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24.9: Relating Angular Momentum to Angular Velocity

  • Page ID
    30521
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    It’s easy to check that the angular momentum vector is

    \(L_{i}=I_{i j} \Omega_{j}\)

    since

    \begin{equation}
    \mathbf{L}=\sum \vec{r}_{n} \times m_{n} \vec{v}_{n}=\sum m_{n} \vec{r}_{n} \times\left(\vec{\Omega} \times \vec{r}_{n}\right)=\vec{\Omega} \sum m_{n} r_{n}^{2}-\sum m_{n} \vec{r}_{n}\left(\vec{\Omega} \cdot \vec{r}_{n}\right)=\mathbf{I} \vec{\Omega}
    \end{equation}

    Exercise: verify this by putting in all the suffixes.


    This page titled 24.9: Relating Angular Momentum to Angular Velocity is shared under a not declared license and was authored, remixed, and/or curated by Michael Fowler.

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