Moment of inertia of rectangular plate rotating about axis parallel to width

[paddlewheel99]

How to Calculate Moment of Inertia for a flat rectangular plate of length 'l' & width 'w' with axis of rotation along the width 'w' (the axis of rotation is parrallel to edge of width)

 

[berkeman]

How to Calculate Moment of Inertia for a flat rectangular plate of length 'l' & width 'w' with axis of rotation along the width 'w' (the axis of rotation is parrallel to edge of width)

This should help you out:

http://en.wikipedia.org/wiki/Moment_of_inertia

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[paddlewheel99]

No actually it is not easy as it looks. After doing a lot of googling, i got the required equation on http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia
the equation is: I = bh^3/3
Can anyone give a link to the complete derivation of this formula or provide it themselve.
With the complete calculus and intergration involved in it.
Also will the parrallel axis theorem have any role in the derivation.
Thank You

 

[Doc Al]

the equation is: I = bh^3/3

Careful... that's the area moment of inertia. (You'd need to multiply by the density.)

What you want is simpler (but equivalent, of course). Hint: Can you find the moment of inertia of a stick (thin rod) about one end? That's the same problem, believe it or not.