Moment of inertia for inclined plates

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Discussion Overview

The discussion revolves around calculating the moment of inertia for a rectangular plate that is inclined at an angle other than right angles with respect to an axis passing through its centroid. The scope includes theoretical approaches, mathematical reasoning, and potential applications in physics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant inquires about the moment of inertia for a rectangular plate inclined at an angle, seeking clarification on the calculation method.
  • Another participant suggests using the projection of the plate along the plane perpendicular to the axis of rotation to find the moment of inertia, asserting that this method is valid due to the properties of the moment of inertia.
  • A different participant proposes using direct integration to calculate the moment of inertia, noting that the moment of inertia is a tensor and that the transformation law differs depending on the conditions, specifically mentioning the product of inertia.
  • One participant warns that using the formula for angular momentum (L=Iω) may yield incorrect results since the axis in question is not a principal axis of the body, although it can still be used for other calculations like angular acceleration.
  • Several participants express frustration and seek further guidance on the problem, indicating a need for additional help in understanding the topic.

Areas of Agreement / Disagreement

Participants present various methods and considerations for calculating the moment of inertia, but there is no consensus on a single approach or resolution to the problem. Multiple competing views and techniques remain in the discussion.

Contextual Notes

There are limitations regarding the assumptions made about the axis of rotation and the conditions under which the moment of inertia is calculated. The discussion does not resolve these complexities.

Who May Find This Useful

This discussion may be useful for students and practitioners in physics and engineering who are dealing with problems related to rotational dynamics and moment of inertia calculations.

abhisheak
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What is the moment of inertia of a rectangular plate making an angle except right angle or multiple of right angle with it's axis which is passing through the centroid of the plate?
 
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Just take the projection of the rectangular plate along the plane perpendicular to the axis of rotation. And now find the MOI of the projection using regular techniques. That will give you the MOI.

This works because displacing any component of a system of particles , parallel to the axis , cannot change the MOI.
 
do it in ordinary way by direct integration.you should know that the quantity is a tensor and transformation law for it is different.if product of inertia is zero then

I=Ixxcos^2(theta)+Iyysin^2(theta)
 
Thanks for your answers, i shall work on it ...
 
Keep in mind that you are dealing with an axis that isn't a principal axis of that body. So if you try to find angular momentum using L=Iω, for example, you'll get an incorrect result. It is adequate for computing angular acceleration from torque or rotational kinetic energy, however.
 
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could anyone please work this for me?
 
please guide me in doing this ... got mad in finding out
 

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