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Particles are referred to as having "spin" and i was wondering what it is. Is it the rotation of a body around its own axis or is it something else? If it is the rotation of a body around its own axis is it possible to increase a particle's spin? Wikipedia also says that a particle's magnetic field is induced by its spin so if the particle spins faster then will the magnetic field increase?

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No. Unlike the angular momentum in a top, the total quantum spin is fixed. In this the spin of an elementary particle is very different from that of a classical rotating body. Indeed, when the idea of the electron having "spin" was first mooted, Pauli objecetd because to get a spin of magnitude $\hbar/2$ the surface of the an electron of "classical" radius would be moving faster than the speed of light. (The "classical radius" is that at which the electrical field energy of a charged particle is equal to its rest mass energy)

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@mikestone's answer is very good but there is one specific point I would like to mention because it might get you to scratch your head as you learn more: nuclear spins, i.e. the spin of the nucleus of an atom. Indeed it can increase or decrease but this is just a linguistic trap as spin is not the correct word here, even though it is customary for historical reason. Mike was careful to specify "the spin of an elementary particle". A nucleus is a composite particle and what we call its spin shall actually be called its total angular momentum, which is the sum of the spin of its constituent protons and neutrons, and of the angular momenta arising from the relative motion of the said constituents. But a nucleus is so small at the scale of atomic physics that it almost behaves as a point particle, hence the habit which lingered to call the total angular momentum of the nucleus its spin instead.

And then, that the total angular momentum can change is not specific to the nucleus, it is also true for atoms. When their quantum state change, their angular momentum may change too.

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