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When do we use L=r x P and L=I x Omega (angular velocity)?
in old 8.01x  Lect 24, I pasted here link of the lecture, which will take you at exact time (at 27:02)he says "spin angular momentum" in classical physics lecture and why? I expected to hear "angular momentum" vector.
Normally, "spin angular momentum" we deal with it in quantum mechanics.
So, how should I understand this correctly when to use L with moment of inertia or when to use L with r x P? I know both dimensionally equal.
My current understanding is that, I would use L with moment of inertia, when I see object spinning with mass isolated itself with different 3d solid or hollow geometry. Since we have each formula for respective moment of inertia.
I would use L= r x P when I see planetary motion in orbits objects separated by distance "r" or to prove Kepler's second law.
Can we independently take different vectors using right hand rule (individually) and combine actual direction of torque, angular momentum, etc into one diagram of cross products ? This combination in itself is a new vector perpendicular to plane of two vectors (taken from right hand rule) ? although they do not form a formula in combination ?
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