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11.6: Moment of Inertia
https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/11%3A_Rotational_dynamics/11.06%3A_Moment_of_Inertia
Using the linear mass density, the mass element, $\Delta m$ , has a mass of: $\begin{aligned} \Delta m = \lambda \Delta r\end{aligned}$ The rod is made of many such mass elements, and the moment of...Using the linear mass density, the mass element, $\Delta m$ , has a mass of: $\begin{aligned} \Delta m = \lambda \Delta r\end{aligned}$ The rod is made of many such mass elements, and the moment of inertia of the rod is thus given by: $\begin{aligned} I &= \sum_i \Delta m r_i^2 =\sum_i \lambda \Delta r r_i^2\end{aligned}$ If we take the limit in which the length of the mass element is infinitesimally small ( $\Delta r \to dr$ ) the sum can be written as an integral over the dimension of th…

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