The earth orbiting around the sun has an angular momentum. But at one moment of time, each atom on earth is moving translationally, and the combined linear momenta of all the particles on earth would equal $MV$ where $M$ is the mass of earth and $V$ the velocity of earth tangential to the rotational axis.
Then how is angular momentum not a "simplification" of calculating the linear momentum of every atom? This is like the moment of inertia being a "simplification" of adding up the force it would take to move every atom in a object (with different velocities as an object farther from the axis would need more force to get to that speed) in the direction tangent to the axis.
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