Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.5 Masses and Moments, #22 · Calculus · Applications of integrals

A region has … if

A region has $\overset{x}{ˉ} = 0$ if $M y = \int x (height of strip) d x = 0$ . The moment of inertia about any other axis $x = c$ is $I = \int (x - c)^{2} (height of strip) d x$ . Show that $I = I y + (area) c^{2}$ . This is the parallel axis theorem: $I$ is smallest around the balancing axis $c = 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.5 Masses and Moments, #22

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