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I was working on a problem of finding the kinetic that a point of a rectangular piece of wood will have after it swings and hits something. I have the following diagram:

enter image description here

The rectangle has length $L$, height $H$, and thickness $t$. I want to measure the amount of kinetic energy that point $X$ has when it hits the wall, which is a distance $r$ on the rectangle. I will be able to measure the linear velocity the moment it hits the wall, $v$. I have found the equation for energy at this point to be $E = \frac{M L^2 v^2}{6 r^2}$ by calculating the mass moment of inertia. My question now is will the friction from the hinge that connects the door to the wall affect this at all and need to be accounted for? I suspect it will not since all that would affect is the velocity, but I'm able to measure the velocity, so that will already account for it. My only other thought is that the door will have an effective mass that would be some multiple of the actual mass of the door, but I don't think that is true either and just want to confirm that I don't need to care about the friction from this hinge.

I had a previous post about this at Is mass moment of inertia measured to the point of interest or the entire object? where I explained my calculation a bit more. I have been doing a little experiment at home and was going over it and this is one of the things that crossed my mind.

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  • $\begingroup$ Mass and velocity are the only things that affect the kinetic energy of the point. Friction may have contributed to the velocity but doesn't appear in the expression of KE when that is of the form $\12 mv^2$ $\endgroup$ – Floris Sep 14 '17 at 23:19
  • $\begingroup$ Friction in the hinge will slow the door down and the kinetic energy will be lower. Your formula is definitely not accounting for it. I can't really tell what is going on in your picture but this should be a conservation of energy time problem and the whole thing should be converting potential energy into kinetic energy - energy lost due to friction. The thing I don't get is what you are trying to measure as well since kinetic energy at a point doesn't really make sense since points don't have mass. $\endgroup$ – A. C. A. C. Sep 14 '17 at 23:40
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    $\begingroup$ Kinetic energy of a point is zero, so that's your answer, problem solved! :P $\endgroup$ – Eddy Sep 16 '17 at 17:39

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