The physics of diving & gymnasitic skiing?

For diving, especially off a one meter board, it seems to me that all the torque (angular momentum) required for twisting & somersault-like dives must be obtained before losing contact with the diving board.

Must skiiers have the twisting torque before take-off? Skiiers move much faster than divers, perhaps allowing the possibility of obtaining twisting torque via interaction with the air.

Can Skiiers manage to obtain twisting torque after no longer being in contact with the take-off ramp? If so, what is the physics describing how this is done?

 

Log in or Sign up to hide all adverts.

Log in or Sign up to hide all adverts.

James R: The following surely seems valid for diving ffrom either a 1 meter or a three meter board.

I suspect it is also valid for skiiers, but wonder if 40 MPH speeds might allow for some aerodynamic effects.

BTW: I was once a very good diver as long as I did not attempt a twisting dive. It had to be due to not getting enough torque along an axis parallel to my spine prior to losing contact with the diving board.

To me a half gainer with a half twist & a one & a half somersault was an impossibility, although the world class divers did it with ease from a 1 meter board. The best ones completed it before getting below the board.

 

Log in or Sign up to hide all adverts.

If you want to fry your mind read about how cats always manage to land on their feet. It involves alternately extending the front and back legs while twisting...very "clever" if they actually understood the physics involved...the end result is that they can land on their feet even if there was no initial torque in their descent! :huh:

So I guess the answer is that total torque is determined while in contact with the ground, yet twisting is still possible. When jumping off a ramp with a motorcycle you can adjust your angle after in the air by applying the throttle and brakes...

 

RJBeery: Apply brakes while in the air?

The throttle might have some effect due to increasing exaust velocity, but what effect could the brakes have?

I would like to see further explanation before believing the above.

Can you drop a cat without allowing it to get some torque by reacting against your hands? I would like to see a video of a dropped cat.

It seems to be a wide spread belief, but I am suspicious of claims that cats can always land on their fet without obtaining obtaining some torque prior to being in free fall.

 

When you jump off a ramp your back wheel is in motion. Apply the brake and that angular momentum is transferred to the entire "bike + wheel" system. Accelerate and the bike moves in the opposite direction to the wheel. I appreciate your skepticism but you don't have to believe me for the effect to occur. The same thing goes for the cat.

Please Register or Log in to view the hidden image!

OK I won't be so snarky. The cat-righting-reflex is described here but unfortunately I can't find the more interesting write-up that I initially read long ago. Think about this: why, when a person is about to fall backwards off a cliff, do they start spinning their arms wildly? (there is a valid reason for it)

 

With a bit of searching, I discovered the following.

Feline Pesematology is devoted specifically to the physics of falling cats. And yes, there really is enough data to merit some study!

The following is what seems to be a plausible explanation of how cats manage to land on their feet.

Note the bolded phrase. Whoever provided that explanation did not seem to rule out initial torque prior to free fall.

I would still like to see a video.

How do you drop a cat upside down without its obtaining some torque from reaction with your hands or whatever is holding him?

• You cannot have him lying on his back on your hands, unless you spent some time training him to relax in that somewhat uncomfortable position.
  
  
• If you hold him upside down by his feet, I do not think he will be passive until you decide to drop him.

Any ideas on how to drop him without his reacting against your hands prior to release into free fall?

The above includes the following.

They are describing a process which starts with the cat falling back first & feet up, and ending with feet down & back up.

If the cat started with zero angular momentum, it does not seem possible for his orientation to change without a change in angular momentum.

I wonder if a proper experiment has ever been done, somehow establshing zero angular momentum at the start of the free fall.

 

I bolded a different phrase than you did. "If any" implies than none is actually needed. The fact that later on the article claims that

should have verified this fact for ya. Spin em, or don't spin em, and they land on their feet. The only real problem they seem to experience is in the 10 foot range, which I would posit is enough to gain a damaging velocity yet not enough for them to twist around fully.

Did you read what I wrote about motorcycles and cliff fallers? Imagine you're in space with ZERO angular momentum (relative to some frame). Now, spin both arms in windmill fashion in the same direction. Your body will spin in the opposite direction. When you stop spinning your arms, your body stops spinning. Orientation has changed.

 

RJBerry: Your motorcycle explanation seems plausible. Throttle & brakes can obviously affect the angular momentum of the rear wheel. My intuition does not tell me whether that angular momentum can be transferred to the rest of the motorcycle. I am not familiar with motorcycles. With the motor running, there would be angular momention due to rotating engine parts. Analysis of the flying motorcycle does not seem easy.

