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. Ugnius

    Rotating body moment of inertia

    I have done some lab work , and now i have to answer some theoretical questions , but i can not find any data about this on the web or atleast i don't know where to search , i will add some pictures of experiment for you to better understand it. I was wondering can someone share their knowledge...
  2. MattGeo

    Torque and Moment of Inertia of a Lever Arm

    I never really considered this back when I was taking physics in college but imagine for the sake of thought experiment that you have an extremely and impractically long wrench and it is fixed to the bolt you wish to tighten. Now the longer the lever arm the greater the torque so if you double...
  3. C

    Confused by Unexpected Results: Acceleration & Moment of Inertia

    Like I said, objects with the higher acceleration are giving me the lowest values. For a hoop, I got I=0.1*MR^2 For a cylinder, I got I=0.7*MR^2 this seems backwards, no?
  4. T

    Moment of Inertia with pulley and two masses on a string (iWTSE.org)

    Note: the working (taken from iWTSE website) refers to inertia as the symbol ‘J’ (in-case there was any confusion).I found equations of motion for mass m and 2m which were ‘T1 = ma + mg’ and ‘T2 = 2mg – 2ma’, respectively. I know they are connected particles with the same acceleration ‘a’.I have...
  5. D

    Engineering Calculating the shear and moment diagrams of a beam with a hinge

  6. D

    Engineering Question about plotting a Bending Moment Diagram

    I am confused why positive value of bending moment is plotted under the axis?
  7. L

    Engineering Cantilever and encastré beams: bending moment and shear force

    I have to discuss the Bending moment and shear forces in cantilever and encastré beams. Does anybody know of good websites showing that is simple to understand showing. All i can find is how to calculate and bending moments and shear force digrams which don't really understand. Can...
  8. mingyz0403

    Engineering Graphing Shear and Moment using singuarity function in Excel

    I had found the singuarity function for the shear and moment. I have a hard time calculating the singuarity function and graphing it using excel. Can anyone explain how to calculate singuarity function and graphing it using excel? Many thanks for your help
  9. K

    Calculating torque from moment results in CFD analysis

    Hi there, attached were the results: https://prnt.sc/v3yg1f Both are negative and need to be added together to get the torque force. Calculations are from a model of specified radius and input air speed, its a turbine. Just need help in understanding what the negative results mean and how they...
  10. wcjy

    Moment of inertia of a uniform 2D triangular plate

    Answer is 37.8 g cm^2 new to latex
  11. andyonassis

    Moment of inertia (Perpendicular axis theorem)

    So i derived the moment of inertia about the axis of symmetry (with height h) and I am confused about the perpendicular axis theorem. The problem ask to find the moment of inertia perpendicular to axis of symmetry So the axis about h, i labelled as z, the two axis that are perpendicular to z, i...
  12. FEAnalyst

    Plate - bending moment equation

    Hi, I'm trying to solve an exemplary case of a cantilever plate (one long edge fixed, all other edges free) subjected to pressure. I've already calculated this using approximation to beam of unit width and the results are good but I would like to use another method too. In a polish book I've...
  13. M

    Mass moment of inertia of a composite shape

    My thought process was to get the mass moment of inertia of the rectangle and then subtract the mass moment of inertia of the quartercircle from it. The MMoI of the rectangle is: (1/3)(0.005*7850*.6*.3)(.3^2)= 0.212 meters The MMoI of the quartercircle is: (1/4)(0.005*7850*¼π 0.3^2)(.3^2) + ? My...
  14. M

    I What is the effect of a magnetic field on an atom's magnetic moment?

    Hello! I want to make sure I understand (mainly qualitatively) what happens to an atom in a magnetic field. Assume we have an atom with an even number of protons and electrons. This means that all proton (electrons) are paired up, except for one of them (I am not totally sure if this pairing is...
  15. goodOrBad

    Beam with a rope - type of problem (Statics)

  16. Jason234578

    Engineering Moment of a force about point O

    G'day. I have a problem with my statics work, i understand its probably quite simple but I am having trouble in my understanding. Essentially problems make more sense to me by using the component method, although in saying that i understand this problem would be quite a lot more simple were i to...
  17. Nexus99

    Moment of inertia of an isosceles triangle

    I did in this way: ## I = \int dm \rho^2 ## Dividing the triangle in small rectangles with ##dA = dy x(y) ## where ##x(y) = 2 ctg( \alpha ) (h - y) ## we have : ## dm = \sigma 2 ctg( \alpha ) (h - y) ## Now i have ## \rho^2 = x^2 + (h-y)^2 ## Now I don't know what I can do because it would be...
  18. F

    Your favorite Eureka moment for proofs

    What was your favorite proof or Eureka moment you remember? Mine was about normal subgroups (##gNg^{-1}\subseteq N##). You learn the definition and prove a few properties and go to the next subject. I remember that I once tried to teach the concept to someone and in the middle of my...
  19. M

