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. C

    Moment of inertia in shear stress

    Homework Statement In the question , the author calculated the Ixx and Iyy , but he used the greater value (Ixx) in the calculation to calculate the shear stress , why did he do so ? why the greater value is used ? Homework EquationsThe Attempt at a Solution
  2. P

    Difference between second moment of area and section modulus

    Hi everyone! Please help, I have spent some considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is .. Moment of inertia is about distribution of mass, the further away from the axis...
  3. P

    Elastic Section Modulus vs Moment of Inertia

    Hi everyone! Please help, I have spent a considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is .. Moment of inertia is about distribution of mass, the further away from the axis the...
  4. J

    Equivalent Bending Moment due to Impact Formula?

    Hi guys and girls, I've been working on this problem for a little while now but I'm not really getting the result that I want. This is what I have: I have what is essentially a big pair of vice grips controlled by a hydraulic cylinder. The cylinder opens and closes both arms of the vice grips...
  5. M

    MHB Prove Moment of Inertia of Annulus w/ Radii 3m & 1m: 5m

    a uniform annulus consists of disc of radius 3 meters with a disc of radius 1 meters removed from its center. the mass of the annulus is m. Prove that the moment of inertia of the annulus about an axis through its center is 5m.
  6. AmKo3

    B Centre of Charges Coincide & Dipole Moment: Explained

    What does it mean when we say "centre of charges coincide"? What is the physical meaning of dipole moment?
  7. J

    Moment of Inertia of Massless Pulley w/String & Mass m Attached

    What is the moment of inertia of massless (ideal) pulley that has a string attached to its center and a mass m attached to that string? If this pulley were hanging from a massless rope that was attached on one side to the cieling and the other side had a tension of mg, what would be the...
  8. Brendan Webb

    Select an Economical Beam Section for Moment Requirements

    If the unbraced length of a beam is 3 m and the maximum bending moment in this unbraced segment is 312 kN-m, and also the maximum moment in the braced segment of the beam is 350 kN-m, select an economical section just based on the moment requirements. Use Table A.2M included in the course...
  9. MartinLoland

    Transfer of forces from a pulley to a beam

    Homework Statement I am trying to understand how forces transfer from a wheel / pulley onto a beam, and then calculating the resulting moment. The image describe the problem. The rope is in tension with force "S", the wheel/pulley can rotate freely without any friction. Homework Equations...
  10. C

    Calculating Moment about a Point: Understanding FDCsin and FDCcos

    1. The problem sttatement, all variables and given/known data i don't understand the moment FDC(sin18.43)(9) , I think it's wrong.. http://imgur.com/a/qPdqf Homework EquationsThe Attempt at a Solution I think it should be FDC(cos18.43)(3), am i right? the r is the perpedicular distance from D...
  11. C

    Moment about a point in trusses

    Homework Statement for moment about C, the author gave [-F_(FE)](5) +3.2(4) +6(5) = 0 i don't understand the working...Why there are moment 3.2(4) and also moment 6(5)? Homework EquationsThe Attempt at a Solution for moment 3.2(4) , it's centered at F, so ,it's not moment about C ,am i...
  12. Erenjaeger

    Calculating moment of inertia and torsion constant

    Homework Statement A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 10.0 g is concentrated around a rim of radius 0.600 cm. a) What is the wheels moment of inertia? kg m^2 b) What is the torsion constant of the attached spring? N m /...
  13. M

    Units of Inertia and Moment of Inertia

    Hi Unit of 'moment of inertia' is kg.m^2, Which I know. But about Inertia itself, is it a quantity phenomenon or quality phenomenon? What is it's unit?
  14. C

    What is the difference between first and second moments in mechanics?

    Homework Statement in my book , it stated that first moment is moment of mass , second moment as moment of inertia , is it correct ? Homework EquationsThe Attempt at a Solution IMO , first moment can also be called as first moment of inertia , with formula of Ix or Iy , whereas for second...
  15. F

    Velocity fluctuations, variance and moment in turbulence

    I'm studying CFD and I'm on turbulence. It states that the fluctuating part of velocity squared and time averaged is the variance but variance in statistical terms is the deviation from the mean squared and averaged. So what is variance in turbulent fluctuating velocity? This variance is also...
  16. F

    Area of Moment Formula Homework

    Homework Statement i'm having problem of understanding the formula of area of moment of uniformly distributed load and uniformly varying load... the shape of graph for moment of uniformly distributed load and uniformly varying load.are similar,right...
  17. C

    Moment of uniformly distributed load

    Homework Statement at R2 , is the moment wrong ? it should be 6R1 -200(2)(1) =1800 , am i right ? Homework EquationsThe Attempt at a Solution it's 200(2)(1) because the uniformly distributed load is from 2m away from R2 , so force should be 200(2) ??
  18. S

