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. M

    Calculating moment of inertia for nonuniform sphere

    Homework Statement A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r a) Calculate the total mass of the sphere. b) Calculate the moment of inertia...
  2. N

    Moment of Inertia, working backwards

    I've to work out b & d in this equasion. I=bd^3/12 I know that the ratio between b & d in this case is 1.166 and I am given the value of I. It is an engineering problem as the software will only allow the use of square/rectangular or round section but we are using H section and we are allowed...
  3. C

    Finding the angle of the velocity vector of a projectile at moment of impact

    Homework Statement A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 16.0 m/s. The cliff is h= 41.0 m above a flat horizontal beach h=41 g=10m/s vi=0m/s vf2=vi2+2gh vi=28.64 h=vi+vf/2xt 41=28.64/2xt 14.32 t=2.86 28.64x28.64, 16x16 Square...
  4. V

    Magnetic moment of a particle suspended in a magnetic field?

    Derive the following expressions for ux, uy and uz: ux(t) = ux(0) cos(wo t) + uy(0) sin(wo t) uy(t) = - ux(0) sin(wo t) + uy(0) cos(wo t) uz(t) = uz(0) wo is angular frequency. wo = g Bo Homework Equations wo of this precession is proportional to Bo u and J have the same orientation: u = g J...
  5. T

    Express the moment (torque) as a function of theta

    Homework Statement The problem shows a wrench with a force being applied to one end. Rotation will occur around point P at the opposite end. The force is applied 43 inches to the left from P, and 6 inches above P. The angle theta is between the vertical axis at the end of the wrench (non-p...
  6. P

    Moment of inertia about a ceiling fan?

    Homework Statement A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.3 kg and radius R = 0.26 m. The rods each have mass mr = 1.2 kg and length L = 0.72 m. What is the moment of inertia of each rod about the axis of rotation...
  7. Hardik Batra

    How is the moment of inertia related to the square of the distance?

    Moment of inertia is I = MR2 object has more mass means more inertia and less mass means less inertia. That means moment of inertia is directly proportional to mass. But how the moment of inertia is directly proportional to the square of the distance.?
  8. M

    How Fast Must a Bullet Travel to Tip a Rotating Cube?

    Homework Statement A solid cube of wood with side 2a and mass M is resting on a horizontal surface. The cube is constraint to rotate about a fixed axis AB. A bullet of mass m and speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube. Find the...
  9. D

    MHB Second moment of the Poisson random variable

    With a Poission random variable, we know that \(E[X] = var(X) = \lambda\). By definition of the variance, we can the second moment to be \[ var(x) = E[X^2] - E^2[X]\Rightarrow E[X^2] = var(X) + E^2[X] = \lambda(1 + \lambda). \] The characteristic equation for the Poisson distribution is...
  10. Prashasti

    Spin Magnetic Moment: Does an Electron Really Spin?

    Does an electron really spin about its own axis? If not, what does spin magnetic moment imply? My physics teacher said "Besides the orbital moment, an electron has an intrinsic magnetic moment, it is called the spin magnetic moment, But I hasten to add that it is not as though the electron is...
  11. N

    Moment Of Inertia Of a Weld Profile

    Im needing to calculate the Zxx and Yxx for 2 shapes. The shapes are an H profile and a + profile however its not the basic profiles I am needing but the moment of inertia for the weld profile surrounding them as the theory is they are welded to a vertical metal surface then a load is applied...
  12. Lord Crc

    Rigid body, torque and moment of inertia

    Hi, it's been quite some years since I took some entry-level mechanics at uni, and my book is no longer with me, so I'm struggling a bit here. I'm making a very simple rigid body simulator just for fun, but the angular velocity is not working out right. I suspect I've forgotten something...
  13. Feodalherren

    The moment about a point on a post

    Homework Statement Find the moment about point A Homework Equations The Attempt at a Solution Calling counter-clockwise positive (300N)(1m) + 500cos(30)(.2) - 250(4/5)(.5) = 286.6Nm Not the correct answer. What am I doing wrong?[/B]
  14. E

    Total moment of shear stress about the center line of a cylinder

    http://postimg.org/image/onxjqc26l/ I have found the shear stress of the inner cylinder to be 405 Pa like in the solution but I am having trouble visualizing the total moment of this stress about the center line. I was wondering if someone could explain where that d(theta) in the moment...
  15. J

    Moment of inertia ice skater problem

    Problem: Consider an ice skater spinning in a circle. We will approximate the body as a cylinder with a radius of 0.25 m. The total mass of the skater is 50kg. When the skater has her arms extended we will approximate her body as a cylinder with two rods attached. Each arm is 0.75 m long and has...
  16. ajayguhan

    Linearly varying force and bending moment problem.

