Relation between particle spin with gradient

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Can we approach spin by gradient. For example, spin 1/2 can be written as 180 degree turning in 360 degree space while spin 2 is 720 degree turning in 360 degree space?

If I have a ball spinning with angular momentum perpendicular to rotation plane, what is the spin value of the ball? Can some object wobble in the space so the angular momentum is not perpendicular to rotation plane (forming angle)? If that so, what is the spin value of that object?
 
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