Moment Definition and 1000 Threads

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. ognik

    Magnetic moment of current loop integral

    The question states: The calculation of the magnetic moment of a current loop leads to the line integral ∮ r x dr I am puzzled - shouldn't this be ∮ r x dl where r is the radius of the loop and dl is the small change along the loop? (I think dr would be in the same direction as r, so no cross...
  2. F

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  3. D

    Find moment of inertia via torque and acceleration parameter

    Homework Statement 2-1. A constant torque of 4 Nm is applied to an unloaded motor at rest at time t = 0. The motor reaches a speed of 1717 rpm in 4 s. Assuming the damping to be negligible, calculate the motor inertia in Nm·s2. Homework Equations T = J(eff) * dw/dt J = kg*M^2 The Attempt at a...
  4. lovethepirk

    Understanding moment of inertia values

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  5. J

    Solving a Moment Problem: Find the Answer!

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  6. S

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  7. Shaheen Uqab

    Calculate moment of inertia of a "L" angle bent in a parabola

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  8. 2

    How can calculus be applied to determine wind force and moments on a wall?

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  9. schrodingerscat11

    What does a magnetic moment of an atom mean?

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  10. K

    What does Young's Modulus x 2nd Moment of Area Equal

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  11. Fantini

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  12. C

    How to Calculate Aircraft Pitching Moment of Inertia

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  13. C

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  14. M

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  15. S

    Polar moment of inertia in a rod?

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  16. A

    Finding Pure Bending Moment for Simply Supported Beam

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  17. longnh

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  18. P

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  19. S

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  20. TrickyDicky

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  21. T

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  22. P

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  23. J

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  24. T

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  25. gracy

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  26. 462chevelle

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  27. L

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  28. R

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  29. andyrk

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  30. A

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  31. M

    Why does a hydroquinone has a non zero dipole moment?

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  32. E

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  33. M

    How Do You Calculate Shear Force and Bending Moment for a Boom?

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  34. T

    How Do You Calculate the Moment of Inertia for a Door?

    Homework Statement A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges. 2. Homework Equations I=∫x^2dm The Attempt at a Solution [/B]The way I set it up was that I made into strips of length H (height) and width dr...
  35. Dikshant

    Defining Moment: Understanding the Physical Significance of Moment in Physics

    Hii guys,i'm having problem in understanding momen. is it a effect of particular physical quantity at some distance like effect of force on some other point where it is not acting? N if it is,then why it shows effect of force 0 on where force is acting bcoz force have some effect on where it...
  36. R

    Moment of Inertia about the CoM

    Homework Statement A puck of mass 82.0g and radius 4.09cm slides along an air table at a speed of v = 1.59m/s. It makes a glancing collision with a second puck of radius 6.97cm and mass 130g (initially at rest) such that their rims just touch. The pucks stick together and spin after the...
  37. L

    Non-Uniform Gear Moment of Inertia

    I'm working on a project involving analyzing the motion of a reciprocating saw. This saw converts rotational motion from an electric motor to linear motion by means of a slider crank mechanism. The power transmission goes from motor and attached driving gear, to crank, to connecting rod, to...
  38. Crush1986

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  39. S

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  40. Q

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  41. C

    How to Graph Moment of Inertia and Frictional Torque?

    Homework Statement The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation: rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants...
  42. D

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  43. P

    Finding the Dipole Moment of a Cylinder

    Homework Statement I am trying to calculate the dipole moment of a cylinder of volume charge density ##\rho_0## of radius ##R## and height ##H## with is center coinciding with the origin. My guess is that it should be 0 because of the symmetry but I am not able to show it. Below is my...
  44. Feodalherren

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  45. D

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  46. L

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  47. S

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  48. R

    Moments Problem -- 2 friends carrying a crate up a flight of stairs

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  49. M

    A spinning space station exhibits a change in moment of inertia.

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  50. R

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