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. P

    What is the moment of inertia for a water bottle?

    Hi, I'm setting up an equation for initial gravitational potential energy, and I'm just wondering what the moment of inertia, I, would be for a water bottle rolling down an inclined ramp? Is it mr2 or ½mr2 Or would it be something else?
  2. kasoll

    Inertia tensor v.s pincipal axes moment of inertia

    Is there a method to calculate inertia tensor form principal axes moment of inertia? Like now we have moment of inertia: (Ix,Iy,Iz)=(20,18,25), and hot to calculate the inertia tensor like (Ixx,Ixy,Ixz Iyx,Iyy,Iyz, Izx,Izy,Izz)? I have read about this page several times, but still have no idea.
  3. Physicsterian

    Extending an aircraft landing gear that has gotten stuck

    Imagine an aircraft of which the its wing is connected to its landing gear by means of a hinge (joint), and then the gear suddenly gets stuck midway. If, subsequently, the aircraft makes a turn around its longitudinal axis (see picture), it seems to hold true that then the angle between the...
  4. A

    What is the size of the magnetic dipole moment?

    Consider the magnetic field B generated by a magnetic dipole. The intensity of B measured along the axis of the dipole, at a distance of 10 cm from the dipole itself, is 1.0 10-5 T. What is the size of the magnetic dipole moment? (μ0 =4π10-7 mkg/C2) a) 0.050 Am2 b) 5 10 -4 Am2 c) 0,1 Am2 d) 1 10...
  5. Beth N

    Equilibrium of Rigid Bodies. Rafter. What is moment arm?

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  6. C

    I Time Since Big Bang: One Moment Everywhere?

    Is the time since the Big Bang the same for every point in our universe? If so, does that imply there really is a "present" moment everywhere and not just in my immediate locality?
  7. M

    Thickness from Moment of Inertia

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  8. D

    Experimental determination of the moment inertia of a sphere

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  9. Andres Padilla

    FBD of an aerogenerator (Windmill)

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  10. Krushnaraj Pandya

    Moment of inertia of a leftover square

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  11. Math_Maniac

    Moment of Inertia of Solid Sphere - Proof

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  12. Islam Hassan

    I If the Universe’s Mass was 100 At the Moment of the Big Bang....

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  13. Krushnaraj Pandya

    Moment of inertia of a metal plate about three points

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  14. thee qs

    Magnetic moment and magnetic field and dot product

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  15. symbolic

    Moment of inertia with system of rods

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  16. BadgerBadger92

    B How large was the Universe at its moment of creation?

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  17. Prof Sabi

    Stargazing Spotting the ISS With My Binoculars: A Lucky Moment

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  18. T

    Total magnetic moment of hydrogen in weak magnetic field

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  19. R

    Where is the hinge point? & what is the moment of inertia of a square?

    Homework Statement :[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions. 1) The angular velocity of system...
  20. lc99

    How to Calculate Moment of a Couple Using Cross Products?

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  21. P

    A beam: need to calculate its max moment and deflection

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  22. Raghavendar Balaji

    Moment of Inertia of an inclined disk

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  23. WeiShan Ng

    Deriving magnetic dipole moment from multipole expansion

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  24. P

    Moment Arm: Determine Torque Vector & Qty

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  25. P

    Find the moment of inertia of a washer

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  26. P

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  27. P

    Moment of inertia of a meter stick

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  28. Muhammad Danish

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  29. Muhammad Danish

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  30. V

    Moment of inertia of a half disk about an axis

    Homework Statement Consider a half disk (of uniform density) with the flat end lying on the x-axis, symmetric about the y-axis (i.e. being cut into two quarters by the y-axis). Calculate the moments of inertia about each of the axes. Homework Equations $$I_{rr}=\sum_{i}m_ir_i^2$$ The Attempt...
  31. P

    How Is Torque Calculated in This Physics Problem?

    Homework Statement , [/B] Please see the attached picture. But I'm trying to do is figure out where this moment would be created and how much torque would be applied based upon this example. Homework Equations T = fxd The Attempt at a Solution [/B] I would suspect that any weight added to the...
  32. yecko

    Why Use Area Instead of Mass in Moment of Inertia Formula?

    Homework Statement Homework Equations I=1/12*bh^2+Md^2 The Attempt at a Solution for the highlighted 600mm^2 (and the 300mm^2 below) in the middle of the page, when finding the moment of inertia, what the solution used is an area, yet for related formula required the use as for mass in the...
  33. Matthew Titus

    Calculating Elastic plastic bending moment

    1. The problem statement, all variables, and given/known data Good day I am preparing for a strength of materials exam and I can't seem to solve this problem. I am unsure if the section below the neutral axis is fully plastic before the edge of the flange experiences the yield stress. Could...
  34. CivilSigma

    Modeling Moment and Shear Connections

    Homework Statement I am trying to model a structure that has moment connections between some beams and columns, and shear connections between the remaining beam and columns in 3D. The software I am using (S-Frame 11) gives me an error when running the analysis for the nodes that I have...
  35. F

    Why Do Airplane Wings Have a Natural Forward Pitching Moment?

