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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.5 Masses and Moments, #21 · Calculus · Applications of integrals

The moment of inertia around the point … of a rod with…

The moment of inertia around the point $x = t$ of a rod with density $ρ (x)$ is $I = \int (x - t)^{2} ρ (x) d x$ . Expand $(x - t)^{2}$ and $I$ into three terms. Show that $d I / d t = 0$ when $t = \overset{x}{ˉ}$ . The moment of inertia is smallest around the center of mass.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.5 Masses and Moments, #21

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