Last moment of inertia problem I have

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SUMMARY

The problem involves calculating the moment of inertia for a system of four small spheres, each with a mass of 0.200 kg, arranged in a square with a side length of 0.400 m. The moment of inertia (I) is determined using the formula I = mr², where 'm' is the mass and 'r' is the distance from the axis of rotation. The correct distance from the center of the square to each sphere is 0.2828 m, derived from the diagonal of the square divided by 2. The user struggled with calculating the distances correctly, particularly in applying the components of the vectors to find the correct distances from the axis of rotation.

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  • Understanding of moment of inertia and its calculation
  • Familiarity with the formula I = mr²
  • Basic knowledge of geometry, specifically properties of squares
  • Ability to perform vector component analysis
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Homework Statement


Four small spheres, each of which you can regard as a point of mass 0.200kg , are arranged in a square 0.400m on a side and connected by light rods .

Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure).

YF-09-29.jpg



Homework Equations


I = mr2


The Attempt at a Solution



Okay now where I am having trouble with this one is finding the distances of these particles from the axis of rotation. When thinking on it, It seemed that I could use components to find a vector that reaches out to the particles. (the y and x components would both be .2m and the angle at 45degrees). But in doing this, my answer wasn't right. I don't know if I am missing something mathematically here but how does one go about finding that distance?
 
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