Calculating Moment of Inertia for Square Particle System

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SUMMARY

The moment of inertia for a system of four particles, each with a mass of 30 grams located at the vertices of a square with a side length of 90 cm, is calculated using the formula I = mr². The distance from the center of the square to each particle is 45 cm, derived from the hypotenuse of a right triangle formed by half the side lengths. The total moment of inertia is obtained by multiplying the individual moment of inertia by four, confirming the correctness of the approach.

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  • Understanding of moment of inertia concepts
  • Familiarity with basic geometry and right triangles
  • Knowledge of mass and distance relationships in physics
  • Ability to perform basic calculations involving squares and square roots
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Homework Statement


There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm.
What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?

The Attempt at a Solution


My idea is to use the moment of inertia I = mr^{2} (Point mass m at a distance r from the axis of rotation.)
Then the distance will be the hypotenuse of a right triangle that has each side with 45cm and putting that into the moment of inertia and multiply by 4

Is this correct?
 
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Yes, that is correct.
 
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