When you swing your hands, I would expect the torso & legs to turn in the opposite direction to conserve angular momentum. Would your body continue to rotate as long as you swung your arms? When you stopped swinging your arms, would your body stop rotating? Would stopping the arms cause a reverse transfer of angular momentum?

The cat explanation that I found matches the one at the link you provided. It is interesting. Bending the body & pulling in one set of paws seems to allow more rotation of one set of paws. Again, I am not sure why straightening out would not result in changing back to the original orientation of the body.

It surely seems possible for the cat to change paw orientation enough to get one set of paws landing first & then react against the ground to orient the other pair of paws. This could result in the appearance of landing feet first if the second set of paws were oriented quickly.

I wish I could find a slow motion video. As mentioned in a previous post, it seems difficult to drop a cat without its reacting against the hands holding it.

 

It has to - there's nowhere else to go.
Imagine that you are the brakes. You're looking at a fast spinning wheel, and you slow it down by grabbing it. It makes sense that the wheel will pull you around, right? That the angular momentum you remove from the wheel is taken up by yourself?

Similarly with the engine. The mechanics of the engine aren't all that relevant - the biggest factor is that the engine pushes on the wheel to make it spin, and that the wheel pushes back.

 

Yep your body will rotate until your arms stop. This should be proof enough that you can change orientation with zero initial torque.

The trick is in the cat extending its front legs while retracting its hind legs, then twisting, then retracting its front legs and extending its hind legs and twisting back. The moment of inertia is equal to m*r^2, so the cat is selectively making its front and hind halves have a "higher moment" than the other. This is the same reason a tight-rope walker uses a very long pole - the pole can be relatively light but have a very high moment of inertia (therefore the pole has a lot of resistance to rotational change which provides stability to the walker). :thumbsup:

 

You can cause yourself to rotate in free space without changing the angular momentum. Imagine extending your arms out and spinning them one way- your body goes the other way to conserve angular momentum. If you then bring your arms in and square them with your body again, your body will rotate in the opposite direction, but not as much as it did in the first direction. End result: your body has now performed a rotation in free space, yet total angular momentum was zero at every stage. I remember seeing a high school science video where astronauts on the space shuttle were performing a funny-looking series of movements to rotate themselves, without pushing against the air or touching anything. This would be good for course corrections, but not so good for performing high-speed rotations. The high-speed rotations divers make come from picking up angular momentum off the diving board, and then tucking themselves in so they have to spin faster to preserve this momentum. Same as in figure skating, where they start off with a slow, wide spin which gets much faster as they bring their arms in.

 

CptBork: The following is more convincing to me than explainations.

 

Great, three days of trying to explain the physics is trumped by a fuzzy anecdotal memory. I guess it's a good thing I'm not a teacher

Please Register or Log in to view the hidden image!

 

RJBerry: Sorry about the following

I am sure that videos of astronauts in a weightless environment have been made. I would expect astronauts to experiment with changing orientation in a weightless environment. I do not suspect CptBork of fabricating or having a faulty memory, although either could be the case. Surely such a video would be more convincing than a verbal description of the falling cat.

I should make it clear that I do not deny that a cat can manage to land feet first, and that perhaps the feat is accomplished as described by changing orientation without changing net angular momentum. The problem is that the verbal descriptions are not really an analysis of the relevant physics. In my life I have encountered all sorts of cogent verbal arguments which seemed convincing, but which I later discovered were invalid.

I tend to believe that the cat can manage the feat, but am not convinced in the absence of a good slow motion video. I think the problem is difficult enough that a true analysis of the dynamics of a cat would be formidable, if not impossible.

BTW: It might be possible to create a simple non-biological model of a falling cat & use it to provide a convincing analysis.

Every time this topic is discussed, remarks like the following are usually included sooner or later, making me wonder about the various explanations being presented.

The analysis of tight rope walking with a long pole is easy to understand. It is not relevant to this thread, which makes me suspicious of other remarks on the subject. .

The long pole provides a high moment of inertia resisting rotation. Since any tendency to fall to one side or the other occurs very slowly, the tight rope walker has ample time to shift the position of his hands on the pole, allowing gravity to counteract the falling motion. The tight rope walker changes his net momentum.

For the tight rope walker, gravitational force changes the angular momentum. For the Olympic diver, the initial angular momentum is obtained by reacting with the diving board. The Olympic skier might also obtain angular momentum due to reacting with the ramp, although he is moving at 40MPH & aerodynamic forces might be pertinent. These explanations are easy to understand. The falling cat is a complex situation. A slow motion video might show or rule out initial interaction with the hands of the person dropping th cat.

