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How the interaction between orbital angular momentum and spin angular momentum occurs to give resultant angular momentum?

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Relevant answers:

What is the difference between linear momentum and angular momentum?
angular mmtm is a cross product unlike linear momentum
When is angular momentum conserved?
Always.
Why is angular momentum quantised?
In the macroscopic world it is not.
The angular momentum of the earth is constant?
More or less. There is a law of conservation of angular momentum, according to which Earth can't gain or lose angular momentum on its own - if for example it loses angular momentum, it has to go...
Is angular momentum a vector quantity?
Angular momentum is a vector quantity. Angular velocity, which is a vector quantity, is multiplied by inertia, which is a scalar quantity.