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. O

    Second moment of inertia for a bent rectangle

    Hello. I am currently working with a beam with the following cross-section: It consist of three bended sections with the following parameters, alpha = 90 degrees, Thickness = 4 mm, Radius = 50.59 mm. The top section consist of a small triangle and a rectangle. the triangle have a width = 4 mm...
  2. oohaithere

    Moment of Inertia of equilateral triangle about vertex

    Homework Statement A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. Homework Equations Slender rod, axis...
  3. K

    B Resolve Moment: Force & Distance Explained

    Why can we not resolve the force and the distance to find the moment? I attempted a question where it does not work.
  4. W

    Simple bending moment calculation

    Hi, Really need some help with figuring out the max bending moment in the diagram shown below (I'm aware this is extremely simple but time and stress appear to have the better of me, so any help is appreciated) I think I've worked out the reactions at each support by doing m=wL as the...
  5. Kumaken

    Application of integrals to find moment Inertia

    I need to make a project that integrates physics with math, involving the use of integrals to find moment inertia of areas. The theory could be read here :http://www.intmath.com/applications-integration/6-moments-inertia.php I need to make an object that applies the theory above. Can anybody...
  6. E

    Moment of inertia for this assembly

    Homework Statement A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end of the rod, and a small 0.0500-kg sphere is welded to the other end. The rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from...
  7. J

    What is the Angular Speed of a Rotating Object with Varying Inertia?

    1. A 3.0 kg vertical rod has a length of 80 cm. A 4.0 kg rectangle attached to the top of the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal. 2. Using...
  8. D

    Moment of Inertia of a Propeller?

    Is there an equation for the moment of inertia of a propeller? If so, what is it? If there isn't one, can I use the moment of inertia of a rectangular slab? Thank you in advance.
  9. H

    Understanding Moment and Center of Gravity in One Dimension

    Homework Statement The book I am reading says that given a point mass(m) at the point x, the quantity mx is the "moment about the origin)" It then defines the moment of a collection of points as M = m(1)x(1) + m(2)x(2) + ... m(n)x(n) where m(1) = mass of first point and x(1)=distance of first...
  10. M

    Parts of the design of an aircraft that affect the pitching moment

    If I wanted a higher value for pitching moment due to a change in pitch rate, Mq, what are some design alterations I might make to an aircraft to incorporate this. I am guessing changes to the airfoil or maybe the tailplane but I am not sure what changes you would make to get a desired result.
  11. Vitani11

    Finding moment of inertia of cone

    Homework Statement Why is it that when you integrate to find the moment of inertia of a cone standing on its vertex (like a spinning top) with height h mass M and radius R do you integrate the R limits as 0 to (R/h)z in the triple integral (cylindrical coordinates) below? Homework Equations I =...
  12. OrlandoLewis

    Moment of inertia of a set of spinning disks

    Homework Statement The shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M = 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O...
  13. T

    Calculating inertial moment of a disk

    Hi, I have a disk of diameter r, and the mass of the disk is 1kg. I'm going to rotate the disk at its center. my question is: 1. let's say I put a load of m kg on top of the disk, does the moment inertia of the system is as simple as (m + 1kg)r2/2? 2. does the shape of the load put on top of...
  14. R

    Finding the Moment of Inertia for a Rectangular Sheet

    Homework Statement The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the...
  15. Vitani11

    Deriving the moment of inertia of a sphere

    Homework Statement A uniform spherical ball of mass M and radius R, initially spinning about a horizontal axis with angular speed ω0, is placed gently on the floor. The initial center-of-mass velocity of the ball is zero. Derive that the moment of inertia ICM of the ball about an axis passing...
  16. D

    How to determine direction of a moment

    Homework Statement I am following the first problem on this online pdf: http://www.ce.udel.edu/courses/CIEG212/Homework_1_2007.pdf Homework Equations Equilibrium equations for forces and moments. The Attempt at a Solution I know how to solve the problem, that part is straight forward. However...
  17. Cocoleia

    Dipole moment, electric potential

    Homework Statement I am given this picture and I know that |q1|=2nC, |q2|=5nC, d=1mm I need to first find the total dipole moment of the system. Then I need to find an equation that represents the electric potential due to this net dipole moment for all (everywhere) Homework Equations p=qd...
  18. G

    1st, 2nd and mass moment of inertia

    I know most of the formula's but I'm trying to get a conceptual understanding of everything and finding it very hard to get concise information about everything all in one place especially when there are so many names for the same thing. Most resources just rehash the formulas without explaining...
  19. F

    Understanding Absolute Max Moment: Example and Explanation

    Homework Statement In the first 2 notes , i was told that the absolute max moment will occur under the largest force lying nearest the resultant force of system . but , in the example that i have uploaded , i found that the absolute max moment will occur under the 6kN load instead of 8kN p/ s...
  20. doktorwho

