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Integral

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If you have ever seen a tall chimney fall, you will have observed that they break up on the way down. This is because of the effect you have found.Galileo said:Take a flat board of uniform density. Mass M and Length L.

Now hold the board horizontally at the edge of a table. So you hold one end of the board at distance L from the edge of the table, while the other end is resting on the table.

Now release the board. Gravity will exert a torque about the axis where the board touches the table. The gravitational force will act on the center of gravity of the board, so:

[tex]\tau = \frac{L}{2} Mg[/tex]

The moment of inertia of this board about an axis at the edge is

[tex]I=\frac{1}{3}ML^2[/tex]

So the board will rotate with an angular acceleration of:

[tex]\alpha = \frac{\tau}{I}=\frac{3}{2}\frac{g}{L}[/tex]

That means for the part of the board at the loose end at the moment of release an acceleration of:

[tex]a=\frac{3}{2}\frac{g}{L}L=\frac{3}{2}g[/tex]

Faster than freefall!!!

:surprised

Some of you may not be surprised by it, but I was.

I realize that the normal force at the end is responsible, but still. It's kinda counterintuitive. I didn't expect it.

Does anyone else got funny and surpising physics about which you say "I didn't expect that?".

EDIT: Fixed a typo. Thanks Brad.

What is even more interesting a cylinder falling in that manner will break into 3 large pieces and some crumbs (about .14 ) so the chimney breaks in to [itex] \pi [/itex] pieces.