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. P

    Relativistic angular moment of electron in electric field

    Homework Statement Consider an electron with spin ##\vec{S}## and magnetic moment ##\vec{\mu}=-\frac{e}{m}\vec{S}##. It is moving with the velocity ##\vec{v}(t)## relative to the inertial frame of reference ##I## through the electric field ##\vec{E}##. Calculate the angular momentum the...
  2. F

    Volume moment to mass moment

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  3. Ssnow

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  4. G

    Constraint of moment about an axis

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  5. Suraj M

    Magnetic moment and magnetic properties

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  6. A

    Understanding Dipole Moment: The Measure of Electric Strength Explained"

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  7. R

    Relative orbital angular moment in nuclear reactions

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  8. S

    Resultant Moment of Force Around Point O: 20 Nm Clockwise

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  9. D

    Producing a shearing force diagram and bending moment curve

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  10. J

    Derivation of moment of inertia of a solid sphere

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  11. H

    What is the required force on the handle for 850N?

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  12. A

    How to Calculate the Moment of Inertia for a Half Disk System?

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  13. I

    Electric field of dipole moment

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  14. Arman777

    Moment of Inertia of Half Ring (Half Circle)

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  15. dumbdumNotSmart

    Angular acceleration in moment of inertia

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  16. NinjaChachi

    Physics Lab Help - Moment of inertia and acceleration

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  17. vetgirl1990

    Moment of inertia for composite objects

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  18. G

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  19. I

    Moment of inertia of a cylinder

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  20. vetgirl1990

    Moment of inertia for composite object

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  21. T

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  22. W

    Finding second moment of inertia about x axis

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  23. D

    Shear force and bending moment diagrams question

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  24. U

    What is the Momentum Change in Pairs Figure Skating?

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  25. M

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  26. W

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  27. tshah321

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  28. R

    Total Moment of Inertia of Two Rods

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  29. C

    Finding moment of inertia of irregular object with calculus?

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  30. A

    How do you find linear density given mass per kg?

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  31. S

    Calculating Moment of Inertia Homework: Soccer Ball

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  32. A

    Moment of Inertia of Rod About Axis XX': ML2/3sin2α

    1. The problem statementα, all variables and given/known data The moment of inertia of a Rod over an Axis XX' passing through the center of mass of the Rod at an angle α is- Homework Equations Moment of Inertia of Rod about the end, I =ML2/3 The Attempt at a Solution I=ML2/3 Answer of the...
  33. little neutrino

    Finding k from Moment Generating Function at t=0

    Homework Statement If M[X(t)] = k (2 + 3e^t)^4 , what is the value of k Homework Equations M[X(t)] = integral ( e^tx * f(x) )dx if X is continuous The Attempt at a Solution I tried differentiating both sides to find f(x), but since it is a definite integral from negative infinity to infinity...
  34. dumbdumNotSmart

    What is the acceleration of a cylinder when a torque is applied to it?

    Homework Statement Got a spicy one for you today. There is a cylinder of mass 5kg (M) with no angular velocity and no velocity, on a surface of static friction constant μ=0.6 . It's radius is .1 meters (R). Its baricentric moment of inertia is characterized by I=.5MR^2 . Gravity is 10m/s...
  35. K

    Fixed Support Moment Homework: Find Moment at Point A

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  36. little neutrino

    Statistics - Moment Generating Functions

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  37. RJLiberator

    Calculation of Seismic Moment

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  38. C

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  39. J

    Finding the friction before slipping

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  40. T

    Lab experiment on moment of inertia dynamic

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  41. S

    How Do You Calculate the Moment of Inertia for a Tapered Tube?

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  42. J

    How does the mgf relate to the probability distribution?

    mgfs can be used to find the moments of a random variable with relative ease. But you have to evaluate the function at t=0. Many times these functions are such that t can be all real numbers. How would you interpret an mgf evaluated at t=1. How does t relate to the probability distribution.
  43. J

    Same Moment Generating Function, Same Prob. Distribution

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  44. D

    Solving Torque & Moment: Deriving V=PQsintheta

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  45. Kushwoho44

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  46. W

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  47. C

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  48. David Lewis

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  49. G

    How Does Torque Apply When Using a Screwdriver or Nut Driver?

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  50. G

    Moment about distributed load (trapezium)

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