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Am I being stupid? Isn't this mind-numbingly obvious? Collapse the shape into a function describing the area of the left side if you were to cut the shape at th
by fluoridation 1mo ago
Am I being stupid? Isn't this mind-numbingly obvious? Collapse the shape into a function describing the area of the left side if you were to cut the shape at that X coordinate in that orientation. On one end the function has value zero and on the other its value is the area of the shape. Is there any reason why this function might not be continuous?
- analog31 1mo agoAlong similar lines, if you hang the shape by a string, the line of the string will go through the center of mass, and you can cut along that line.
- asplake 1mo ago> 3. Why the Obvious Answer Fails: The Center-of-Mass Trap
- fluoridation 1mo agoI'm pretty sure that's incorrect. The whole point of the center of mass is that it's at the intersection of all the bisecting lines. If you slice a shape in two and you don't get two parts of equal area then you didn't pass through the center of mass.
- gus_massa 1mo agoThe vertial bisection of this: XX XX XX|XXXXXXXXXX XX XX is the | symbol, but the center of mass is near the o in the next graphic. XX XX XXXXoXXXXXXXX XX XX
- fluoridation 1mo agoYou're just asserting that. Why would the center of mass be further to the right from the vertical bisection? That would make it so the left side has a mass of 12.5 versus 8.5 on the right. If you were to pivot that shape freely from that point, it wouldn't stay balanced, it would swing until it ends up as an upside-down T.
- gus_massa 1mo agoYou must consider how far away from the point they are in the horizontal direction. https://en.wikipedia.org/wiki/Center_of_mass#Definition https://en.wikipedia.org/wiki/Center_of_mass#Definition This is very unbalanced: 30 to the right and 55 to the left. 21 21 21|123456789A 21 21 This is almost balanced (my graphic is not perfect). 38 the right and 36 to the left. 43 43 4321o12345678 43 43
- fluoridation 1mo agoFair enough. I was thinking of center of mass as equivalent to the centroid and only taking into account geometric shape, not leverage.
- analog31 1mo agoAh, thanks. Now that I think of it, the "center of mass" is the center of equal torque.
- happytoexplain 1mo ago>Isn't this mind-numbingly obvious? Yeah, I think so. >Collapse the shape into a function describing the area of the left side if you were to cut the shape at that X coordinate in that orientation. On one end the function has value zero and on the other its value is the area of the shape. Is there any reason why this function might not be continuous? Not for this reason, though...
- fluoridation 1mo agoWell, I'm listening.
- IAmBroom 1mo agoContinuous is not necessary - a break in the area can still have a halfway point.
- fluoridation 1mo agoUm, sure, but my argument is that the function will always be continuous, as long as you're slicing a single shape.
- WithinReason 1mo agonot every orientation will be
- fluoridation 1mo agoFor example?
- happytoexplain 1mo agoSorry, I wasn't challenging your logic, I was implying that it's intuitively obvious - it's funny to see the term "blindingly obvious" followed by a paragraph of formal logic.
- DougN7 1mo agoI was thinking the exact same thing. There is no way it’s not continuous (except maybe inside a black hole where space-time rules break down?)