    I have attached both the question and my attempt at solution. My problem is reducing the equation further to get the value of a/L
  17. S

    Why Is the Mass of a Wheel Concentrated on the Rim?

    A small confusion ! Why is most of the mass of the wheel concentrated on the rim ? I know that it is to increase the moment of inertia , but what is the practical use of doing so ? Thanks in advance !
  18. S

    Moment Deflection Relationship Problem

    Homework Statement An electrical engineer in your semiconductor company is working on a design of an electrical contact with a Si wafer. The electrical contact is in the form of a thin Cu “finger” touching the back side of a wafer as shown below. The electrical engineer claims that he is...
  19. SteliosVas

    Angular velocity with time varying moment

    Hi there, I have been given this question, and I have not even the slightest of clue's where to start. I know angular velocity is equal to ω=v/r But besides that I have no idea. Where can I start?
  20. P

    Problem with values for a bending moment diagram

    Homework Statement I have a 5m long simply supported beam, with supports at points 0m and 5m. There's a UDL of 10kNm^-1 from 0m to 4m. It has downward forces acting at 2m (10kN) & 4m (15kN). I need to sketch a bending moment diagram to determine the position & value of the max bending...
  21. L

    Finding the dipole moment of a molecule in an electric field

    Homework Statement "A molecule has its dipole moment aligned with a 1.8 kN/C electric field. If it takes 3.5x10^(-27) J to reverse the molecule's orientation, what is its dipole moment?" Homework Equations Potential energy of dipole in an electric field U = -p*E = -p*E*cos(theta) U...
  22. I

    Calculating Bending & Shear Moment: Homework Statement

    Homework Statement (a) Calculate the maximum bending moment (b) Calculate the maximum stress in the beam (c) At the point of maximum stress sketch a graph of the stress distribution through the thickness of the beam, indicating which are tensile and compressive stresses. (d) Determine the...
  23. B

    Moment of Inertia of Hollow Cylinder Derivation

    For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...
  24. I

    Calculating change in Magnetic Dipole Moment

    In one moment in time you have a charge going about in a circle of radius r. in another moment in time the charge goes in the same circle but faster, where Δv is the difference in speed. i want to find the change in the magnetic dipole moment Δm.if magnetic dipole moment m=IA (assuming uniform...
  25. S

    Need help regarding transition dipole moment

    Hi, I have been trying to get the expression for the transition dipole moment of hydrogen but I am not able to get the expression. Hope someone can help me with that. I want to evaluate \vec{d}(v)=<v|\hat{r}|0> where v is the free state and 0 is the 1s wave function for hydrogen...
  26. Mogarrr

    Moment generating function DNE

    Homework Statement Write the integral that would define the mgf of the pdf, f(x) = \frac 1{\pi} \frac 1{1+x^2} dx Homework Equations The moment generating function (mgf) is E e^{tX}[\itex]. The Attempt at a Solution My question really has to do with improper integrals. I must...
  27. B

    Moment of inertia and torque problem

    The Question : A cylinder of mass M , and moment of inertia around its center Io, is initially rotating around its central axis with angular velocity wo. İt is gently placed on a homogeneous thin plate of mass m which rests on a smooth horizontal surface. Assume that the plate is sufficiently...
  28. deep838

    Is the Moment of Inertia strictly different

    I would like to know if there is any proof as to whether the moment of inertia for two bodies (the masses of each body are distributed on a line) about their respective center of masses, is strictly different. If not, can anyone provide me a link to where the work is computed.
  29. stateofdogma

    Moment of inertia of rectangle without dd int

    Homework Statement I found the moment of inertia of a rectangle, with the axis perpendicular and going through the center using double integration. But I also used what i thought to be an equivalent method, but it didn't work.Homework Equations dI=r^2dm \int dI The Attempt at a Solution I was...
  30. B

    Moment of Inertia for Half Disk

    1. Question: What is the moment of inertia of a thin, flat plate in the shape of a semicircle rotating about the straight side (Fig. 12.28)? The mass of the plate is M and the radius is R The diagram is attached for reference. Homework Equations Moment of Inertia: I = ∫R2dm...
  31. nmbr28albert

    Stern-Gerlach Experiment (spatial consistency of the magnetic moment)

    In the Stern-Gerlach experiment, we have an inhomogeneous magnetic field aligned with the axis labeled z. The two distinct deflections are caused by the force from two distinct magnetic moments \mu = \gamma S. I understand that the spin larmor precesses around the field and that the expectation...
  32. M

    What is the method of moment estimator for θ?

    Homework Statement Let ##X_1, X_2, ..., X_n## be a random sample from ## f_θ=2x/θ^2## , ##0≤x≤θ##. Find a maximum likelihood estimator for θ. Find the method of moment estimator for θ. The Attempt at a Solution I have already found that the MLE is max{##x_i##}. I just need to find the...
  33. C

    Free electrons and intrinsic spin magnetic dipole moment orientation?

