= Angular momentum decomposition about the centre of mass
{title2=$\boldsymbol L=M\boldsymbol X\times\boldsymbol V+\sum_i m_i\boldsymbol r_i'\times\boldsymbol v_i'$}
Write each position and velocity as its <centre of mass> value plus a relative value. Expanding the total <angular momentum> gives the displayed split into orbital angular momentum of the centre and internal angular momentum about it. The cross terms vanish because $\sum_i m_i\boldsymbol r_i'=\sum_i m_i\boldsymbol v_i'=0$.
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