Determining the Moment of Inertia about an angle θ to the x axis

AI Thread Summary
The discussion revolves around calculating the moment of inertia about an angle θ to the x-axis. Participants express skepticism about using the components of inertia since it is a scalar quantity. The Perpendicular Axis theorem is deemed unsuitable because the required inertia is in the same plane. An alternative approach is suggested, involving an axis GH that lies in the plane of the square and is perpendicular to a specific line. The conversation concludes with gratitude for assistance in resolving the issue.
pranjal verma
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Homework Statement
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides.CD is a line in the plane that passes through the centre of the plate and makes an angle θ with the axis AB as shown in figure. The moment of inertia
of the plate about the axis CD is equal to
Relevant Equations
I[SUB]z[/SUB]= I[SUB]x[/SUB] + I[SUB]y[/SUB](Perpendicular Axis theorem)
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  • I thought about solving it using components of IAB but since it is a scalar quantity it doesn't seems to be correct .
  • I don't think Perpendicular Axis theorem will work as required Inertia is in the same plane.
 

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pranjal verma said:
I don't think Perpendicular Axis theorem will work as required Inertia is in the same plane.
This theorem might be useful. Consider an axis GH that lies in the plane of the square, passes through the center, and is perpendicular to CD.
 
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TSny said:
This theorem might be useful. Consider an axis GH that lies in the plane of the square, passes through the center, and is perpendicular to CD.

Thank you very much sir for helping me.
 
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