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. S

    Fully restrained beam moment diagram

    Homework Statement Find the shear and bending moment diagram for a fully restrained beam with a length of 5m, a uniform distributed load of 1kN/m from x=0 to 2m, a point load of 1kN at 2m, and another uniform distributed load of .9kN/m from x=2, to x=5. Homework Equations The...
  2. F

    Why Are Clockwise Moments Negative and Anti-Clockwise Moments Positive?

    Why are clockwise moments taken as negative and anti-clockwise moment as positive? Why not the other way around?
  3. H

    Moment of Inertia vs. Inertia Constant

    The following equations are found in the following reference (Page 119): http://www.eeh.ee.ethz.ch/fileadmin/user_upload/eeh/studies/courses/power_system_dynamics_and_control/Documents/DynamicsPartI_lecture_notes_2012.pdf By definition, the inertia constant for a synchronous machine is...
  4. J

    Moment of inertia of a suspended cylinder

    Homework Statement A uniform cylinder 20 cm long, suspended by a steel wire attached to its mid-point so that its long axis is horizontal, is found to oscillate with a period of 2 seconds when the wire is twisted and released. When a small disc, of mass 10 g, is attached to each end the...
  5. G

    Moment of Inertia of spherical masses

    Homework Statement Three small spherical masses are located in a plane at the positions shown below. The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3...
  6. R

    Moment Coefficient for a 3D Rotating Cylinder

    Hi, I'm looking for the Moment Coefficient (Cm) for a 3D Rotating Cylinder, this means, I there is a free stream of fluid and there is inmerse a cylinder rotating about its own axis , and also rotating about an axis parallel to the free stream. I found in the book of Peter Childs, called...
  7. T

    Finding rate of change of moment of inertia tensor

    Homework Statement The Wikipedia article on spatial rigid body dynamics derives the equation of motion \boldsymbol\tau = [I]\boldsymbol\alpha + \boldsymbol\omega\times[I]\boldsymbol\omega from \sum_{i=1}^n \boldsymbol\Delta\mathbf{r}_i\times (m_i\mathbf{a}_i). But, there is another way to...
  8. K

    Dipole moment of given charge distribution

    So, I've got a charge distribution given by: \begin{equation} \rho(r,\phi,z)=\frac{q}{2\pi R}\delta(r-R)\delta(z)\cos(2\phi) \end{equation} This, if I'm not mistaken, translates into a circular charge distribution located in the z-plane, a distance R from origo. Thus \begin{equation}...
  9. I

    What determines the starting point of a bending moment diagram?

    In the bottom left, why does the BM diagram start at -4kNm rather than 4kNm? I understand that if you make a cut you yield this result but if you don't make a cut how would you know whether it starts at -4kNm or 4kNm? Thanks
  10. B

    Rotating parts of a motor have a moment of inertia

    Homework Statement The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...
  11. B

    MHB Moment of Inertia: Motor, Shaft Speed & Torque Calculation

    The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of 80 kg and a solid...
  12. F

    Expression for the moment of inertia

    Homework Statement The thin, homogeneous bent rod has the mass m and the total length of 4b. It rotates with the angular speed of ω = ω0(24i + 12j - 6.0k) (only rotation) Determine the expression for the moment of inertia with consideration of the center of mass of the rod The figure...
  13. J

    Structural Mechanics. bending moment and bending stress

    [b]1. Homework Statement [b/] A timber beam, with rectangular cross section (h × b) is reinforced with additional full width (b) steel plates. There is a plate of thickness t securely connected on the bottom and a plate of thickness 2t on the top of the timber to ensure composite action in...
  14. R

    Calculating the saturation magnetic moment (Condensed Matter)

    Show that the experimental data are consistent with a Lande g factor of 2 for each of the ions by calculating the saturation magnetic moment. Explain what this means for Cr. I've calculated J using Hunds rules and have the equation M = gμJn, where M is the saturation magnetic moment. BUT...
  15. S

    Is it possible to impart a moment with soundwaves?

    Can one adjust the properties of a sound wave to use it to spin an arbitrary object of shape S in a medium comprised of the same material. My intuition tells me that it would be much more difficult (if not impossible) to do this with spherical objects, so for now we can assume the object is...
  16. R

    Resultant Moment Couple Problem

    Determine the resultant R and the point on the y-axis through which the line of action of the resultant of the loading system shown passes I have attached an image of the problem In my attempt to solve the problem I went about the following steps: 1- I chose my axis to be right in the middle...
  17. A

    Calculate the moment of inertia

    Homework Statement A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r. Assume there is no friction.The mass is released from rest and falls a distance S after time t. Find the moment of inertia of the axle.(represents I in...
  18. Z

    Relative difference between moment of inertia for the earth

    Homework Statement The Earth is slightly thicker around the equator and hence $I_{0}\neq I_{\zeta}$ I am curious in finding the angular velocity for the **precession** between using the fact that the distance between the spin axis and the precession axis is 10 meters on the surface of earth...
  19. kontejnjer

