist itself after landing. What the cat actually does is just bending its body cyclically as shown in the video above at 0:43. The body halves are relatively swinging around, rather than relatively spinning around.

 

[256bits]

This would be a great project for the engineering to build a robotic cat that can right itself when falling!

 

[BruceW]

A cat is flexible, but it doesn't "twist" it's body in the sense of a torsion. That would be painful even for a cat. And the cat would have to untwist itself after landing. What the cat actually does is just bending its body cyclically as shown in the video above at 0:43. The body halves are relatively swinging around, rather than relatively spinning around.

well, I think the cat only needs to twist its body so that it can move its head first, to see where the ground is. (which you mentioned before). This is not the bending motion required for the cat to turn itself around. But the cat still does the twist anyway, since it wants to know where the ground is :) Also, I think the cat untwists itself before landing. So really, the twisting motion doesn't help the cat turn it's body around, but it does let it move its head first to see the ground.

 

[A.T.]

well, I think the cat only needs to twist its body so that it can move its head first, to see where the ground is. (which you mentioned before). This is not the bending motion required for the cat to turn itself around. But the cat still does the twist anyway, since it wants to know where the ground is :) Also, I think the cat untwists itself before landing. So really, the twisting motion doesn't help the cat turn it's body around, but it does let it move its head first to see the ground.

That's correct. There is some temporary torsion because of the front body priority. But the mechanism itself doesn't depend on torsion, which is crucial for an animal. A robotic cat on the other hand, could just have a 360° torsional joint, and rotate the body halves in opposite directions.