Relation between particle spin with gradient

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The discussion explores the relationship between particle spin and angular momentum, suggesting that spin can be conceptualized through the lens of rotational gradients. It highlights that a spin-1/2 particle can be represented as a 180-degree rotation in a 360-degree space, while a spin-2 particle requires a 720-degree rotation. The conversation also raises questions about the spin value of a ball with angular momentum perpendicular to its rotation plane and the implications of wobbling objects that do not maintain perpendicular angular momentum. Participants are encouraged to reference existing threads that debunk the notion of directly associating quantum spin with classical spinning objects. Overall, the thread emphasizes the complexity of understanding spin in quantum mechanics.
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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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Please note that there are numerous threads already indicating the myth of the spin quantum number being associated with the classical object spinning. Browse through threads in the quantum physics forum.

Zz.
 

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