    Engineering Solve Value of R: Moment & Equilibrium

    Summary:: I need some help with moment when using equations of equilibrium Edit: Sorry I forgot to say what the question was! The question was to solve the value of R based on the diagram below alone. I was solving the question below and I tried to resolve R into a force that is perpendicular...
  20. G

    I Electron's magnetic moment

    Is Peskin and Schroeder book, page 187 when they try to connect the electron form factors to its magnetic moment they get the expression $$\bar{u}(p')\left(\gamma^i F_1(q^2)+\frac{i \sigma^{i\nu}q_\nu}{2m}F_2(q^2)\right)u(p)$$ Where ##p##, ##p'## are the momenta on on-shell electrons and...
  21. Nexus99

    Moment of inertia, center of mass and vincular reaction of a rod

    I'm struggling doing point 5, i have no idea how to solve that question. In point 1 i obtained the following result: ## I=\frac{ML^2}{2}## calculating the integral of dI, the infinitesimal moment of inertia of a small section of the rod of length dr. 2) Through the conservation of angular...
  22. Nexus99

    Moment of inertia of two coaxial disks

    The total moment of inertia is: ##I_{tot} = 2 M_1 R^2 + \frac{1}{2} M_2 R^2## We have ## M_1 = (4 \pi R^2) \sigma ## and ##M_2 = (\pi R^2) \sigma ## , where ## \sigma ## is the density of the disks. We also know that: ## \sigma = \frac{m}{ \pi 5 R^2} ## this leads us to say that: ##I_{tot} =...
  23. B

    How Do You Calculate Load Inertia for a Lead Screw System?

    In order to choose a DC motor according to the article titled: APPYING MOTORS IN LINEAR MOTION APPLICATION by PITTMAN - step 4 : "determine the total reflected inertia (Jt) back from the load to lead screw shaft " . The formula is: Jt = Jscrew + Jload. This calculation relies on the fact...
  24. B

    I Schiff moment in classical electrostatics

    Hello! I just found out about the Schiff moment. This is the paper where I encountered it, equations 3 and 4. The paper covers other things, too, that are not related to my question. The main question I have is that, it seems like the derivation from equation 1 to 4 is purely classical (one can...
  25. mingyz0403

    Engineering Moment of forces about the axes

    I reslove Ma and Mb into y and z component. Ma=1200sin(20)j+1200cos(20)k Mb=900sin(20)j+1200cos(20)k Mc=-840i I looked at the solution and it states that the y component of Ma is negative (-1200sin(20)j+1200cos(20)k). I understand that Mc is -840i because it is Clockwise. How do you determine...
  26. jaumzaum

    A Gravitational Energy: Field x Moment

    Hello! I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment, as we do with the magnetic and electric energy? Would this require the existence of bodies with negative mass? How could we relate this to the existence or total...
  27. Y

    Moment of inertia where mass and torque are at a different positions

    The formula for moment of inertia is: I=mr^2 A common derivation for this is: 1. F=ma 2. τ=rma 3. τ=rmrα = r^2 mα This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration...
  28. H

    Electric dipole moment vs electric current dipole moment

    I have to estimate the electric dipole moment of an NV center in units of Am. I know that for a regular electric dipole moment it can be estimated using p=ed. With e=1.6*10^-19 and d=0.1 nm (interatomic distance), this however is in units Cm. I don't know how to go to Am
  29. Tymofei

    Calculating the Moment from a Different Vantage Point

    Summary:: Just a simple 3d rigid dynamics question which I am trying to solve by placing coordinat system differently from original solution.Everything looks ok but results are different. Mod note: Post moved from technical section. Thats my question.As you see coordinate system was located...
  30. M

    Exploring Moment of Inertia & Angular Acceleration for Drone Propellers

    Hi, I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...
  31. D

    Engineering Understanding Moment Connections in Structural Design

    I Think it's moment connection. Because the end plate must be able to resist the moment transferred from the beam to the column. Please correct me if I am wrong.
  32. LCSphysicist

    How do calculate this moment of inertia?

    Inertia moment of a thin square side 2b about the center of mass... I put the coordinates in the center of the square and came to: Integral of (x²+y²)dm = Integral of (x²+y²)*(dxdy)M But, the interval of the integral is [0,b] to x and y And, since this consider just the integral of one...
  33. J

    Calculating Moment of Inertia from Ball Accelerations

    Hey guys. Im trying to figure out how to calculate the moment of inertia from a homogeneous ball based on a series of accelerations. The ball is released from the top of an incline plane (3.33 deg) and with a motion sensor, 5 values of acceleration where captured . Together with the radius and...
  34. G

    How to get the magnetic moment for this loop?

