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. Buzzdiamond1

    What is the formula for calculating the moment of inertia of a double cone?

    What is the correct formula for a double cone, is it 3/10 mr^2, or 3/5 mr^2..?
  2. Andrew VanFossen

    Moment of Inertia: Non Uniform Rod

    Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...
  3. P

    Moment of Inertia of a hollow cone about its base

    Homework Statement Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)## Homework Equations ##I=\int r^2dm## where r is the perpendicular distance from the axis Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}## The...
  4. P

    Induced Magnetic Moment (vector) vs. Induced EMF (scalar)

    When I induce magnetic flux through a closed loop, I should expect the lines of flux produced by current in that loop to oppose the change of flux through that loop. But what happens when that loop, say a rectangular loop, is curved into the shape of the letter J (like a candy cane) and my flux...
  5. bluejay27

    A more direct approach in determining moment of inertia?

    is there a directly knowing the moment if the moment of inertia would be lower for an object? I am emphasizing on knowing the value of the constant value. For a sphere is 2/5 and for a cylinder 1/2, this constant values will be placed at c of cMR^2 without directly going into calculus. A...
  6. A

    Moment of inertia of a wheel: linear to angular motion

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  7. Sudhir Regmi

    A Spin magnetic moment in half metals.

    I read that the stoichiometric half-metallic compound has integer spin moment. For this, n(up)-n(down) should be integer. Since n(up) +n(down) is always integer, either n(up) or n(down) should be integer to make total spin moment integer. I could not understand how the presence of energy gap in...
  8. M

    Calculate the moment and the sag

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  9. R

    If evolution is true then why there is a monkey until this moment

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  10. N

    I Resultant force after adding a force to a couple moment?

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  11. F

    Moment of inertia in shear stress formula

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  12. kamhogo

    What is the force exerted by each hinge on the door?

    1. Homework Statement The door has a mass of 30 kg, is 200 cm long and 90 cm wide. The hinges are installed at 25 cm from the bottom (R2) and 25 cm from the top (R1). What are is the magnitude of the force exerted by each hinge on the door? The door is in a state of static equilibrium...
  13. deusy

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  14. J

    Can a force generate rotation with moment arm=0 ?

    I wait for your thoughts on this topic... and maybe then I will give you a small surprise. edit: Ok, there was a misconception on my side that I want to clarify changing the original title by this one: If there are two planets, rotating one around the other, and only gravity is acting. Is it...
  15. T

    B The moment we observe superposition

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  16. C

    Shape of bending moment diagram

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  17. C

    Is Torque the Same as Moment of a Force? A Confusing Semantic Issue

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  18. D

    A Dipole moment at the sub atomic level

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  19. C

    Replacing 10kip Load at 2ft: Understanding Forces and Moments in Beam Structures

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  20. C

    Graph of bending moment doesn't return to 0

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  21. K

    A Calculation of magnetic moment of an atom in the compound

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  22. C

    Shear force diagram and bending moment diagram

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  23. R

    Moment about a point in an incline plane

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  24. R

    Moment about a point of a hammer

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  25. R

    Moment about a point of a crane

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  26. Destroxia

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  27. RJLiberator

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  28. BiGyElLoWhAt

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  29. L

    Finding Moment of Inertia of a wheel experimentally

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  30. M

    How do you calculate the moment of a spinning wheel

    What is the moment of the wheel. Dimensions: r= 1 m h= 5 cm m= 1000kg a = 4120 rad/s2 I used the formula T = I * a The moment of inertia can be calculate by Iz =(1/2)mr2or Ix=Iy= (m/12)* 3r2 +h2) wich one do i need to use?
  31. Vanessa Avila

    Statics: Finding the moment on point B?

    Homework Statement [/B] Determine the moment about point B of each of the three forces acting on the beam. Homework Equations M = F*d⊥ The Attempt at a Solution I went and found the components for each of the forces. Please double check it if I did them right: F1 : Fx = 0 Fy = 375 lb F2: Fx...
  32. Frankenstein19

    Help with Statics -- Moment of a Couple

    Homework Statement This is the problem I'm having problems with. Homework Equations M=F x r The Attempt at a Solution Let me explain what I've been doing with the practice problems before it, because I fear I may have the wrong understanding. For this exercise I just found the...
  33. C

    Calculating Moments Using the Method of Joints: A Tutorial

    Homework Statement For the moment about B , Cy(0.8) +Ay(0.8) + Cx(0.6) = 0 , right ? Why the author only give ,-Ay(0.8) = 0 Is it wrong ? Homework EquationsThe Attempt at a Solution
  34. E

    I Moment and the Larmor precession

    Hi, In the Larmor precession, we tend to define the magnetic moment as the current multiplied by the surface (for an electron rotating around a nucleus), sometimes this moment is defined (generally) as the sum of the vectoriel products of half of the position vector and the charge times the...
  35. Amru123

    About which axis the moment of inertia of A body is minimum

    I remember my teacher saying it to be the axis along the centre of mass but the centre of mass has all the mass concentrated in it and hence moment of inertia should increase as moment of inertia is proportional to mass?
  36. T

    Statics Homework: Finding Tension and Force in a Walkway Supported by Rollers

    Homework Statement Given: A 300 kg walkway supported by two rollers(at points A and B) with center of mass at G. Find: The tension T in the horizontal cable attached to the cleat at point B and the force under the roller at A. Homework Equations ∑M = 0 ΣFx = 0 ΣFy = 0 The Attempt at a...
  37. S

    Moment of Inertia for connected, hinged panels

    Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...
  38. M

    How to find the maximum moment of a force about an axis?

    Homework Statement Calculating the moment of force F about the axis isn't hard; how do I determine how to produce the maximum moment? Homework Equations Maxis = ûaxis ⋅ (r×F) F = 30N (This doesn't change at all during the problem) The Attempt at a Solution I would guess that since the...
  39. Alex Katko

    What variables are needed to find a moment?

    Homework Statement You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures. Homework Equations Mo = r x F The Attempt at a...
  40. J

    Moment effect of canoe paddle stroke

    Videos of racing canoes/kayaks show some submersion or greater draft of aft area during each paddle stroke. If we disregard entry and exit and assume power is applied straight back in direction parallel to water surface at a point perhaps 2ft below water surface please explain how and why this...
  41. JulienB

    Direction of dipole moment in e-field of another dipole

    Homework Statement Hi everybody! I'm trying to solve a problem about dipoles, but there is something I don't quite get about it. Well, first here is the problem: An electric dipole ##\vec{p}_1## is placed at the zero-point and shows in the z-direction. A second electric dipole ##\vec{p}_2##...
  42. S Aditya

    About the Orbital Dipole Moment

    I was going through the chapter Chemical Bonding in one of the books and found something about orbital dipole due to lone pairs. In each diagram the orbital dipole due to lone pair was directed from the central atom to the end of the hybridized orbital (lone pair). Why is that so?
  43. M

    MHB Moment of Inertia: Disc+Point Mass | Help Needed

    Find the moment of inertia of a disc of mass m and radius r with a point mass of m on its circumference. i can't work this out can someone help me. i can work out that the moment of inertia of the disc is 1/2mr^2 but i don't know what to do with the point mass. i think it could have to do with...
  44. T

    Does a Magnetic Moment μ exist for any closed current loop?

    I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...
  45. 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
  46. 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...
  47. 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...
  48. 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...
  49. 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.
  50. 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?
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