This is good footage of a cat twisting to land right side up, but I’m still unclear on how it’s conserving momentum. It really does look like it can bring its rear end around without twisting anything else in the opposite direction. Obviously, (and against what the veterinarian in my church group says), that’s impossible without something to push on. (Her: “It can push on itself internally.” What???)
Can someone explain to a physical science teacher how this is really working? How are the parts of the cat in the video offsetting their momentums and keeping the same inertia until it touches the ground? In one of the shots, I see the tail twirling conspicuously. Is that what’s offsetting the other movement? It has the advantage of being much further from the center of rotation, giving it more angular momentum.
OK, I looked at the video and I think this is roughly what happens (in addition to air resistance effects):
-Draw in forepaws, lending the front of the body a small moment arm, rotate the front of the body (the rear rotates slightly in the opposite direction)
-Extend forepaws fully, lending a greater moment arm
-Rotate rear of body (tending to reverse the previous rotation of the forepaws, but to a lesser extent, because they’re now extended)
-Dump any unwanted rotation to the tail.
As a sort of analogy (to explain how things can rotate without any starting angular momentum, or application of external force), picture a cylindrical spaceship, floating in zero g with a man holding onto rungs of a circular ladder which runs all the way around the inside diameter). The man pulls himself around the inside the ladder once - he’s travelling in one direction, so the ship rotates in the opposite direction, but because it has much greater mass than the man, it rotates more slowly.
When he returns to the same place on the ladder, he stops and the force he exerts to stop himself travelling also stops the ship rotating.
He has completed a full circuit of the inside diameter in one direction, but the ship has rotated less than a full turn in the opposite direction.
-So the attitude of the ship has changed, without any external forces being applied. The centre of mass of the whole system hasn’t budged at all though - so this isn’t an inertialess drive or anything impossible like that.
I agree that the center of mass hasn’t shifted in the horizontal planes (obviously, it’s falling through the vertical plane), but if the cat started feet up, and ended up feet down, work has been done (something happened), and the conservation of momentum has been conserved. Considering that the push against the air without wings and in about 1 second is minimal at best, we can say that the cat must conserve momentum within itself.
I do like your explanation in post 3. Does anyone have something to add or contradict with that?
It’s probably worth acknowledging that cats aren’t hollow with little homunculi climbing around inside them, but the principle (I believe it may be called vanishing angular momentum) is the same - I think the cat actually achieves it by sweeping parts of its body back around behind its centre of mass (which, when it is falling with legs extended, might actually be at a point outside of its body).
Something to note is that the tail can impart rotational momentum. With its tail it can both begin a rotation and end it. Thus, even in an ideal situation, discounting friction with air and everything else, the cat can start in an inverted position, use its tail to rotate its body and stop in a … verted … position.
Something of a tangent but years ago I read about a study into cats that had fallen from apartment balconies and windows in New York. I wouldn’t have thought that was a common enough occurrence to study but there you go. Anyway from less then a certain height the cats would land on their feet and be fine, and past a certain height the cats had simply been killed in the fall. In between though, there was a point where cats that were falling longer distances were more likely to survive then cats that had fallen shorter distances.
It was conjectured that in a fall, the cats instinctively prepare for an impact on its feet but once they realised they had a big fall they panicked and lost their catly mojo. Those falling further again had time to pull themselves together and fared better. Those falling still further again simply went splat of course regardless of their state of mind.
I recall reading about this. My memory, being only about 512K now, may be faulty, but I thought part of the deal was that in longer falls, they tended to flatten themselves out (like a flying squirrel) and thus slowed the rate-of-fall somewhat.
Interesting aside. “High-rise Syndrome” is a term used to describe the common pathology seen when a cat falls from a height. It is not uncommon fro a cat to be lounging on a window sill, roll over, then fall. Limb fractures, pelvic fractures, fractures of the mandibular symphysis, and pneumothorax are commonly seen depending on the height of the fall.
Back in the late 80’s (IIRC) there was a paper published describing the injuries, survival, etc of a number of cats correlated to the height of the fall. It was a retrospective study. That is, records from a number of veterinary hospitals were evaluated. It was a nice paper.
Someone at PETA read the paper and misunderstood it to have been an experiment in which the authors hauled cats to different heights, then dropped them to see the results. Moron. So, PETA protested loudly. Until finally somebody explained to them what retrospective meant. And PETA said, “Never mind”.
To this day I stay away from PETA.
On preview, this is likely the study Eolbo recalls.
I cut a time-lapse picture of a cat being dropped upside-down and landing on his/her feet out of one of my old physics books from college. I used to keep it taped to my monitor at work as “inspiration” for those moments when I found myself dangling perilously from the hands of Coroporate America. One of my favorite aspects of the picture was the “Eat my litter-covered sh*t and die!!” look on the face of the cat prior to being dropped.
These folks at MIT (video w/ audio warning)
appear to have created a device that mimics a cat’s dexterous movements. The picture at the top is the exact same one that I refer to above, but they cut off the top-most picture with someone’s hands still holding the cat, which was the best part.
Scientific American once had a great cover, multiple exposure, that showed the cat bending at the waist and pivoting the two parts of its body in separate directions to effect the turn.
The cover was repeated to show how high divers manage to rotate in mid air.
Since nobody’s stated it explicitly yet, angular momentum is conserved. At every point in the fall, the cat as a whole has zero angular momentum. Parts of the cat have nonzero angular momentum, which is how it twists about, but they all cancel out.
just kidding honestly.