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Hi Mr. Dychko,
For solving for the inertia of the horizontal rod, why do we use the I = (1/12 M L^2) equation and not the I = (1/3 M L^2) equation?

Hi aheumangutman, the position of the axis of rotation affects which equation to use. The textbook has some good illustrations on pg. 210 in Figure 8-20. This particular question says the axis of rotation is positioned at the center of the rod, which is what makes the equation $I=\dfrac{1}{12}ML^2$.

All the best,
Mr. Dychko