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.

View More On Wikipedia.org
Recent contents Top users
  1. D

    Magnetic moment and current of permanant magnet

    Every magnetic dipole has a magnetic moment associated to it. Magnetic moment of electromagnets could be found by ##M = iA##. But for permanant magnets how it is measured? If we use this formula it implies that there must be some internal current flowing in permanant magnet. Is it true? What...
  2. physea

    How Does a Flywheel Begin to Move with Constant Speed After Adding a Mass?

    For this problem, I don't understand how can the system be at rest and immediately after placing the mass, to move with constant speed. But anyways, can you tell me please how to proceed? On the hanging mass, there is mg acting and T the tension of the rope. On the flywheel, the tension of the...
  3. alaa amed

    Why would his weight be zero at the moment of the fall?

    Homework Statement A person of weight w is in an upward-moving elevator when the cable suddenly breaks. What is the person's apparent weight immediately after the elevator starts to fall?
  4. Daisy Muller

    Moment of Inertia of pulley

    1. Homework Statement In each question: you place mass m on the mass holder, and released the system from rest. The system includes the long rod with two point masses on it (see the picture next to the list of equipment). Since this is a rotational and translational motion, I set up two...
  5. C

    Total magnetic moment of simple system.

    Homework Statement If there's a current I flowing through the rectangular conductor and it's located in the magnetic field in such way that normal vector of the surface that this rectangle forms closes the angle of 60 degrees with magnetic induction vector find total magnetic moment of this...
  6. Halest0rm3

    Statics problem(simple beam/three supports/one moment)

    Homework Statement I have to solve for Ay, By, and Cy reaction forces. The constant C is a couple acting at A in a clockwise direction Homework Equations Sum of all forces = 0 Sum of Moments about any point = 0 The Attempt at a Solution I solved for all four reaction equations(one force sum...
  7. S

    Determine the absolute maximum bending stress of the beam.

    Homework Statement If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa. Homework Equations I'm not too sure how to go about my calculations. Please help! The Attempt at a Solution I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6 F = 74*24*1000? [/B]
  8. S

    Thin rod w/linear charge density, dipole moment

    Homework Statement A thin rod of length 2L has a linear charge density that isλ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero. Given E = −kλ0/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d)) for a point P that is...
  9. K

    I How can we increase the second moment (moment of inertia) in a physical system?

    Hi there, I am reading a math book with a lot of examples on mechanical physics. I saw a math term about second moment. In wiki, it is said that second moment is just moment of inertia in physics and has definition as below ##\int(x-\mu)^2f(x)dx## here ##\mu## is the average and ##f(x)## is...
  10. i_hate_math

    Moment of inertia rigid body problem

    Homework Statement A rigid body is made of three identical thin rods, each with length L = 0.530 m, fastened together in the form of a letter H, as suggested by the figure here. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body...
  11. P

    Moment of inertia avoid double integral?

    Homework Statement Determine the moment of inertia of the shaded area about the x-axis. Homework Equations I(x)= y^2dA The Attempt at a Solution In order to determine the moment of inertia of the shaded area about the x-axis I first looked at the portion above the x-axis, integrate it with...
  12. S

    Does Adding Multiple Point Loads on a Continuous Beam Reduce the Maximum Moment?

    Is the moment in a continuous beam maximum when there is one point load because if you had multiple point loads they would cancel each other out since there are several pin connections along the beam? For example, if I had a 20 kip load moving across a continuous beam and found the maximum...
  13. i_hate_math

    Question on Moment of Inertia/Rotational Inertia

    Homework Statement In the figure, a wheel of radius 0.42 m is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to a 2.7 kg box that slides on a frictionless surface inclined at angle θ = 28 owith the horizontal. The box accelerates down the...
  14. P

    Moment of inertia (double integral)

    Homework Statement Determine the moment of inertia of the shaded area about the x axis.[/B]Homework Equations Ix=y^2dA The Attempt at a Solution Okey so I now get how to do this the standard method. But I want to know if the method I tried is correct as well or where my mistake lies. My...
  15. P

    Moment of inertia of a collinear system of particles

    Homework Statement Landau&Lifshitz Vol. Mechanics, p101 Q1 Find the moment of inertia of a collinear set of molecules Homework Equations I=sum m_i*(r_i^2) The Attempt at a Solution r_i= r_i'-r_cm where r_cm=sum m_i*r_i/sum m_i I=sum m_i r_i^2 I= 1/M sum m_i m_j (r_i' - r_cm)^2 I=1/M sum m_i...
  16. H

    Prove principal axes of moment of inertia are orthogonal

    What does the first two equations mean? I can't make sense of the notations. Does it mean taking the x-axis to be parallel to one principal axis and the y-axis to be parallel to the other principal axis? Source: http://hepweb.ucsd.edu/ph110b/110b_notes/node29.html EDIT: I figured it out. They...
  17. Rheegeaux

    Moment of inertia of a cross system

    Homework Statement Two identical rods, each with mass 5.00 kg and length 2.00m are welded as shown in the figure. If the moment of inertia of a rod about an axis passing through its center is Icm = 1/12ML2, what is the moment of inertia of the system of rods about an axis perpendicular to the...
  18. K

