A Physics Lesson: Why Cats Land on Their Feet
mentalfloss.com
mentalfloss.com
Thank you for submitting this. You made my weekend!
Also, it's really cool to see videos like this that go such great lengths at explaining difficult stuff in such an interesting way, providing enough detail to get you started, but little enough so that you have to look it up in detail if you really want to know.
"Sometimes I think that the only projects worth doing are the ones which require building a new tool"
Now how they do it is a different question all together.
Ps, awesome video http://www.youtube.com/watch?feature=player_embedded&v=R... , article is pretty useless.
Practice question: imagine you're floating in space and facing away from the earth. How would you turn around to face it?
[1] Usually by making sudden lateral movements with outstretched limbs whilst bringing them inward, much the same as the cat.
A linear analogy would be a two balls connected by a spring oscillating in a vacuum. If one ball is much lighter than the other -- like a football connected to a cannonball -- it moves a lot, while the cannonball moves very little. Let's say the football and the cannonball are on a football field (a frictionless, vacuum-filled football field, of course.) The cannonball is on the 50 yard line, staying roughly stationary, and the football is oscillating back and forth between the 49 yard line and the 47 yard line. The system can't go anywhere if it starts with zero linear momentum, because the mass (linear inertia) of the balls remains fixed. But imagine you can change the masses of the balls at will. When the football reaches the 47 yard line, you swap the masses of the balls, so the football becomes very heavy and the cannonball becomes very light. Now the football stays almost stationary at the 47 yard line, and the cannonball oscillates between the 48 yard line and the 50 yard line. When the cannonball reaches the 48 yard line, you swap the masses so that the cannonball is once again very heavy and the football is very light. Now the football is oscillating between the 47 yard line and the 45 yard line. By swapping the masses repeatedly you can move down the field all the way to the end zone.
Because of conservation of mass/energy, you can't actually do that trick with linear inertia, but you can do it with angular inertia. The front and back half of the cat are like the football and the cannonball, and the cat controls the angular inertia of each half by tucking and extending its legs. When the cat is upside down, it increases the angular of inertia of its back half by extending its back legs, and it decreases the inertia of the front half by tucking its front legs. Its back half acts like the cannonball, and its front half acts like the football. That allows it to twist its front half around while the back half stays almost stationary. Once the front half is right side up, it extends its front legs and tucks its back legs, effectively swapping the football and the cannonball. In zero gravity, a cat could twist itself around that way as many times as it wanted: just like the football and the cannonball working their way down the football field, except that it wouldn't violate any physical laws.
In the video, the cats started their falls with no angular momentum, and so they finish their falls with no angular momentum. The problem the cat has to solve is to get itself in an upright position.
In natural falls, they won't always start with no angular momentum. For example, consider a cat walking along a branch and a gust of wind shakes the branch and the cat tips off. There's a good chance the cat will get angular momentum in that kind of accident.
In that situation, merely getting upright is not sufficient as the initial angular momentum remains. There are several approaches that cat could take to deal with this.
1. Wait until near the ground to do the "get upright" operation, so that there isn't time between that and landing for the rotation to take the cat too far out of position.
2. Get upright, and then whenever the rotation takes the cat too far out of position, repeat the uprighting operation.
3. Get upright, and then use a constant counterrotation of the tail to maintain the upright position.
I would guess that the long tailed cats would do better on natural falls that are high enough to need angular momentum management.
but i think what you're asking is why do we have fairly compact flywheels rather than longer, more extended "tails"? and the answer is probably that it makes more engineering sense. you can increase the angular momentum stored in something by making it "bigger" or by spinning it faster. i imagine it's a lot easier to spin a small flywheel to thousands of rpm than to make a "tail" (spinning at a very low speed) thousands of times larger.
also - unless i missed it - this video doesn't really explain all of it. by itself a cat's tail isn't nearly large enough or rotating fast enough to spin a cat's body. the cat is also very "intelligently" (presumably "designed" through natural selection) doing much of the rotation while in a U shape. that reduces the net angular momentum considerably (the two "arms" of the U effectively cancel).
and, from what i remember elsewhere, they also reduce the amount of rotation needed by rotating to only get one pair of legs perfectly aligned. as long as those touch down first there is a little time (i admit i am not sure it is sufficient) to then rotate the other legs while "holding on" to the ground.
1. size (obvious) 2. Torsional/shear stress - most materials are bad at tolerating shear stress. A bigger flywheel would require immense amounts of torque to get it moving. Generating a higher torque would impose huge amounts of torsional stress on the shaft driving the wheel.
There's a whole section where they discuss how it's not the tail at all, and even bobtail cats can land on their feet. So you definitely missed it!
For the humor value: http://www.mentalfloss.com/blogs/archives/87351
I lost it here "The cat and gluing dispositive will actually come together, but the cat spins so fast due to the invariance in the center of gravity that, following the law of time travel, it goes backward in time.
This has led to another theory stating that at the beginning of time there is an infinite number of antigravitatory cats, and therefore, causing the creation of the universe in the first place, due to the excessive gravitational forces produced by the infinite number of cats, they cause the big-bang. "
In fact towards the end of the video, another cat makes a brief appearance (the guy just wanted to present her to the camera, no throwing or falling involved at all) and it serves as a good demonstration what it looks like when they're not in the mood for human shenanigans.