In quantum mechanics, spin is an intrinsic form of angular momentum of a particle. But if we talk about classical spin how can we explain the classical spin?
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From the point of view of an observer, spin is the angular momentum in the rest frame. (By "rest" frame I mean no linear motion.) From a pure QM point of view of the "spinning" object,. there is only a quantum number that gets interpreted as spin angular momentum by external observers. The same is true of "orbital" angular momentum which, at the level of quantum states is just another number that describes how particles couple together via "vector coupling" coefficients.
Classical (non-relativistic) spin is that of a macroscopic object, such as a spinning top, a cricket ball or even a planet. It is a rotational motion about an axis passing through the object. Such a spin gives a rotational kinetic energy which is 1/2 I ω2, where ω represents an angular velocity of the object. Interestingly, all observed stars and planets display a rotational motion and a related kinetic energy.
Quantum spin is an intrinsic spin. This is a conserved quantum number which arises in the relativistic case, by which one can label quantum states. One can also classify elementary particle states by it's intrinsic spin quantum number. Unit of intrinsic spin is hbar. If a particle has zero or integral units of spin such as 0,1,2... or -1,-2,.. then it is a Boson because it follows the Bose-Einstein statistics, and if it has half integral amount of spin such as (1/2,-1/2,3/2,-3/2...) then it is a Fermion or a particle which follows Fermi-Dirac statistics.
Emrul, just another little point which I would like to mention. If you change applied torque, you can change angular velocity of a classical object. The relation is τ=Iω̇ where I is the moment of inertia and ω̇ is the time rate of change of angular velocity. However for the quantum case, the intrinsic spin is fixed for a given type of elementary particle. We do not know how to change it. That is we do not know how to convert a Fermion into a Boson. Theoretically this is done by the application of supersymmetry, which has not been experimentally found yet. This is why people think that it will be very important to discover whether supersymmetry exists or not. If the answer is yes, it will be a way to change a particles intrinsic spin.
Note: Mass and spin corresponds to two different Casimir invariant operators of the Poincare group. In the relativistic case, be it a classical theory or a quantum one, the notion of intrinsic spin of a point particle exists.
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