    Are there any experiments or theories about the relation between magnetic dipole moment orientation and velocity vector of free electrons?
  34. C

    Moment of Inertia - Find Area Around Y-Axis

    This is my first time posting in this site so if I left out any information or the information needs to be formatted differently I apologize ahead of time. Homework Statement Determine the moment of inertia of the area about the y axis. The curve is represented by y2=2x, and the shaded...
  35. kartikwat

    Exploring the Intrinsic Magnetic Moment of Electrons

    What does the term magnetic moment mean and how to look at it intellectually .what are its effects,what are its type
  36. Greg Bernhardt

    What is the Moment of Inertia? A 10 Minute Introduction

    Continue reading...
  37. Greg Bernhardt

    What are Moments of Area and How Do They Measure a Body's Resistance to Stress?

    Definition/Summary Moments of area are properties of rigid bodies, they depend only on shape and not on density, and they are scalars (numbers), and are measured relative to a particular axis. First moment of area measures a body's resistance to shear stress along an axis. Second moment...
  38. R

    Moment Balance - Angled Wine Bottle Holder

    Hey all! I think I have the problem within my grasp, just would like a second opinion to help me cross the finish line... Homework Statement Consider the following diagram of the bottle holder assembly (see attachment). The weight of the bottle is 11N, and the weight of the board is...
  39. A

    What is meant by moment of particles?

    What is meant by moment of particles ? Why the algebraic sum of moments of all particles about centre of mass must be zero ?
  40. A

    Why torque is moment of force & angular momentum is moment of momentum

    Why the torque is called moment of force and angular momentum is called moment of linear momentum ? Please explain.
  41. J

    Composite moment of inertia question:

    Good morning PF, I am having some difficulty finding info on calculating a composite moment of inertia. The section I am working with is 8 separate columns (WT5x15) arranged evenly spaced around the circumference of a circle. You can see what I'm taking about in the attached jpg. I found...
  42. B

    Bending Moment of a Cantilever Beam

    This is a problem from Michael Lindeburg's FE Review Manual. It is in Chapter 20, Number 11 if you have the book. PROBLEM: There is a picture of a cantilever 2 m in length attached to a wall. There is a force applied at a 30 degree angle from the horizontal at the free end of the beam...
  43. M

    Simple statistical moment question

    hi pf! so i am going to take the skewness and kurtosis of a sample. however, if i already have a pdf, is there really any reason for doing this? thanks! josh
  44. K

    Differential moment of inertia

    Homework Statement since it's asking us to find the moment of inertia with respect to y-axis, why did they draw the differential element to x-axis? Homework Equations The Attempt at a Solution because of the initial problem.. i don't know how to start.. so dA = x dy I(y) =...
  45. N

    Need help in proving this Moment of Inertia equation

    Homework Statement Suppose I have a rod with a know length, L, and 2 point-liked mass with know mass, m, each of them are fixed at both ends of the rod. And the rode has an axle connected at its midpoint where the axle is connect to a circular spring. The rod(with the 2 mass) is rotated 180...
  46. S

    Resultant of Three Forces and a Moment?

    I'm looking to find the resultant force of three forces and a moment: Fx, Fy, Fz, and Mx. I intend to graph multiple resultants. Would I just need to do the following to find the magnitude? Sqrt(((Fx+Mx)^2)+Fy^2+Fz^2) Thanks
  47. J

    Moment of inertia of rectangular tube with welded flat bar

    hello, I am trying to find the new moment of inertia total for a rectangular stainless steel 4"x2"x.25"thk with a 3"x.75" flat bar welded on top of the short side of the rectangular tube. The short side (.75") of the flat bar will be welded to the center of the rectangular tube to the 2"...
  48. I

    Angular Momentum & Moment Of Inertia

    Homework Statement Two children on opposite ends of a merry-go-round of radius 1.6 m throw baseballs at the same speed of 30 m/s but in opposite directions as shown. The mass of each baseball is 0.14 kg, and the moment of inertia of the merry-go-round and children combined is 180 kg-m^2. If...
  49. L

    Where Should a 150N Weight Be Placed on a Ladder to Achieve Equilibrium?

    Homework Statement A ladder weighing 200N is being held by a man. The man shoulder acts as a pivot. His arm is pushing an upward force F. http://i.imgur.com/dMrcRtK.jpg Where could a weight of 150N be hang upon, so that force F do not need to counteract the weight of the ladder...
  50. B

    Problem with shell model and magnetic moment of Lithium-6

    I have a problem with the calculus of magnetic moment of Li-6. The configuration of protons is 1p_{3/2}, and the neutrons' one is the same. I have to add the magnetic moment of uncoupled proton and uncoupled neutron. I use the following formula for J=l+\frac{1}{2} (J is the particle...
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