Moments of Inertia, almost got it

AI Thread Summary
The discussion focuses on calculating the moment of inertia for a structure made of three identical thin rods welded perpendicularly. The user has identified the inertia for one rod connected to the rotation axis and for the rod parallel to the axis but is struggling to find the moment of inertia for the third rod. They are considering the parallel-axis theorem but are unsure of its applicability since the rods are joined at their midpoints. Clarification is sought on the use of the parallel-axis theorem in this specific configuration. The assembly resembles an xyz coordinate system with the midpoints at the origin, indicating that the theorem may not be necessary in this case.
sisigsarap
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The problem is:

Three identical thin rods, each of length L and mass m, are welded perpendicular to one another. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. Determine the moment of intertia of this structure.

Ok what I know is that the rod which is connected to the axis of rotation has inertia of I = 1/3ML^2
And I know that the rod which is parallel to the axis has inertia of I = ML^2

So far I have (1/3ML^2) + (ML^2) and I just need one other moment of intertia which I am having difficulty finding.

I believe I need to apply the parallel-axis theorem, but I don't understand why.

If someone could please explain why you would use this theorem it would be very helpful! Thanks!
 
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Can you elaborate? There are MANY ways to join three rods at right angles to each other. Are they joined at their midpoints, ends, something in between or other permutations?
 
The three rods are joined at their midpoints.
 
sisigsarap said:
The problem is:

Three identical thin rods, each of length L and mass m, are welded perpendicular to one another. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. Determine the moment of intertia of this structure.

Thanks!

do you mean the assembly looks some what like an xyz coordinate system with all of the centers of mass(midpoints) at the origin and rotating about one of the axes? If that's the case I don't think that the parallel axis theorem applies.
 
Yes the assembly looks some what like an xyz coordinate system with all of the centers of mass (midpoints) at the center.
 

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