 

Well I was just cracking a joke about the "fuzzy anecdotal memory". I've been there where a technical explanation does nothing for me but a visceral example makes things click in my head.

Anyway I just wanted to point out why the tight-rope walker was a valid example: it's because the benefits to the walker come from twisting the pole, NOT shifting it back and forth. If the walker wanted to simply shift the pole and rely on gravity to change his net angular momentum he could do that with a very short heavy one. The long pole allows for a very high moment of inertia (read: resistance to rotational change) while remaining light. (Another possible benefit of such a long pole is a lower center of gravity if the pole bends, but I've also seen rigid tight-rope walker poles.)

It is directly relevant to this thread because the cat uses the same principle - first making its front legs "long poles" which resist rotational change and its hind legs "short poles" which rotate easily, then making its front legs "short poles" and its hind legs "long poles" so that when it twists again its orientation has changed. Make more sense?

 

I was trying to look on Google/Youtube for some NASA videos of astronauts doing the maneuvre, but couldn't sift through all the junk. I'm sure the maneuvre has a name, wish I knew it. I remember the one I saw, from more than 10 years ago, had 2 astronauts floating side by side. They had these goofy fake grins on their faces and were performing some kind of strange sequence with their legs kicking/twisting/pedalling like on a unicycle. They did it in synch with military precision, was pretty neat to watch but hard to understand at the time (was a second year high school physics class).

By the way, as far as the cat goes, you're all wrong. The cat clearly has a secret gyroscope aligned in its liver somewhere.

 

Here's your cat video although the original write-up I read suggested that cat's may need to go through the motion many times before righting themselves.

 

RJBeery: The cat video was interesting, but unfortunately did not show the start of the fall. I suppose the poor lighting was due to its being a video of opportunity rather than a planned experiment.

It is suggestive of the description given elsewhere.

I am partially convinced, but wish there was a better video available. I think that a video of astronauts in a weightless environment would be more convincing that a video of falling cats. A cat would be active immediately after being dropped, making it difficult to judge the presence/absence of angular momentum. The astronauts could show almost zero motion prior to attempting to change orientation.

I was never a naysayer on the falling cat issue, but was never a believer, and am not convinced. Due to this thread, I am more inclined to believe than previously. If forced to make a bet prior to seeing a really convincing video, I would bet that the cats can do it.

BTW: I disagree with your analysis of tight rope walking, except for the statement that the long pole provides a high moment of inertia resisting rotation. Without the long pole, the walker would have to react faster to any force tending to unbalance him.

The only commonality between the cat & the pole-using tight rope walker is the fact that moment of inertia is significant in the analysis. The tight rope walker makes no signficant changes to his moment of inertia & can change his angular momentum.

The circus performers who work indoors often (usually) do not use poles. Those who work outdoors use them because of wind which would be tough to cope with without the increase in moment of inertia slowing the rotational effects of an unbalancing force.

I am not familiar with the dynamics of working without a pole, although my not reliable memory tells me that the circus performers usually have their arms extended. I think I remember some who worked with an unbrella in one hand. They can shift their center of gravity by changing the position of their arms. This would seem to be sufficient for indoor tight rope walking with the major destabilizing force being gravity acting when the center of gravity is not directly over the wire. With a bit of practice, the center of gravity can be kept very close to being directly over the wire, minimizing the efforts required to maintain balance.

Outdoors high off the ground, wind can be very destabilizing, requiring much faster & stronger restabilizing actions in the absence of the long pole.

Talking about the cats legs acting like long & short poles does not make what they do at all analogous to the pole used by tight rope walkers.

 

Dinosaur I don't mind the banter but you will forgive me if I think you're being overly stubborn or maybe even intellectually dishonest. I mention the theory behind cats landing on their feet, and you say "cats can't do that without initial torque". I explain the physics on why it would work in theory. You say "cats can't do that unless I see video". I provide video and draw the analogy to tight-rope walking to help you internalize the idea. You claim the video has "poor lighting" and that tight rope walkers shift the pole laterally rather than spin it, and therefore the analogy is false. I'm now providing a link that proves that tight-rope walkers twist their poles rather than shift them...MEANWHILE CptBork mentions a video he saw once in HS and you announce that you're a true believer solely due to his anecdote (I wonder how the lighting was in that video?)!

Please Register or Log in to view the hidden image!

Dude no offense but I'm checking out of this conversation.