    Moment of inertia around displaced and rotated axis

    Homework Statement A homogenous disk with radius R and mass m lies in the xy plane so its center matches the origin O. Point O' is on the z axis at a distance s from point O. Axis y' passes through point O' at an angle \theta with the z axis. Find the moment of inertia around axis y'...
  20. S

    Problem on moment of inertia

    Find moment of inertia of a uniform quarter disc of radius R and mass M about an axis through its centre of mass and perpendicular to its plane ... I tried in the following way: I considered the relation. I= Icm + Md2 Where d is the distance between required axis and centre of...
  21. K

    Moment of inertia of an ellipse

    Homework Statement To calculate I, the moment of inertia of an ellipse of mass m. The radius are a and b, according to the drawing. Homework Equations I=mr^2 Ellipse: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow y=b\sqrt{1-\frac{x^2}{a^2}} Area of an ellipse: \piab The Attempt at a...
  22. M

    Finding support reactions for shear and moment diagrams

    Draw the shear and moment diagrams for the beam in the figure. Clearly show all values, including the maximum shear and maximum moment and their positions on the diagrams. Assume the supports at A and C are rollers and D is a pin support. note there is a hinge at point B. I am having trouble...
  23. M

    Question on finding moment of inertia about the center of mass

    So I have a question. I (moment of inertia) is basically mr^2 right? And r is supposed to be the distance from the axis of rotation. When the axis of rotation is directly through the center of mass, how is there Icm (moment of inertia about the center of mass). It's confusing to me, because so...
  24. Dethrone

    Deriving the moment of inertia of a thin rod.

    Homework Statement I need to derive the moment of inertia of a thin rod with its axis of rotation at the end of the rod. http://en.wikipedia.org/wiki/List_of_moments_of_inertia The third one. Homework Equations I = mr^2 The Attempt at a Solution I completely understand how the...
  25. L

    Moment of Inertia of a Wheel

    Twelve uniform, thin rods of mass and length are welded together to form a “wheel” as shown in the figure. What is the moment of inertia of this wheel for rotation around an axis through its center and perpendicular to the plane of the wheel? The welds contribute no mass to the wheel. I...
  26. Feodalherren

    Moment of inertia, double integral

    Homework Statement Homework Equations The Attempt at a Solution For part B, why is he using the formula for the moment of inertia about the y-axis? Why isn't he using the formula for the moment of inertia about the origin...
  27. carllacan

    Doubts about the electron magnetic moment.

    Hi. According to this page and other sources I found the z-component of the electronic magnetic moment is greater than the classically calculated value due to relativistic effects. Which makes me wonder: 1) What about the x and y components? I am completely lost as to why only the z axis...
  28. carllacan

    Why does the electron have a magnetic moment?

    Hi. I thought magnetic moment arose from closed loops of charge currents. How does then the angular momentum of the electron produce a magnetic moment? I mean, the electron is not a loop. Am I wrong in my initial assumption or am I understanding things too "classically"? Thanks.
  29. Rococo

    Moment of Inertia about axis through body diagonal of a Cuboid

    Homework Statement Consider a cuboid of lengths a, b and c along the x, y and z axes respectively, centred at the origin. The task is to show that the moment of inertia of the cuboid of mass M and mass density ρ about an axis along the body diagonal, from (-a/2, -b/2, -c/2) to (a/2...
  30. C

    Kinetic Moment about the center of gravity

    Hi I need some help explaining kinetic moment and moment of the center of mass. This is an example: http://session.masteringengineering.com/problemAsset/1529176/3/Hibbler.ch17.p107.jpg Okay I know that when you do moment equations: The Moment forces about some point is = to the kinetic...
  31. B

    Short webpage title: Calculating Moments of Inertia and Magnetic Moment

    Homework Statement For any flat object, located in the x-y plan applies to the equation: Ix+Iy=Iz where Ix,Iy,Iz is the moments of inertia about the x-axis, y-axis and z-axis. A flat circular coil has n windings and radius r. The mass of the coil is m. The coil is located in the x-y plan...
  32. P

    Why is Ix/Iy used instead of Iz for the mass moment of inertia?

    Homework Statement for the mass moment of inertia, why did they use Ix/Iy and not Iz? Homework Equations Ix=Iy= 1/12 m (3(r^2) + (h^2)) Iz= 1/2 m (r^2) The Attempt at a Solution
  33. B

    What is the moment of inertia of the flywheel?