    About this figure, the current in the opposite wires are parallel (and not anti-parallel). So, for instance for the first option the torque is zero; but I wanted to know what is the magnetic moment of this loop. Since I rely only on formula I've have no idea how to compute for this one.
  35. K

    Find Inner & Outer Radius of Hollow Circle from Second Moment of Area

    Hi! I am trying to find the inner (r2) and outer radius (r1) of a hollow circle based on its second moment of area. I have the equation that I=π(r1^4-r2^4)/4. I think I need to use a simultaneous equation and then sub this in for one of the radii. However, I am unsure of another equation I could...
  36. R

    Determining moment (or torque) around a certain point on a wrench

    Here's a diagram of the problem. There are 3 possible solutions: 163 in-lb clockwise, 163 in-lb counterclockwise, 82.7 clockwise or none of them. After attempting the problem the closest I got to was 82.7 but that was wrong so I'm still stuck.
  37. SymNeric

    Analysing a ##C_M## graph (pitching moment data)

    Hi guys, I hope everyone is safe and well. I'm currently nearing the end of my third year dissertation, and I'm looking at analysing pitching moment coefficient (CM) data over a full range of angles of attack for airfoils with different serrations on the trailing edge. What are things to look...
  38. S

    Understanding Bending Moment Calculations in Mechanical Systems

    But the correct solution is M= P* (b2+b1). I don't understand how b2+b1 is the perpendicular distance.
  39. cwill53

    How can I calculate the moment of inertia of any object?

    Apologies if I make anyone frustrated. To start, I've only had up to Calculus II so far but I was curious how to use and evaluate integrals used for moment of inertia. I know that the moment of inertia is basically an object's resistance to rotation, and is the rotational analog of mass. I know...
  40. LCSphysicist

    Moment of inertia of a cone -- Why do we divide the equation dI = dm*r^2 by two?

    Why we divide the equation dI = dm*r^2 by two when we calcule the moment of inertia of a cone relative to its symmetry axis?
  41. Rongeet Banerjee

    Moment of Inertia for a Triangle with Masses at the Vertices

    If I take the three masses individually and try to calculate the moment of inertia of the system separately then I=(m*0²)+(m*(l/2)²)+(m*l²) =ml²/4 +ml²=(5/4)ml² But If I try to calculate Moment of Inertia of the system using its Centre of mass then As centre of mass is located at the the...
  42. Iqish

    Calculating Moment of Inertia for a Curved Rod with Respect to a Specific Axis

    Given:Thin, homogeneous, curved rod with radius of curvature 𝑅 See figure to the down. Find: The moment of inertia 𝐼𝑥′𝑥 ′ with respect to 𝑥′- the axis passing through the center of mass (point 𝐺). Can someone who can help me ?
  43. VVS2000

    Moment of inertia (experiment)

    So in the above image, I intend to find the moment of inertia of that black rotating object which rotates due to torque which is provided by placing mass on the pulley. But the thing is that this rotating object is kind of like a ball bearing kind of system and even for a small torque it starts...
  44. Ashish181

    Have You Calculated the Maximum Bending Moment Yet?

  45. Eggue

    Moment of inertia of a rod bent into a square

    I tried to find the moment of inertia of 2 rods connected at the corners by adding up their moments of inertia: \frac{1}{3}(\frac{M}{4})a^2 + \frac{1}{3}(\frac{M}{4})a^2 = \frac{1}{6}Ma^2 I then tried to solve for the moment of inertia at the center of mass of the 2 rods using the parallel...
  46. D

    How Many Seconds Make Up Eternity in The Shepherd Boy?

    I have read a short story by the Grimm Brothers, named "The Sheperd Boy" and there is a riddle that sounds like this: So we have a mountain made of pure diamond, and it takes 1 hour to climb it, 1 hour to go around it and 1 hour to go down into it (I assume from its peak to its base). And...
  47. A

    I Quadrupole Moment Time Variation: Does Coordinate Choice Matter?

    [Moderator's note: Thread spun off from previous discussion due to topic change.] Does the observed quadrapole moment change over time when considering a relatively moving object, for certain choices of observer coordinates? My suspicion is that it does (Terrell-Penrose rotation implies...
  48. Andrea Vironda

    I Why Does the Polar Moment of Inertia Use r^2 in Its Formula?

    Hi, A well-known part of the formula for calculating the deflection stress is ##I_z=\int \int r^2 dA## Usually a moment of inertia is something related to how difficult is to move an object. In this case is understandable but i don't understand the meaning of the double integral. Using ##r^4##...
  49. harryiverson

    First moment of area and second moment of area

    i am perplexed as to the first moment of area and second of area; i would like to know 1. why they come (how they are figured out and distinguished from each other) 2. what is meaning of these 2 moment of area in terms of physics what i have learned is that the first moment of area is used to...
  50. brotherbobby

    Net force and moment on a wooden bar fixed at one end

    Here is the diagram to the right. (a) Clearly, owing the fact that the bar is pinned at P, the net force on the bar is zero: ##\boxed{\Sigma \vec F = 0}##. The pin P applies an equal and opposite force to the one applied. This force keeps the bar from translating to a different position in...
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