    Moment of Inertia: kg mm2 vs. mm4 - Explained

    Hello i have known moment of inertia to be kg mm2 i.e. the product of mass and distance but i was looking at the euler buckling formula and it has moment of inertia in it which has units of mm4.whats the differnece between the two inertias.please help
  19. I

    Balancing Mass: Solving for Bar Length

    Homework Statement The bar has a mass of 3 grams/cm. When a mass of 15 grams is hung on the left side, the system is balanced. Calculate the length of the bar. Homework Equations F1*r1 = F2*r2 The Attempt at a Solution I thought that the moment on the left should be equal to the moment at the...
  20. N

    Help with Magnetic Dipole Moment

    Im looking to find the resultant magnetic moment of a permanent magnet inside of a steel housing. Some of the remnant flux density is absorbed by the magnet and the field is altered. I want to figure out the total magnetic dipole including the presence of the steel housing. I've been using...
  21. C

    Why is the moment restricted at the wall 0.594)(1200)(8/3)?

    Homework Statement in the area-moment diagram , why the moment restricted at the wall is 0.594)(1200)(8/3 )? Homework EquationsThe Attempt at a Solution I think \the 8/3 should be 1+3(2/3) , am i right ? Since we know that , the centorid of triangle is 2/3 from the right end , and the...
  22. C

    Understanding Moment Direction: Analysis and Solution for Homework

    Homework Statement why does the moment -400Nm only act at region B and C? Why it doesn't act from A to C? http://imgur.com/a/5tfCg Homework Equations The Attempt at a Solution As we can see from figure, there's moment 400Nm on the beam at B at the top part and also the below part...
  23. F

    Why Is There an Extra Term in the Distributed Load Calculation?

    Homework Statement For region 8<x<12 , why there's an extra (60-30y +3.75y^2 ) - (30y-7.5y^2) ? How to get that? I have no idea at all... Homework EquationsThe Attempt at a Solution here's my working, i have divided the triangle into three parts, i gt 129-80 -75- (60-30y=3.75y^2) -...
  24. C

    Understanding Moment Diagrams: Exploring the 400Nm Straight Line Drawing Method

    Homework Statement for the moment diagram, why the 400Nm straight line is drawn from the point of moment to a only? Homework EquationsThe Attempt at a Solution Is it wrong? I think it should be drawn throughout the entire length of beam? since moment can act at anywhere on the beam...[/B]
  25. Guidestone

    Bending moment in an axis doesn´t match

    Hey guys, first of all, this isn't a homework question, I just want to know why the results are what they are. I've been trying t obtain the same numbers using moment equilibrium but they still don't match. This is the example: W are the forces applied by the gears in force-pounds. The gears...
  26. J

    Moment of Inertia for Simple Polygon

    I am trying to determine if a function I have is working correctly. The function computes the moment of inertia for a polygon. To test the function I created a polygon that has 4 points and represents a square of 4 units by 4 units. The answer I am getting is 32. I believe the answer should be...
  27. C

    Sign convention of shear force and moment on beam

    Homework Statement I don't understand why the sign of moment of beam at left (clockwise) and moment at the right of beam (anticlockwise) are considered as positive... Why we can't assume the clockwise moment as positive and anticlockwise moment as negative? Homework EquationsThe Attempt at a...
  28. F

    Solution to Problem 624: Moment Diagrams by Parts

    Homework Statement http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/solution-to-problem-624-moment-diagrams-by-parts First , 1st solution, the author taking moment about 2m from A? secondly, the 800Nm is clockwise moment, so it is positive? why the 2400Nm on the...
  29. C

    Understanding Negative Shear Force in Beams: Explanation and Graph Analysis

    Homework Statement in this notes, the shear force is negative because at LHS, shear force cause the beam to turn counterclockwise , am i right? at RHS, the shear force cause the beam to turn anticlockwise, so that the shear force is also negative? Homework EquationsThe Attempt at a Solution...
  30. C

    Sign convention of shear force and bending moment

    Homework Statement http://nptel.ac.in/courses/112107146/22[/B] in the notes, the author define upward shear force as positive (LHS) , he take downward shear force as positive as positive (RHS)? Homework EquationsThe Attempt at a Solution why the author didnt fix downward shear force as...
  31. C

    Moment at Two Ends of Beam: Understanding Variations and Direction

    Homework Statement in the first diagram , i notice that the moment is constant throughout the beam... why in the second notes, for the moment 20kNm at 2 ends of beam, why the moment varies from -20kNm to 0 from one end to another end? Homework EquationsThe Attempt at a Solution Which is...
  32. C

    Understanding Moment Diagrams: Why is the Maximum Moment at Point B?

