Pauli exclusion is important in any matter that has radiated down to its ground state (such that there aren't many more transitions left to happen, if any.) These systems include:
Blocks of metal, whose electrons occupy something fairly close to one giant pile of degeneracy.
Atoms, like you...
There are fields internal to the object that can perturb the angular momenta. If this was not possible, magnetism would not experience thermal effects. See also: relaxation in NMR. Angular momentum can travel around in large thermal-energy-scale systems quite freely.
EDIT:
An external field...
Yes, the idea is that the decrease in the total spin angular momentum (m_j from all of the s-es) is balanced out by the object's macroscopic rotation. Like a reaction wheel on a satellite, except instead of reaction wheels you have lots of electrons that are having their spin projection quantum...
I just did a little napkin calculation:
delta angular momentum going from spin up to spin down = 1 hbar
delta angular momentum from relaxation = 1 hbar * (number of electrons or silver atoms) / 2
moment of inertia of 1cm radius ring = (number of atoms * mass per atom)*( 1cm^2 )
Angular...
There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.)
I...