    Homework Statement An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.4 MJ when the flywheel is rotating at 21,300 revolutions per minute. What is the moment of inertia of the flywheel? Homework Equations K= Ktranslational + Krotational Krot=...
  34. chongkuan123

    Rotational Energy, Moment of Inertia Problem

    Homework Statement Energy is released by the Crab Nebula at a rate of about 5×10^31W, about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once...
  35. J

    Finding the bending moment for maximum stress

    Hi, I am looking to use My/I to find the maximum bending stress for a beam My problem is I don't know how to find the bending moment- the reason why: The beam has more than one point of load, aside from the reaction points. (Pin joint cantilever beam) The sum of all moments equal 0...
  36. P

    Zero dipole moment in stationary state?

    P.W. Anderson in his essay "more is different" said that: "no stationary state of a system has an electric dipole moment". He used an example of NH3 to illustrate that. I then checked online and found that, Chemists said there is dipole moment in NH3 molecule, but (nuclear) physicists claim...
  37. stripes

    Finding the joint moment generating function given the joint PDF

    Homework Statement Homework Equations The Attempt at a Solution The problem is the integral is non-elementary, so now what? Part (b) follows trivially from part (a). But is there some kind of shortcut I have to take, because no matter what substitution I do, the integral...
  38. G

    Find Moment of Inertia Around CoM: Summation Formula & Point Mass

    How do I find the moment of inertia around the CoM of an object when the axis of rotation is not through the CoM? When Are summation formula used in equations and what exactly constitutes a point mass? regarding moments of inertia?
  39. M

    Bending Moment and Shear Force Problem

    Homework Statement Hi all, I have a problem determining the moment and shear force at a location. The moment, I think, I have already solved. But I get stuck at calculating the shear force at the same location. It is for a element that is suspended in water, thus the weight of the element...
  40. E

    Magnetic moment of singly ionized helium

    Homework Statement Find the magnetic moment of singly ionized helium in terms of Bohr Magneton I know the expression for the Bohr Magneton -- I am not trying to get a walk-through here as I want to do this myself, but I just want to know if I am correct in assuming that to get the problem...
  41. Y

    Statics - finding a moment of a force in xyz plane

    Homework Statement I attached the question. Homework Equations M = r x F M = F x d Resolving forces, Fx/Fy/Fz = F cos/sin theta (depending on which angle you take) The Attempt at a Solution I can easily find the moment of the 100 N and 120 forces, but I'm having trouble finding...
  42. E

    Moment of Intertia of a cylinder rolling inside a cylinder

    Hi all, I just have a troublesome time wrapping my head around the concept of moment of inertia of a cylinder inside a cylinder. For example, in the attached figure The moment of inertia of the cylinder with radius 'r' around the point o, according to my understanding should be I_o = I_s+...
  43. majormaaz

    Earth's Magnetic Dipole Moment

    Homework Statement The Earth's magnetic dipole moment is 8.0 x 1022 A m2. (a) What is the magnetic field strength on the surface of the Earth at the Earth's north magnetic pole? You can assume that the current loop is deep inside the earth. 6.17e-5 T (b)How does this compare to 5.0 x...
  44. I

    If you have a moment (at the end of a rod)

    Homework Statement Lets say you have some moment (given) at the end of a rod going clockwise. Do you have to factor this into the equations for forces? My professor has some notes written about it, but I don't know if he's incorrect.Homework Equations The Attempt at a Solution So if the moment...
  45. A

    Determination of moment of inertia

    Homework Statement I've been trying to find out what is the period os this kind of pendulum decribed here: http://www.eng.uah.edu/~wallace/mae364/doc/Labs/mominert.pdf The thing is, I've came to the same result shown in equation (11) but my reasoning it's different. I would even say that...
  46. B

    MHB Moment of Force F & P: Calculation & Solution

    I just don't know where did the numbers 5,4, and 3 came from. please explain. I'am asked to do this assuming clockwise moments as positive, compute the moment of force F = 200 kg and force P = 165 kg about points A, B, C, and D. the solution picture is here
  47. P

    How are moments defined and used in physics?

    moment of a force, magnetic moment, moment of momentum etc what is a moment in general?
  48. S

    Problem with the weigth of the moment arm

    Hi A rod comprises a counterweight (a) a handle and a hook which hangs mass (m), the rods mass is 400g counterweight mass (a) = 1600g and the rod is 0.8m long. Equilibrium exists when the handle is at position X = 12.0cm How I did 1: calculated the length of the handle to (m) which was...
  49. A

    What is the maximum bending moment for this beam?

    Homework Statement Problem: For the beam according to the image, solve graphical and analytical: 1.) Reactions in the supports, 2.) Bending moment diagram, 3.) Maximum bending moment Given variables: F = 14 kN q = 40 N/cm a = 100 cm b = 55 cm l = 180 cm Homework Equations This is a Beam...
  50. N

    Moment of inertia and angular velocity

    Homework Statement (a) Calculate the moment of inertia I of the disc when it rotates about the pivot as shown in the figure. (b) If the disc is released from rest, determine the angular speed, ω, of the disc at its lowest point. Homework Equations a) Id = Icm + md^2 Icm = 1/2*M*R^2...
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