The three rods A,B,and C shown in the figure | vedclass

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(A) The system consists of three rods $A$,$B$,and $C$. Rod $B$ acts as the axis of rotation.$1$. For rod $B$: Since the axis of rotation passes throug

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$\frac{M L^2}{6}$

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(A) The system consists of three rods $A$,$B$,and $C$. Rod $B$ acts as the axis of rotation.$1$. For rod $B$: Since the axis of rotation passes through its longitudinal center,the moment of inertia of rod $B$ about this axis is $I_B = 0$ (assuming the rod is a thin line).$2$. For rods $A$ and $C$: The axis of rotation passes through the center of rod $B$. Since rods $A$ and $C$ are perpendicular to rod $B$ and attached at its ends,the axis of rotation passes through the center of rods $A$ and $C$ perpendicular to their length.The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to its length is $I = \frac{M L^2}{12}$.Since there are two such rods ($A$ and $C$),the total moment of inertia of the system is:$I_{total} = I_A + I_B + I_C$$I_{total} = \frac{M L^2}{12} + 0 + \frac{M L^2}{12}$$I_{total} = \frac{2 M L^2}{12} = \frac{M L^2}{6}$

The three rods $A$,$B$,and $C$ shown in the figure have the same length $L$ and the same mass $M$. If the system rotates such that rod $B$ acts as the axis of rotation,what will be the moment of inertia of the system?

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