Moment of Inertia: Proving Mass, Side & Axis | 1/12 md²

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SUMMARY

The moment of inertia of a uniform square with mass m and side length d about an axis through its center, parallel to one side, is definitively proven to be 1/12 md². This conclusion is reached through the application of integration techniques, which are essential for deriving the moment of inertia. Participants in the discussion emphasize the importance of writing out the integral and performing the integration to validate the proof. The process involves understanding the definition of moment of inertia and applying it correctly to the given shape.

PREREQUISITES
  • Understanding of moment of inertia and its definition
  • Basic knowledge of integration techniques
  • Familiarity with uniform shapes in physics
  • Concept of axes of rotation in rigid body dynamics
NEXT STEPS
  • Study the derivation of moment of inertia for various shapes
  • Learn advanced integration techniques relevant to physics
  • Explore applications of moment of inertia in engineering contexts
  • Investigate the relationship between mass distribution and moment of inertia
USEFUL FOR

Students of physics, mechanical engineers, and anyone interested in understanding the principles of rotational dynamics and moment of inertia calculations.

Chadi B Ghaith
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I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
 
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Chadi B Ghaith said:
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.
 
BvU said:
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.
Hi,
Yes I know the definition of inertia. What I am asking is how to prove the above statement. I am bit confuse in procedure.
 
Good you know it. Write down the integral and attempt to do the integration in your next post. The outcome of your calculation is your 'proof'.
 

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