'Spin' is an intrinsic property of many subatomic particles - it's been likened in some ways to the 'angular momentum' of a spinning ball, - but more accurately is a mathematical 'vector' or 'property'.
After the discovery that protons are composed of three quarks and their associated 'gluons', it was assumed that the proton's spin property must be derived from the 'spin' of its constituent quarks.
A 1987 experiment at CERN (which has subsequently been replicated by other experiments) showed that this is not the case. It's now thought that the quarks only contribute between 4% and 24%.
This surprising and puzzling result was termed the “proton spin crisis”. The problem is considered one of the important unsolved problems in physics.
Source : Wikipedia
Note that the as yet unexplained anomaly also applies to the Neutron, which is also built from three quarks.
For a technical description, see The Spin Structure of the Nucleon Reports on Progress in Physics Volume 82, Number 7,at arXiv.org
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