Moment of inertia for inclined plates

[abhisheak]

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?

 

[suhasm]

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.

 

[andrien]

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)

 

[abhisheak]

Thanks for your answers, i shall work on it ...

 

[K^2]

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.

 

[kajeeva]

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[abhisheak]

could anyone please work this for me?

 

[abhisheak]

please guide me in doing this ... got mad in finding out