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. A

    A Third and fourth central moment of a random variable

    My question is as follows. In the attached paper a formula is given on page 272 for the expectation of Tn (formula 23) and for the variance of Tn (formula 24). Now I would like to know what the formulas look like for Tn 's third and fourth central moment.
  2. V

    Moment of inertia, conservation of angular momentum and energy

    When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.
  3. T

    Bending Moment & Bending Stress

    Hello all I was wondering if anyone could figure out the what the equation below means, specifically the W term? The equation to calculate bending stress for a cross section that i have used and i know is correct is:- Bending Stress = Moment (M) * Distance From Neutral Axis (Z) / Second...
  4. T

    Why Use the Parallel Axis Theorem with the Second Moment of AREA?

    Hi all I was wondering if someone could help clear up some confusion about the Parallel Axis Theorem. I am trying to understand the purpose/benefit of applying the Parallel Axis Theorem with respect too the Second Moment Of Area. For example I have a beam that is under load. I have found its...
  5. T

    Understanding the Value of the Second Moment Of Area

    Hi all I was hoping someone could help shed some light clearing some doubt on 2nd Moment of Area. I know that if i had a beam that was loaded then the top of the beam would experience compressive forces. As i moved down towards the neutral axis these compressive forces would become zero. And...
  6. B

    Instantaneous moment of inertia of an object

    Can someone guide me on how to approach this question? I tried to draw a quick diagram of what I think is happening here Does the question imply that this object is undergoing horizontal circular motion in the shape of a conical pendulum? Thanks for any help!
  7. B

    Rotational motion and finding the moment of inertia

    Here is the problem that I am finding difficult to answer I had tried using conservation of energy to do this question Where I know that the gravitational potential energy at the top of the slope equals to the sum of both the linear and rotational kinetic energy at the bottom of the slope...
  8. L

    Calculate the moment of inertia of this body

    I use the moment of inertia I = 1/12ml2 for an axis perpendicular and passing through the center of mass of a rod. In a cube built out of 12 rods I have 8 rods at a perpendicular distance l/2 from the axis through the midpoint of a cube. These 8 rods contribute the moment of inertia I1 =...
  9. H

    Engineering How to find the first area moment of inertia (Q) for an I-beam with flanges

  10. Elder1994

    Find the electric dipole moment for a water molecule

    The equation that we saw in class is for a continuous charge distribution, I think that for this exercise I need to treat the system as a discrete charge distribution but I'm not sure. Also, I don't know how I can calculate the intensity of the electric field needed to move this charge.
  11. D

    Engineering Do Axial Forces Affect Bending Moments in Beam Calculations?

  12. J

    Moment of Inertia: Thin Spherical Shell

    Homework Statement: Derive the formula for the moment of inertia of a thin spherical shell using spherical coordinates and multiple integrals. Homework Equations: Moment of Intertia is (2MR^2)/3 I = (2MR^2)/3
  13. V

    Calculating the normal force due to moment load on a thrust bearing

    Hello all! I have a mathematical question for you. I'm trying to design a thrust bearing that can withstand axial and moment loads. I've added a picture of a similar design. The design consists of two rings (grey) and sliding pads (blue) fixed on the bottom ring. The top ring slides over the...
  14. dlxgains

    Moment of inertia project help- experiment 1: Bifiler Rod

    Homework Statement: So i need to find equations to help me with a bifiler suspension experiment in which i will use a rectangular drop bar as the oscillating object, also any help with the method of this experiment would be greatly appreciated. The end goal is to find the moment of inertia...
  15. A

    Maximum of the First Moment of Area

    I am reading about beams under distributed loading and shear stresses and needed to use the equation τ = VQ/It, where Q is the first moment of area. I understand that Q is zero about the neutral axis, and that this is, in fact, how the neutral axis is defined. The first moment of area above the...
  16. A

    What is the direction of the torque in this scenario?

    I=(1/2)(6kg)(0.4^2 + 0.52^2) = 1.29 kg*m^2 initial: 34 mph= 15.2m/s 15.2m/s = (ω) (0.52m) ω= 29.2 rad/s after: 19 mph = 8.5m/s 8.5m/s = ω(0.52m) ω= 16.3 rad/s acceleration = (16.3 rad/s - 29.2 rad/s) / 5s= -2.58 rad/s^2 torque= |-2.58 rad/s^2 |(1.29 kg*m^2 ) = 3.3 N*m I am confused...
  17. Heyxyz

    Moment of Inertia: Car vs Sphere

    Hello, I tried to put it in an equation, but it didn't really work out. In this situation, the car was about the size of a model, and, while not exact, the radius of each wheel couldn't have been more than like a centimeter. Conversely, the ball was like twice the size of the car and had a...
  18. jisbon

    Moment of inertia of 2 uniform thin rods

    So to start off, what I will do find the center of mass of each of the rods. So for the top rod, COM is at where y= 0.5 L and COM of the rod at the bottom is at x = 0.5 L. From there, how do I proceed in finding the moment of inertia using parallel axis theorem? Do I simply treat: ##I...
  19. I

    Dipole moment from electrostatic potential equation

    Hello to everyone. The question or debate here is how you obtain the commonly known equation of dipole electric moment: from the electrostatic potential equation for a multipole of order n: I understand it is related with Dirac delta functions but a step by step solution might be helpful.Thank...
  20. kepherax

    Moment of Inertia of a Rectangular Picture Frame

    https://www.physicsforums.com/attachments/250905 I know the answer, but am not certain how they got Lsin(angle) for R?
  21. K

    Engineering Fluid Mechanics Problem: Water Forces on a Parabolic Gate

  22. J

    A How can a spin moment align parallel to an external field?