    I Simple Fulcrum Force Calculation Question

    Hello all, I have a (at what first seemed) fairly simple question about calculating the forces on this fulcrum design I have. Here is an image of the sketch and free body diagram that I drew: Basically, the pivot point in my real life application is actually a cam, but for the sake of this...
  19. G

    Moment of Inertia of dysprosium-160

    Homework Statement The nucleus dysprosium-160 (containing 160 nucleons) acts like a spinning object with quantized angular momentum, L2 = l(l + 1) * h_bar2, and for this nucleus it turns out that l must be an even integer (0, 2, 4...). When a Dy-160 nucleus drops from the l = 2 state to the l =...
  20. Narwhalest

    Moment of thin Rod at pivot when acted upon by a Force

    This is of my own interest/ practice. Homework Statement A thin rod (of width zero, but not uniform) is pivoted freely at one end about the horizontal z axis , being free to swing in the xy plane (x horizontal, y vertically down). Its mass is m and its CM is a distance a from the pivot. The...
  21. M

    I Second moment of area of a quad copter arm?

    does anyone know how to calculate the second moment of area of a typical quadcopter arm like this? what should I approximate the cross section as...
  22. F

    Magnetization (M) / magnetic moment (m) of NdFeB?

    Dear All, Hi, I am pretty new in the area of magnetism. Please pardon me for some questions that might be pretty fundamental and basic here. I am trying to understand the difference between magnetic moment and magnetization. I thought I understood magnetization as the degree to which a magnet...
  23. zaakir

    Calculating Shear Force and Bending Moment

    hi all Basically I need to find the shear force and bending moment of a beam using octave. The length of the beam as well as forces and their distances are given. However the SF and BM must be calculated at every o.ooo5m. The forces can be Point Loads or Uniform Distributed Loads and there can...
  24. pbutter

    What gives rise to a magnetic moment in a proton/neutron?

    Homework Statement Describe, with examples, what is meant by magnetic moment. What gives rise to a magnetic moment in a proton/neutron? Homework Equations The Attempt at a Solution I know what a magnetic moment is, just struggling with the other parts of the question. So what I'm thinking is...
  25. firefox

    Negative Moment of Inertia from Atwood Machine Experiment?

    I'm currently completing an Atwood Machine Experiment with two 100g weights on either side of the pulley, with a variance in weight created by attaching dimes and pennies to either side of the weights. The point of the experiment is to validate: (m1 – m2)g = (m1 + m2 + I/R2) Homework Statement...
  26. JulienB

    Angular momentum and moment of inertia

    Homework Statement Hi everyone! I'm preparing an exam and reviewing some old problems until then, to clear up some misconceptions I might have! A stiff massless bar is frictionless rotatable about a point O. Two mass points m1 and m2 are fixed at its ends, respectively at distances d1 and d2...
  27. N

    A Transition dipole moment - polarized absorption

    Hi everyone, I am interested how is polarized light absorbed by a molecule or an atom. Unfortunately, I come to a problem in the derivation where a complex vector in a real space appears. This is something I never seen before and I do not know how to interpret it. Therefore I would like to ask...
  28. Cosmos

    Can any object have moment of inertia greater than that of a hoop?

    Can any object have moment of inertia greater than that of a hoop?
  29. JulienB

    Moment of inertia and torque of a yoyo

    Homework Statement Hi everybody! I know that is a classical problem, but I haven't been able to find an answer to my questions in the other threads so here we go: We have a yoyo made of 3 aluminium disks (density ρ). The two side disks have a radius R and thickness D, and the middle disk has...
  30. L

    Can I Find the Moment of Inertia with Only 8 Equal Parts in My Homework Problem?

    Homework Statement http://i.imgur.com/7ZRsVj5.png Homework Equations I can't apply correct method ! The Attempt at a Solution In bigger figure, i cut into 8 equal parts.So , total moment of inertia=8 I But it's wrong ! I know it's wrong because i can't able to find angle between any two...
  31. RoboNerd

    Angular Acceleration and Moment Arm

    Homework Statement [A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v , then its escape velocity on Planet X is a) 2 v b) (√2)v c) v...
  32. V

    Moment of Torque; Am I solving this correctly?

    Homework Statement A metal rod of length 90cm has a disc of radius 24cm fixed rigidly at its centre(refer to picture attached). The assembly is pivoted at it's centre. Two forces, each of magnitude 30N, are applied normal to the rod at each end so as to produce a turning effect on rod. A rope...
  33. JGBuck94

    Magnetic moment between 2 bar magnets

    Homework Statement A bar magnet floats above another bar magnet. The first has mass u1 and magnetic moment m1=m1k^ and is on the ground. The second has mass u2 and mag. moment m2=-m2k^ and is a distance z above the ground, find z 2. Homework Equations I assume I need to calculate the magnetic...
  34. B

    Moment of Inertia for a Thick Spherical Shell

    Homework Statement A) [/B]Consider a hollow sphere of uniform density with an outer radius R and inner radius \alpha R, where 0\leq\alpha\leq1. Calculate its moment of inertia. B) Take the limit as \lim_{\alpha\to1} to determine the moment of inertia of a thin spherical shell. Homework...
  35. R

    How do I use the parallel axis theorem for moment of inertia in this homework?

