Inertia of System: Find w/ Pink Dot & Diagonals

AI Thread Summary
The discussion focuses on calculating the inertia of a system with a rotation axis through the center of mass, indicated by a pink dot. The user initially believes the radius (r) should be the square root of 13, but is corrected that r represents the perpendicular distance from the mass to the axis of rotation, which is 3 (half of 6). This clarification emphasizes the importance of understanding the definition of r in relation to the axis of rotation. The conversation highlights the need to review definitions and concepts related to rotational dynamics. Accurate interpretation of these concepts is crucial for solving inertia problems effectively.
Hanin
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Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the rectangle).

upload_2017-12-8_20-27-53.png

 

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Review your definitions. r is the perpendicular distance from the mass to the axis of rotation, which is that entire line through the center, not the distance from the mass to the point in the center.
 
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Likes Abhishek kumar and Hanin
I think you were thinking rotation about the c.g. into/out of page.
 
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