@david.watts
This is the "second post" I promised. I want to (try to) explain the "higher than G" issue that you are thinking about. So this bit of your post:
...regarding the “tip” of a rotating beam moving faster than freefall: Yes, it makes sense to me that while free falling and rotating downward the tip would be moving downward at greater than free fall.
However, is not an additional (not just gravity ) force acting on the tip? Centrifugal force would be in play, would it not? Interestingly, when studying basic physics I seem to remember that centrifugal force is not an actual force, but only an apparent one. I’ll need to check that out; I may well be wrong....
I guess a better way to say it might be that two vectors apply and not just the free fall vector. The other being of course the ‘spinning,’ or ‘rotational,’ vector. (I don’t know what else to call it, but you know what I mean.) They would be added together to get “faster than free fall.” And of course, that same tip would be travelling slower than free fall when it is rotating upward. The vectors would be, in essence, opposite in direction.
There are three distinct aspects in the three paragraphs I have quoted.
1) Your first comment
...regarding the “tip” of a rotating beam moving faster than freefall: Yes, it makes sense to me that while free falling and rotating downward the tip would be moving downward at greater than free fall.
...is true - but not for the obvious reason and there is a complication we need to watch - I'll deal with it in the third section.
2) your second paragraph is about the forces involved:
...However, is not an additional (not just gravity ) force acting on the tip? Centrifugal force would be in play, would it not? Interestingly, when studying basic physics I seem to remember that centrifugal force is not an actual force, but only an apparent one. I’ll need to check that out; I may well be wrong....
This where the concept of "free body" physics come into play. The falling beam is the simplest example of a "system" acting as a "free body" and the key aspect we need to understand is the distinction between "external" and "internal" forces. There are two "External" forces - gravity and air resistance. I will ignore air resistance for simplicity in this post. You have asked about "centrifugal force" and two issues are significant:
a) It is "internal" to the system of the falling spinning beam. It has no effect on the overall system or on falling; AND
b) Centrifugal force is an actual real force in this setting - the ends of the beam will be pulling away from each other. If you cut the beam at midpoint and insert a measuring device you could measure the centrifugal force. If you joined the cut ends with a spring the centrifugal force would stretch the spring...and I'll leave it there.
The need to separate "external" from "internal" is the foundation to understanding "free body physics" and we have started with the simplest model. I can progress to a more complicated model if we need to. Understanding the "over G" aspects of WTC7 collapse needs two full levels greater complexity but we can progress those two extra levels if you need to. (Step One - would be move to a multi element but one dimension model; Step Two - would be translate into three dimensions so we can apply to WTC7)
So we have the necessary forces identified and sorted into "internal" and "external" - Lets move on to the:
3) velocity and acceleration aspects.
...I guess a better way to say it might be that two vectors apply and not just the free fall vector. The other being of course the ‘spinning,’ or ‘rotational,’ vector. (I don’t know what else to call it, but you know what I mean.) They would be added together to get “faster than free fall.” And of course, that same tip would be travelling slower than free fall when it is rotating upward. The vectors would be, in essence, opposite in direction.
You nearly have it there - with the whole system/beam falling bodily at V
FB the falling tip has a rotational velocity of V
TR and at the beam horizontal point - the maximum and minimum VELOCITIES are V
FB + V
TR and V
FB - V
TR
It is tempting to think that there is more acceleration at those points where there is more velocity. It is a trap - I nearly fell for it myself whilst thinking about this post.
What we have added are velocities. What we are looking at is "over G" - an acceleration.
And at those maximum/minimum velocity points the added acceleration due to the spin is....zero. The model doesn't fully fail but the outcome is not as simple as it appears. We need a different model. We had one with WTC 7 North Façade - but I will pause the explanation at this stage to see if what I have posted so far helps.
And if anyone wants to identify or explain the problem with the beam/dumbbell model.
Or why the "ball and lever'" model does not have that problem.
