Calculating Moment of Inertia help

[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.

 

[rwisz]

Calculating the moment of inertia for a flat rectangular plate with an axis of rotation along the width can be done using the formula I = (1/12) * M * (l^2 + w^2), where M is the mass of the plate, l is the length, and w is the width.

First, we need to determine the mass of the plate. This can be done by multiplying the density of the material by the volume of the plate, which is l * w * t, where t is the thickness of the plate.

Next, we can plug in the values for M, l, and w into the formula to calculate the moment of inertia.

It is important to note that the moment of inertia is a measure of an object's resistance to rotational motion. So, the larger the moment of inertia, the more difficult it is to rotate the object. In this case, since the axis of rotation is along the width, the moment of inertia will be larger compared to if the axis of rotation was along the length.

I hope this helps with your calculations. Remember to always double check your units and make sure they are consistent throughout the calculation. Good luck!