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. S

    Moment Question / inclined triangle

    Homework Statement In this I tried to resolve the components. So first thing, I converted the 12kg into Newtons so it would be 117.72 Newtons. Then found the perpendicular distance which is to g: cos(30)x1 then multiply the answer by 117.2N to give the weight down as 102N. As the moment...
  2. H

    Relation between torque and magnetic moment

    The magnetic moment ##\vec{M}## of a charged particle is defined as ##\vec{M}=\frac{1}{2}q\,(\,\vec{r}\times\vec{v})##. Starting with torque ##\vec{N}=\vec{M}\times\vec{B}##, I arrive at a contradiction. Consider a charge particle moving at a constant speed ##v## anticlockwise in a circle of...
  3. V

    Moment of force exerted by water on tube

    Homework Statement Homework Equations Bernoulli's equation : ##P + \frac{1}{2}ρv^2 + ρgh ## = constant The Attempt at a Solution The pressure at the interface is ##P_{int} = P_0 + ρgH## . Applying bernoulli's equation between point at the interface of two liquids and exit of the tube ...
  4. P

    Determine the mass moment of inertia of the assembly

    Homework Statement Determine the location of y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the mass of the semicylinder is 5 kg. Homework Equations -parallel...
  5. S

    Why doesn't N3- have a dipole moment arrow from the central atom?

    My teacher posted on his website, Lewis structures of different compounds. One of them were N3- Why isn't there a dipole moment arrow pointing from the central atom to the other Nitrogen? Does the arrow only point from neutral atom to negatively charged atom?
  6. D

    Moment of inertia and angular KE confusion

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  7. 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...
  8. physea

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

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  9. 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?
  10. Daisy Muller

    What Happens to Angular Acceleration and Moment of Inertia in a Pulley System?

    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...
  11. 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...
  12. Halest0rm3

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

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  13. 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]
  14. S

    Thin rod w/linear charge density, dipole moment

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  15. 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. Rheegeaux

    Moment of inertia of a cross system

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  24. K

    I Simple Fulcrum Force Calculation Question

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  25. G

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  26. Narwhalest

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  27. M

    I Second moment of area of a quad copter arm?

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  28. F

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

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  29. 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...
  30. pbutter

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

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  31. 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...
  32. 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...
  33. 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...
  34. 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?
  35. 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...
  36. 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...
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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?
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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}(...
  49. 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?
  50. 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...
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