    Hello Everyone, From what I read, an airplane's wing always has a forward-pitching moment which is a torque that tends to rotate the plane nose down. Is this moment nonzero for any angle of attack (zero, positive, negative)? A torque needs a force and a distance (lever arm). I think the force...
  36. Z

    What is the relationship between slope and bending moment in a penstock beam?

    << Mentor Note -- Thread moved from the technical forums, so no Template is shown >> Hi , Please I have to understand the solution of an exercice about calculating bending moment in penstock : It is assumed that maximum moment from penstock beam bending occurs at supports. The bending moment M...
  37. lc99

    Moment of Inertia in Planet System

    Homework Statement Two planets are masses stuck to end of long thin rods. These model systems (Rod + mass) will be rotated by a motor at their other end of the rod, as shown in the figure. the length of the rod is proportional to the orbital distance of the planet, and the mass at the end is...
  38. yecko

    Solve Force & Moment Homework: Why Don't Consider P at C?

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  39. C

    A Angular Moment Operator Vector Identity Question

    In my EM class, this vector identity for the angular momentum operator (without the ##i##) was stated without proof. Is there anywhere I can look to to actually find a good example/proof on how this works? This is in spherical coordinates, and I can't seem to find this vector identity anywhere...
  40. G

    I Do Polarized Atoms Imply Shifted Electron Orbitals?

    When neutral atoms become polarized from ambient EM radiation, does this automatically imply that electrons have shifted orbitals,or do they remain in the same levels but become deformed? Thanks
  41. lc99

    Quick question about moment of inertia

    Homework Statement Homework Equations I = mr^2 (point mass) The Attempt at a Solution I wasn't sure how to calculate the moment of inertia of this triangle if the axis is going through one vertice perpendicularly. Do i calculate the inerta of 2 sides with Inertia of a rod and the 3 side as...
  42. M

    Finding Magnetic Moment from Pull Force

    For an undergraduate project, I need a magnet with a magnetic dipole strength of 0.3 A*m^2. However, all distributors I can find only list their magnets in terms of "pull force" which appears to be defined as the force between a magnet and a steel plate. How do I find a magnet with the dipole I...
  43. D

    Calculate the course of the Force and Moment

    Homework Statement I shall determine the course of the normal force, the lateral force and the bending moment. And then sketch that as a graph Homework Equations All Moments are 0 All Fx = 0 All Fy = 0 The Attempt at a Solutionhere is my clear cut (is this the right Word in English ? :)...
  44. N

    How Do You Calculate Maximum Torsion in a Spring System?

    I need to find the maximum contortion of a torsion spring, for a given system. Most of the assignment I have done correct, but this last part I simply cannot get right. The pictures below is what I have used, but they are probably not necessary for this problem. In prior parts of the...
  45. W

    I Spin confusion: Stern-Gerlach experiment

    I have some serious issues trying to understand the idea of the spin in the context of the Stern-Gerlach experiment and would appreciate some assistance! Assuming that a homogenous magnetic field ##B## in the "North-wards" ##z##-direction, assume that there is a magnetic dipole moment ##\mu##...
  46. I

    Moment of Inertia Formula Query

    Hello, this formula was given to me in an exam to find the moment of inertia of an I beam, https://ibb.co/jY7ZKG However this formula seems to give a different answer to the standard bd^3/12 method, is the formula in the image wrong ? Thanks
  47. K

    Moment of inertia -- a lump of clay hits and adheres to a rotating stick....

    Homework Statement A thin stick of mass M = 3.9 kg and length L = 1.8 m is hinged at the top. A piece of clay, mass m = 0.3 kg and velocity V = 2.9 m/s hits the stick a distance x = 1.60 m from the hinge and sticks to it. What is the angular velocity of the stick immediately after the...
  48. A

    Stress generated by a bending moment

    Good day all, I have an issue regarding the theoretical concept regarding the stress generated by the skew bending in a rectangular cross section for example the formula used to calculated the stress is while when it is a circular cross section we have the following formula I really...
  49. Conductivity

    I Force-couple system equivalence: 3 moment equations

    In force-couple system equivalence, We can show that two systems are equivalent if the resultant force in both are equal and that it has the same line of action. So Rx1 = Rx2, Ry1= Ry2, Ma1 = Ma2 Now my book says we can use another form of equation: We can choose 3 point and find the moment...
  50. J

    How to calculate the moment of inertia for complex 3D shapes

    <<<moved from another sub forum, no template>>Hi, I need to calculate the moment of inertia for the component in the attached image so that i can calculate the angular momentum. Is it possible? Overall i am trying to calculate the forces on this lug as it passes around a 3" radius at 2M a...
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