    Hello everybody, Lets say we have an atom with an electron that have a spin. That spin can only pointing in 2 directions, in s_1=\hbar*1/2 and s_1=-\hbar*1/2 and therefore the magnetic moment of an electron is pointing on the opposite site. My Problem here is appearing when whe apply an...
  23. Athi Sankar

    Turning Moment of Single Cylinder 4-Stroke Engine | Explanation

    Figure 1 shows the Turning Moment diagram of Single Cylinder four stroke Engine. Can anyone tell me, how the turning moment becomes positive at the end of suction and exhaust stroke. Net force F = Force due to gas pressure - Inertia Force - Reaction Force due to friction If the net force...
  24. jisbon

    Moment of inertia of this shape about the x-axis

    I've attempted this question, but the answer seems to be incorrect. Here's my workings: ##I=\int y^2 dm## - standard equation ##dM = \mu * dy * x## - take small slice and find mass of it ##x = 4y-16## - convert equation in terms of x to sub in later ##dM = \mu * dy * 4y-16## ##I=\int y^2 \mu *...
  25. Kaushik

    Moment of Inertia of a hollow sphere with Mass 'M' and radius 'R'.

    Homework Statement: Derive the formula for moment of inertia of a hollow sphere. Homework Equations: Required answer ##\frac{2MR^2}{3}## Consider a Hollow sphere. At an angle ##Θ## with the vertical, consider a circular ring whose moment of inertia is given by ##MR^2##. The most basic...
  26. S

    Resultant moment of beam fixed at one end

    Hi all, I just wanted to get some clarification on 'resultant moment' when calculated in 2D for a beam which is fixed at one end (point A), and has a load applied at the opposite end (point B). My interpretation of 'resultant moment' would be calculated as sum(M) = Ma + FL, where Ma is the...
  27. I

    How can I calculate the bending moment of a pin in double shear?

    I have attached an Excel-worksheet in which the problem should be clearified. The problem concerns the calculation of the bending moment acting in a pin in double shear, experiencing a certain load from a hydraulic cylinder. The plate thicknesses should be taken into account. Specifications and...
  28. JD_PM

    Finding a method to compute the magnetic moment of an even-odd nucleus

    I am having difficulties computing the magnetic moment for an even-odd (proton-neutron) nucleus. The formula is: $$\mu_J=g_J\times j\times \mu_N$$ I checked this helpful post...
  29. K

    Torsional moment vs bending moment

    The direction of x, y and a axes were shown in the highlighted part.. I think it is wrong. For red circled beam, i kinda agree that Moment about x-axis was defined as torsional moment.. While moment about z and y axes are bending moment... But for blue circled beam, I think that Moment about z...
  30. T

    I Electric dipole moment of the nucleus of an atom

    Summary: Why is the electric dipole moment of the nucleus of an atom equal zero? Summary: Why is the electric dipole moment of the nucleus of an atom equal zero? I read about the hyperfine interactions that cause the altering of the energy levels of the nuclues of an atom. Under the...
  31. A

    Torque: find the force necessary for a body to be in equilibrium

    The question doesn't specify whether we're talking about translation or rotational equilibrium, so I suppose it's both: In order for the body to have translational equilibrium: 60 N + F2 = 0 F2 = -60N However, in order to have rotational equilibrium: 60 N * 3m + F2 *8 m = 0 60 N * 3m - 60 N...
  32. F

    Application point of the lift force and pitching moment

    Hello As the angle of attack of an airfoil changes, the lift force ##L## changes both in magnitude and position (not in direction, always upward). The force location is a point called the center of pressure ##x_{cp}##. It is possible to transfer the force to any another different point along...
  33. K

    I What Exactly is the Anapole Moment?

    Hello! Can someone explain to me what is the anapole moment? I read several papers, and I understand its mathematical expression and its implications (parity violation for example), but I am not sure I understand physically what it is. For example I think of an electric dipole moment as 2...
  34. Benjamin_harsh

    Moment of Inertia: Calculation Method

    Ratio of moment of inertia of a circle and that of a square having same area about their centroidal axis is: Sol: both area and square have same area: ##a^2 = \large\frac{π}{4}\normalsize d^{2}; \large\frac{d}{a} =\large \sqrt\frac{4}{p}## Ratio of moment of inertia of a circle and that of a...
  35. P

    Determining the Moment of Inertia about an angle θ to the x axis

    I thought about solving it using components of IAB but since it is a scalar quantity it doesn't seems to be correct . I don't think Perpendicular Axis theorem will work as required Inertia is in the same plane.
  36. David W Thomson

    B Is There Evidence of Physical Matter Existing Beyond the Present Moment?