    Homework Statement Homework Equations I = (1/3)ML2 Parallel axis theorem: Inew = Iold + mr2 The Attempt at a Solution I already solved part a) and I got (1/12)ML2. For b), I get that I have to use the parallel axis theorem but I don't know how to go from there. We have not gone over this...
  36. E

    What is the Difference Between Ixy and Iz in Moment of Inertia for Pipes?

    Hi, I've been always using eq. I=Pi*(D^4-d^4)/64 to find moment of inertia of a pipe. Recently I've seen that moment can be in different directions, and then it is expressed differently. So what is the difference between Ixy and Iz?
  37. x2017

    Trouble Determining Moment Arm (aka Lever Arm)

    Homework Statement Homework Equations ΣM=Στ The Attempt at a Solution I know how to get the net torque about point P, but I am having difficulty determining where the moment arms for each force should be. I did 9 simpler questions before this no problem, but this diagram is a bit more...
  38. A

    B Learn About Moments & Equilibriums: What Does a Moment Mean?

    Hi, I'm currently learning about moments and equilibriums. I'm able to solve the problems quite properly, like determining different forces, distances and etc. what intrigued me is that when we say that an object has a moment of 1700 Nm about point o. Does it mean that the object will provide...
  39. Titan97

    Is moment of inertia only for rotating objects?

    Homework Statement A rod attached to a ceiling at one end and a disc on the other end is performing SHM. In case (1) the disc cannot rotate. In case (2) the disc can rotate about its centre. Compare the restoring torque and angular frequency in both cases. Homework Equations...
  40. W

    Restoring Moment: Anti-Clockwise Direction?

    Homework Statement why the restoring moment in diagram 3-48 must be in anti-clockwise direction ? can't be in clockwise direction ? pls refer to the last photo ( i sketched it) , if the B' is located on the left of the G , teh restoring moment is clockwise, right ? Homework EquationsThe Attempt...
  41. D

    Finding the Mass of a Helicopter

    The question is: The main rotor blades of a helicopter sweep out an area of radius 4.0m and push air downards with a speed of 15ms^(-1) away from the blades. By tilting forwards 20 degrees, the helicopter stops rising and starts to accelerate horizontally at 3.57ms^(-2). The density of air is...
  42. 1

    Deriving the magnetic moment of a specimen in a given magnetic field

    Homework Statement I'm working on a problem that says that >If $\varepsilon_{\pm}=\mp (\mu \mu_0 H + k \theta \frac{M}{\mu N} )$ is the energy of the atom of a specimen that can orient itself either parallel or antiparallel in a magnetic field, show that $ \frac{M}{\mu N}= tanh(\frac{1}{kT}(...
  43. P

    Understanding Bending Moment Diagrams for Multiple Planes

    can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane? Also, how are the reaction forces at B and C determined each time?
  44. C

    Maximum bending Moment and Maximum Shear Stress Question

    Is the maximum bending moment and maximum shear stress an absolute value? For example, when drawing out a bending moment diagram say if I get -400 kNm at one point and 300 kNm at a different point. If these values are the maximum/minimum points on my diagram would 400 kNm be considered as a...
  45. Brendan Webb

    I on the moment equation here please

    I have come to the point in the equation where I need the moment equation to solve for Ay. I am not sure how to get By in term of Ay though. The moment equation I get for Ay is: ∑Mb = 8(-P2) - 20(-P1) - 32(Ay) + 15Ax I know P1 = 270 - P2 However I am not sure if I even have Ay and Ax right...
  46. 2

    Find the moment of inertia of this disk

    Homework Statement A crucial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it. The hole's center is a distance h from the center of the disk. Find the moment of inertia of this disk (with...
  47. Titan97

    Find spin only magnetic moment of [Fe(H2O)5NO](2+)

    Homework Statement Find spin only magnetic moment of ##[Fe(H2O)5NO]^{2+}## Homework Equations None The Attempt at a Solution When I used Google, the magnetic moment in 3.87 ##Fe## is in +1 oxidation state. So configuration is $$[Ar]3d^64s^1$$ There are 5 unpaired electrons. How does magnetic...
  48. K

    Magnetic dipole moment derivation

    (2) Hi. I am having a problem with understanding how to approximate 1/R in the forms of equations written above. I took this equations from a blog, and it tells that I can use talyor polynomial. but I don't get there somehow.
  49. puggleboy

    Finding dipole moment / Electric Field Problem

    Homework Statement Problem 3 from the attached photo Homework Equations p = qd The Attempt at a Solution I know the magnitude of the dipole moment is p = qd, where d is the distance between the 2 oppositely charged particles. I know the direction of the dipole moment vector is from - to +. My...
  50. K

    Why is the concept of dipole moment significant in physics?

    Hi, I was wondering why dipoles are singled out as a separate section in my physics textbook. For instance, after discussing electric fields the textbook specifies what a dipole is, dipole moment, and the electric field for a dipole. Finding the e-field for a dipole would be the same as finding...
Back
Top