❓Is the centrifugal force tensor symmetric?

Yes, the tensor $T^{i j}$ is symmetric. This is because the indices can be swapped: $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right)$ and $T^{j i}=m\left(\omega^j \omega^i-\omega^2 \delta^{j i}\right)$, and since $\omega^i \omega^j=\omega^j \omega^i$ and $\delta^{i j}=\delta^{j i}$, we have $T^{i j}=T^{j i}$.

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Is the centrifugal force tensor symmetric? | FAQsviadean on Notion