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I often stumbled across the variables for angular momentum L and axial angular momentum Lz, which would be no problem if working in cartesian coordinates, then it would be Lz = px y - py x. Unfortunately I have no idea what to make of an Lz in spherical coordinates:

For example, in equations of motion given in r, θ and φ (radius, latitude and longitude) I have pr, pθ and pφ for the momentum components. But what do I make of an Lz then? Is this the vertical (radial) momentum, or is it the horizontal momentum, or the momentum only in the θ or φ direction? Why does an Lz appear when everything else is given in terms of r, θ and φ? Is it just pθ r, or something else?

And E for the conserved energy is m/2 v² in classical mechanics and mc²γ-mc² or just mγ in relativity?

If somebody more experienced could help me I will give a thumb up!

For example, in equations of motion given in r, θ and φ (radius, latitude and longitude) I have pr, pθ and pφ for the momentum components. But what do I make of an Lz then? Is this the vertical (radial) momentum, or is it the horizontal momentum, or the momentum only in the θ or φ direction? Why does an Lz appear when everything else is given in terms of r, θ and φ? Is it just pθ r, or something else?

And E for the conserved energy is m/2 v² in classical mechanics and mc²γ-mc² or just mγ in relativity?

If somebody more experienced could help me I will give a thumb up!

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