    Homework Statement http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/solution-to-problem-403-shear-and-moment-diagrams taking this as example , we notice that the moment varies linearly (from 0 to max from A to B ) (pls concentrate on part between A and B ) , why the moment...
  33. C

    Beam Moment Solution: Finding EIy for P/2 Force in Standard

    Homework Statement for the first line of solution , i don't undertsand why the author only include one P/2 force only... Homework EquationsThe Attempt at a Solution I think it should be EIy" = 0.5Px -P(x-0.5L) -0.5P(L-x) , am i right?
  34. C

    Why is the maximum bending moment at the center w(l^2) /8?

    Homework Statement why the maximum bending moment at the center is w(l^2) /8 ? Homework EquationsThe Attempt at a Solution shouldn't it be = 0 ? when we take the moment about the center , the reaction force at the left will generate clockwise moment , while the reaction force at the right...
  35. C

    Is Shear Force Always Maximum When Moment is Zero?

    Homework Statement in the book , i was told that when the shear force is 0 , moment is maximum . However , in this question , i found that when the shear foce is 0 , the moment is also 0 . I'm wondering is the ststemnet true ? Homework EquationsThe Attempt at a Solution
  36. C

    What is the relationship between moment diagrams and the area under the curve?

    Homework Statement can someone explain about the area of moment diagram ? taking the circled part as example , why it's 0.5(2)(800)(4/3) ?why shouldn't it be (800)(4/3) ??
  37. C

    Understanding Moment in Beam: Analysis and Solution | Beam Homework

    Homework Statement refer to the circled part , i don't understand the author's working . Homework EquationsThe Attempt at a Solution I think it should be 450x - 150(4-x) -30092)(x-1) , correct me if I'm wrong . (taking moment about x ) ...
  38. C

    What is the moment of inertia I for rotation around r_cm?

    Homework Statement A massless rod of length L connects three iron masses. If the first mass (at x=0) has a mass of 1.90 kg and the second mass (at x=L) has a mass of 8.77 kg and the third mass (located at the center of mass of the system) has a mass of 148 kg, what is the moment of inertia I...
  39. F

    Moment of Inertia: Why Did Author Change Formula?

    Homework Statement we know that the moment of inertia is given by the formula of I = (ab^3) / 12 + A(y^2) ... why in the second photo , the author make it as I = 1443333- A(y^2) ? what is teh purpose of doing so , i don't understand ... Homework EquationsThe Attempt at a Solution
  40. F

    Max Bending Moment: Calculation & Formula

    Homework Statement how the author found the maximum moment = 0.29MNm ? is there any formula ? how to find it in this question ? Homework EquationsThe Attempt at a Solution
  41. F

    Location of moment of distributed load

    Homework Statement why the center of moment due to distributed load 1.11x is located x /3 from the 15kN , shouldn't it be located 2x / 3 from the 15kN end ? Homework EquationsThe Attempt at a Solution is the author wrong ? [/B]
  42. F

    Finding shearing force and moment

    Homework Statement i couldn't understand why the author take the distance of force 129kN for 4<x<6 and 6<x<8 is x-2 ? Homework EquationsThe Attempt at a Solution IMO , for 4<x<6 , the distance of force 129kN to the point should be x , where x is the distance from the 129kN to the...
  43. W

    Non-uniform magnetic fields and magnetic moment

    Hey all, I'm having some issues with electromagnetism here. Let's say we have a particle with magnetic moment ##\vec{\mu} = \mu_0 \hat{x}## and magnetic field ##\vec{B(x)} = B_0 \frac{x}{a} \hat{x}## where ##\mu_0,B_0,a## are constants. If we assume that the magnetic field ##B_0## is far, far...
  44. I

    Calculating moment of inertia of a complicated system

    Homework Statement I am currently doing a lab investigating the relationship between the moment of inertia and speed. I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through...
  45. I

    How to calculate moment of inertia of this irregular system?

    hello all, I am currently doing a lab investigating the relationship between the moment of inertia and speed. I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through...
  46. Z

    What is the moment of inertia of a sphere and how is it derived?

    I know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she got this answer 3/5 MR^2
  47. avito009

    What does moment of inertia depend on?

    I thought moment of inertia depends on mass of the object and also its shape. But prof Lewin says it doesn't depend on mass. See this video:
  48. K

    Moment of inertia of a neutron star

    Homework Statement Homework Equations rotational kinetic energy = 0.5 I ⋅ M ⋅ ω², where I is the moment of intertia, M the mass and ω the angular speed The Attempt at a Solution T = period of revolution K = kinetic energy associated with rotational moviment Since T increases with time...
  49. D

    Moment of Inertia of rod on an axis

    Homework Statement You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.700 kg . 1What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod? Express...
  50. Bhollehday

    Moment of Inertia of a System - Disk with separate masses

    Ive got the following disk I am attempting to find the torque required to turn it 1/4 turn in 1/4 second. Am I correct when I am considering I(D)=1/2mr^2 as its a disk, and I(d)=mr^2? and The final moment of inertia to be I(D)+I(d)? Here is the disk I am speaking of...
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