    Help me first understand the physical Universe that these twins live in. Has anybody ever measured physical matter from a different time frame other than the present moment? In other words, is there physical matter existing in a time other than the present moment? If there is no evidence of...
  37. V

    Man on ladder: jump off instantly vs last moment?

    So there are two cases: a). free fall (straight forward for me) b). ladder rotating and jumping off in last moment (I am interested in trying to understand this case) I believe I should take into account momentum at the time the man hits the ground in both cases? The smaller, the better. Or...
  38. H

    I A bar magnet and magnetic moment in a magnetic field

    Why a magnet bar would become aligned with the external magnetic field while a magnetic moment would precess around the external magnetic field?
  39. Benjamin_harsh

    Exploring the Mystery of Moment of Inertia

    While I am reading this article, it says moment of inertia is same at radius of ring and at the center of it. How is that possible?
  40. Physics lover

    Moment of inertia of a square along an axis inclined at an angle

    My attempt-:I extended the axis and made a triangle by joining other adjacent vertex to the line such that its angles are 15°,75° and 90°.I found the distance between the centre of square and upper vertex of triangle by using law of sines.And then i found out inertia along upper vertex of...
  41. Benjamin_harsh

    How is the moment at A using the Force 1200N calculated?

    A force of 1200N acts on a bracket as shown in the below figure. Find the moment of this Force about point A. Taking moments of components of 1200N force about point A. ∴ ##M_{A} = - (1200.Sin 30^{0} * 140) + (1200.Cos 30^{0} * 140)## ##M_{A} = 40.71 X 10^{3} Nm## I am confused, because...
  42. L

    Spinning top's moment of inertia I (disc on shaft )

    I hope you guys can help me with this problem.. A top in the form of a flat, circular disc spins on a shaft that is inclined at an angle alpha to the vertical. Now I have to find the moment of inertia I for the disc about its centre on the shaft. My attempt was building I with spherical...
  43. EEristavi

    Energy Conservation in Angular motion / Moment of Inertia

    I write Conservation of Energy: Potential Energy loss(change): U = m g ##\Delta##h = m g (R+r) (1-cos##\alpha##) kinetic Energy gain(change): K = (##\frac {m v^2} 2## + ##\frac {I \omega^2} 2##) + (##\frac {M v_2^2} 2## + ##\frac {I_2 \omega_2^2} 2##) U = K m g (R+r) (1-cos##\alpha##) =...
  44. jim mcnamara

    Early moment detection that marks the start of massive tremor events

    Popular science: https://phys.org/news/2019-05-scientists-early-moment-megaquake.html https://advances.sciencemag.org/content/5/5/eaav2032 Image courtesy University of Oregon. 15 seconds into a massive event, there is data to support the concept of a warning of a coming massive event. Data...
  45. I

    General Physics I Question: Moment of Inertia Problem Difficulty

    Hi everyone, I am honestly pretty confused as to where to start with this. Can anyone give any pointers as to where I could possibly go, for (a) and (b)? Thanks!
  46. Benjamin_harsh

    What is the moment for this diagram?

    What is the moment for this diagram? I am getting two moments; ##M = F.S## and ##M = -F^2.S## I am getting confused.
  47. Benjamin_harsh

    Why is moment ##F.S## instead of ##F.\frac{S}{2}## for this diagram?

    Why is moment ##F.S## instead of ##F.\frac{S}{2}##?
  48. P

    A Dipole moment operator and perterbations

    I am reading a PHD thesis online "A controlled quantum system of individual neutral atom" by Stefan Kuhr. In it on pg46, he has a Hamiltonian I am also reading a book by L. Allen "optical resonance and two level atoms" in it on page 34 he starts with a Hamiltonian where the perturbation is...
  49. J

    A problem involving 'stress' and possible moment of force(?)

    Given, ##2A_P = A_Q## (cross-sections) ... (1) and, ##Y_P = 2Y_Q## ... (2) We have ##\frac {Y_P * x}{\Delta L} = \frac{Y_Q (L-x)}{\Delta L}## Using (2) in the above expression we get ##x = L/3## whereas the correct answer is ##x = 2L/3## I feel my initial idea is flawed, and that I am...
  50. EEristavi

    Calculating the moment of inertia of Cone

    I'm Summing the Inertia of "donuts" with width dr and radius - r. I'm also "flattering" the cone into 2D and considering that each donut has different mass - because of the different height - h so: dm = 3 m h / (pi R2 H) dr I = ∫ dm r2 = 3 m h / (pi R2 H) r2 dr from triangle similarities H/R...
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