Consider with the analogy of a goalkeeper. If the goalkeeper jumps in the air and holds a spinning football to stop it, the angular momentum will be transferred to the goalkeeper. Here the goal-keeper can resist rotation in the air, implying the angular momentum being absorbed by the atomic particles in his body. What you think?

If he jumped in the air he would not be able to resist the rotation. Remember the video and the girl on the platform and how she rotated. If the goal keeper is on the ground then the angular momentum will try to turn him but his muscles will resist the force and some of the angular mometum will be dissipated and the rest will be transfered to the earth.

Erm, I don't think angular momentum, being a conserved quantity, gets "dissipated", unless you mean some would go into air vortices as he flailed his arms or something.

A poor choice of words on my part, I was trying to keep it simple. Assume the girl in the video was standing on the gound and the angular momentum from the spinning wheel when turned would result in a force on her. She would resist the force by applying a force in the opposit direction through her muscles. The energy that was expended by her body to prevent her from rotating would result in a decrease in the angular momentum. The rest of the angular momentum would be transfered to the earth. A corrollary is the change in linear momentum from an inelastic collision.

Each time you grab a non-rotating ball and induce it to spin, you transfer an equal and opposite counter rotation to yourself and whatever scaffolding (including the Earth) is supporting your initial non-rotation. This is because angular momentum is conserved. If you begin with an equal number of equal mass/ density balls and spin half of them clockwise and the other half counterclockwise at equal and opposite angular velocities with the same axis/radius of rotation, your net rotation will return to the same value it was before you began the process. The electrons and atoms in the materials constituting the balls also have intrinsic quantum spins. If you could (you can't) stop the rotation of an electron that is quantum entangled with another, both of them disappear completely, for an electron without half integer spin is no longer an electron. In this way, quantum spin is also conserved, but in ways unfamiliar to us on a scale we can directly observe. The Higgs field is quantum entangled everywhere and has no quantum spin at all, which is the only reason a non-rotating universe such as ours has any meaning, and when the Higgs boson, an excitation of that field, imparts inertia to selected particles like electrons, it is through interaction with their quantum spins. If this were not the case, neither mirrors nor prisms nor lenses could be constructed from materials containing electrons in a way that made any geometric sense, as opposed to the precision we have become accustomed to expect of sophisticated optical systems. No wonder Newton had such intense interest in such systems, and was more productive investigating them than he was with Alchemy. So in addition to the inventions of the wheel, the arch, stellar fusion reactors, DNA, evolution, sex, the human mind and photosynthesis (in no particular order), credit nature also with the invention of the lens and a photosensitive retina to use it with. Head spinning yet? Spin and the conservation of angular momentum at all scales makes all of that possible.

A response worthy of you, finally, and a good one. I'm very impressed, at long last. If an electron can be represented mathematically by a periodic wave function, what do you think that means, physically? What kind of physical motion could possibly have inspired such a mathematical idea? Mathematical symbology is full of holes. If you don't make an effort to bridge the gaps, you don't really understand what the symbols are telling you.

Yes, but that is my point. My understanding is that the principle of conservation of both linear and angular momentum is entirely separate from any energy changes that may be going on. Whether or not some energy is "expended" by her body to prevent her from rotating (i.e. some energy in her muscles is converted to heat) has no effect on the transfer of angular momentum to the combined girl/Earth body. The way you are describing it suggests that angular momentum can be "lost" through application of energy in some way. Not so, surely? Ditto with linear momentum and inelastic collisions. Whether a collision is elastic or inelastic affects whether or not kinetic energy is converted to heat, but has no effect on momentum being conserved.

Yes, it does. Funny how they never taught it to us quite like that, isn't it? It's a little more complex an idea than simple linear application of Newton's 3rd. It makes a big difference at what radius you apply the rotational push, and also whether or not you were already rotating when you applied it. With a lever arm long enough, like Archimedes once said, it doesn't take much of a push to affect the rotation of the entire Earth. All you need is a place for you (and the fulcrum, obviously) to stand.

I think conservation of Linear Momentum follows from Newton's 3rd Law. I am not very sure about this. Suppose an observer is holding a ball with both his hands and applies a spin to the ball; both his hands will receive reaction force in the opposite direction. These reaction forces will be absorbed by his hands and i dont think they will generate any counter-spin.

That is obviously wrong. Firstly, your "observer" is not an observer, as he is interacting with the system observed and is thus part of it. Secondly, and more importantly, in order to spin the ball he has to apply a torque to it. By doing so, he experiences an identical torque on his body, in the opposite sense, by Newton's 3rd law, a torque being a force multiplied by a distance from an axis of rotation. You do not "absorb" a force. If you could, Newton's 3rd Law would not be true.

Energy "loss" means only change in the form of energy, because energy is conserved. Energy changes do not cause conservation of angular momentum to be violated. And gravitational waves are quite irrelevant to the problem of what happens when you spin a ball. You are simply creating needless (intended?) confusion by pointlessly ntroducing GR into a simple problem of classical mechanics. Re Newton I cite Wiki, thus: Conservation of angular momentum[edit] A rotational analog of Newton's Third Law of Motion might be written, "In a closed system, no torque can be exerted on any matter without the exertion on some other matter of an equal and opposite torque."[17] Hence, angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved).[18] from : https://en.wikipedia.org/wiki/Angular_momentum

Is it? Well you can consider here the goalkeeper as i explained in post #43, instead of the observer. Actually the goalkeeper applies couple instead of torque to spin the ball. https://en.wikipedia.org/wiki/Couple_(mechanics) You are seeing this from a torque point of view. In my post #54 I was seeing this from a couple point of view. A force can be absorbed in the form of stress as in a spring, where energy is stored. I dont think, this will violate Newton's third Law.