According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$
But if this were true in general, wouldn't it follow that the angular momentum, $$L = \mathbf r \times (m\mathbf v),$$ is always parallel to $\boldsymbol \omega $?
Or is it simply that we can use different reference points to measure $\mathbf r$ in each formula (as appropriate), and thus we end up obliged to have tensors in our equations?
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