quality:corruption
Single particle case

In the case of a single particle moving about the arbitrary origin, r i = v i = 0, r = R, v = V, m = M, {\displaystyle {\begin{aligned}\mathbf {r} _{i}&=\mathbf {v} _{i}=\mathbf {0},\\\mathbf {r} &=\mathbf {R},\\\mathbf {v} &=\mathbf {V},\\m&=M,\end{aligned}}} ∑ i r i × m i v i = 0, {\displaystyle \sum _{i}\mathbf {r} _{i}\times m_{i}\mathbf {v} _{i}=\mathbf {0},} ∑ i I i ω i = 0, {\displaystyle \sum _{i}I_{i}{\boldsymbol {\omega }}_{i}=\mathbf {0},} and equations (2) and (3) for total angular momentum reduce to, L = R × m V = I R ω R. {\displaystyle \mathbf {L} =\mathbf {R} \times m\mathbf {V} =I_{R}{\boldsymbol {\omega }}_{R}.}