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183_notes:moment_of_inertia_ex [2014/11/03 00:07] – [An Example: Moment of Inertia for a Rod Spun About its Center] caballero | 183_notes:moment_of_inertia_ex [2014/11/03 00:08] (current) – [An Example: Moment of Inertia for a Rod Spun About its Center] caballero | ||
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The integral is then calculated to find the momentum of inertia for the rod about its center, | The integral is then calculated to find the momentum of inertia for the rod about its center, | ||
- | $$I = \dfrac{M}{L} \int_{-L/ | + | $$I = \dfrac{M}{L} \int_{-L/ |
$$I = \dfrac{M}{3L}\left[\dfrac{L^3}{8} + \dfrac{L^3}{8}\right] = \dfrac{M}{3L}\dfrac{2L^3}{8} = \dfrac{1}{12}ML^2$$ | $$I = \dfrac{M}{3L}\left[\dfrac{L^3}{8} + \dfrac{L^3}{8}\right] = \dfrac{M}{3L}\dfrac{2L^3}{8} = \dfrac{1}{12}ML^2$$ | ||
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+ | which is precisely the moment of inertia of a rod about it's center. | ||