What is Moment: Definition and 1000 Discussions

In mathematics, the moments of a function are quantitative measures related to the shape of the function's graph. If the function represents mass, then the first moment is the center of the mass, and the second moment is the rotational inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.
For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem).
In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematically in terms of the moments of random variables.

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  1. R

    How is moment of inertia calculated and translated between units?

    Calculating moment of inertia and translating it between units, I've become confused. The example is a mass of 1kg at 2000mm from the pivot. The force is applied at 1000mm from the pivot. Basics as far as I'm aware: Moment of inertia = mass * Distance to center of rotation^2 Torque = Moment...
  2. Romain Nzebele

    Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

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  3. LeoChan

    What is the principal moment of inertia tensor for a lamina?

    The moment of inertia tensor I found out is (1/3) (-1/2) 0 (-1/2) (4/3) 0 0 0 (5/3) The principal moment of inertia tensor I found out is (1/3-I) . (-1/2) . 0 (-1/2) . (4/3-I) . 0 0 . 0 . (5/3-I) det of principal of...
  4. D

    How to calculate the moment of inertia of a bar with two masses on it?

    I first tried to calculate the moment of inertia of the bar. The problem is that I don't understand exactly how are the dimensions of the bar. The fact that it has a width ##a## means that its height is ##a##, or that it has an unknown hight and the width is ##a##, like a parallelepiped? After...
  5. jaewonjung

    Moment of Inertia of this combined system?

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  6. H

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  7. H

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  8. A

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  9. dRic2

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  10. J

    Find the Moment about the ankle

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  11. dRic2

    Showing Charge & Currents in Vol: Proving $\mathbf{p}$ Dipole Moment

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  12. D

    Moment of inertia of a branched cantilever beam

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  13. R

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  14. M

    Electron anomalous magnetic moment

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  15. S

    A Dipole moment of an isolated quantum system

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  16. bardia sepehrnia

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  17. A

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  18. F

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  19. F

    I Arbitrary value of the moment of a force

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  20. R

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  21. F

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  22. IanAlpace

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  23. A

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  24. Taidhg

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  25. R

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  26. K

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  27. K

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  28. Edge5

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  29. H

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  30. S

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  31. S

    Moment of inertia about a perpendicular axis through its center?

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  32. some4544

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  33. R

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  34. T

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  35. T

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  36. A

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  37. B

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  38. Navin

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  39. S

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  40. Eclair_de_XII

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  41. Al_Pa_Cone

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  42. D

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  43. M

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    I was just looking at indeterminate statics problems where you have a beam, three elastic wires (left, centre, and right that are holding it up), and some extra mass. (Just like example 5 in the notes below: http://fast10.vsb.cz/lausova/indeterm_all.pdf). I understand the method that was used to...
  44. T

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  45. P

    What is the moment of inertia for a water bottle?

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  46. kasoll

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  47. Physicsterian

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  48. A

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  49. Beth N

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  50. C

    I Time Since Big Bang: One Moment Everywhere?

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