Four rods,each of mass M and length l,are arr | vedclass

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Question

(A) The moment of inertia of a single rod of mass $M$ and length $l$ about an axis passing through its center $P$ and perpendicular to its length is $

Vedclass · Accepted Answer

$\frac{4}{3}Ml^2$

Vedclass · Answer

(A) The moment of inertia of a single rod of mass $M$ and length $l$ about an axis passing through its center $P$ and perpendicular to its length is $I_{cm} = \frac{Ml^2}{12}$.Using the parallel axis theorem,the moment of inertia of this rod about an axis passing through the center $O$ of the square (which is at a distance $d = l/2$ from $P$) is:$I_{rod} = I_{cm} + Md^2 = \frac{Ml^2}{12} + M\left(\frac{l}{2}ight)^2 = \frac{Ml^2}{12} + \frac{Ml^2}{4} = \frac{Ml^2 + 3Ml^2}{12} = \frac{4Ml^2}{12} = \frac{Ml^2}{3}$.Since the square consists of four such identical rods,the total moment of inertia $I_{total}$ about the axis passing through $O$ is:$I_{total} = 4 	imes I_{rod} = 4 	imes \frac{Ml^2}{3} = \frac{4}{3}Ml^2$.

Four rods,each of mass $M$ and length $l$,are arranged to form a square as shown in the figure. What is the moment of inertia of this square about an axis passing through $O$ and perpendicular to the plane of the square?

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