    Find the position of equlibrium

    Homework Statement From the diagram below find the position of the man (##x##) if the system is in balance. Total length is ##L## and the man is distance ##x## from one end. Homework Equations 3. The Attempt at a Solution [/B] I know that the system must be in balance if all the torque and all...
  21. doktorwho

    Moment of inertia of a rigid body

    Homework Statement Determine the moment of inertia of a rigid body on the picture: The radius of the inner cylinder is R and the outer is 2R. Homework Equations 3. The Attempt at a Solution [/B] I thought of subtracting the big cylinder inertia from the small and adding the hanging body and...
  22. F

    Why Is the Maximum Moment Under the 1.5k Load in Beam Analysis?

    Homework Statement For the maximum moment occur under the 1.5k load , why when we consider the left part of the beam, we just need to consider the forces 2k and 1.5k only ? Homework EquationsThe Attempt at a Solution How about FR = 4.5k and also the 1k ? Cant i just consider all of them ...
  23. doktorwho

    Help understanding torques and moments

    Homework Statement Find the period of small oscillation of this system. Homework Equations 3. The Attempt at a Solution [/B] I understand the concept of moment of inertia but can't comprehend the first equaion here. The other two i get and they are moments of inertia of other two bodies...
  24. M

    Buckling Load Equation for Eccentrically Loaded Rectangular Solid Column

    Homework Statement I'm reading a paper and I'm trying to understand how does the author arrived from equation (1) to the following buckling load equation (2). I know that the author substitutes equation (1) with the dimensions of the geometry but I still could not understand how he comes to...
  25. LiviaPimentel

    Understanding Moment of Inertia: Exploring the Mechanics of a Slender Rod

    Homework Statement The uniform beam shown in the IMAGE below has a weight W. If it is originally resting while supported on A and B by cables, determine the pull on cable A if cable B suddenly fails. Admit that the beam is a slender rod. IMAGE: Homework Equations TotalTorque=I*α...
  26. S

    B Understanding Axial and Radial Moments: Definition and Importance

    Hello can someone explain what is axial and radial moments?
  27. F

    Moment in beam (caused by influence line)

    Homework Statement http://cereference.com/book/structural-analysis/influence-lines-beams In the example , i don't understand the moment in the part of beyond AC . I don't understand why we don't have to consider the momenty due to unit virtual load in the part beyond AC , just like what we did...
  28. F

    Moment distibution (stiffness factor modifications) for a frame

    Homework Statement For the KAb and KCD , they are connected by the same method ... At B and C , we can see that they are connected by the same method , although i am not sure it's fixed or pinned . Homework EquationsThe Attempt at a Solution I assume they are fixed at B and C , so i agree that...
  29. F

    Understanding Moment Distribution in Beam Analysis

    Homework Statement For the circled part , i don't understand why it's 4 and 6 . I know that it's about distribute the moment according to the ratio that we have determined earlier . Homework EquationsThe Attempt at a Solution For 4 , shouldn't it be 240*0.4 = 96 ? For 6 , shouldn't it be...
  30. F

    Moment about a point on a beam

    Homework Statement For the moment about B ' , why there is extra θA L behind ? 2. Homework Equations The Attempt at a Solution is that wrong ? I think there should be no θA L behind in the equation of moment about B '
  31. F

    Exploring the Moment Generated by 0.8NB at Point A

    Homework Statement for the moment about A , why there 's moment generated by the forces of 0.8NB (circled part) ?Homework EquationsThe Attempt at a Solution I think it's not necessary to include the moment 0.8NB(4) because the d = 0.4m is not measured directly from point A ...it's measured from...
  32. Chadi B Ghaith

    Moment of Inertia: Proving Mass, Side & Axis | 1/12 md²

    I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
  33. M

    Moment of inertia of this body

    1. The problem statement, all variables and given/known See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis Homework Equations I=mr^2 The Attempt at a Solution I tried to get the moment of intertia of rod by integration from...
  34. P

    Neutron scattering - determing the magnetic moment for MnO

    I'm told that the MnO crystal resembles in structure that of NaCl (FCC) with lattice constant a, and am first asked to write a general expression for the position vector Rj of the ion j in the unit cell of MnO. I am then asked to find the vector K for MnO in order to use the relation...
  35. R

    MHB Finding Moment of Inertia for Solids: Sphere, Cylinder & Cone

    question 1 The vector field F(x, y, z) = 2xi + 2yey2+z j +(ey2+z + cos z) k is conservative. Find a corresponding potential function. * e raise to power (Y square +z) Question 2 Consider a solid sphere of radius R, a cylindrical shell of outer radius R, inner radius a, and height h, and a...
  36. N

    Moment of Inertia: Rules & Usage Guide

    To find Moment of inertia, there are 2 rules: I = ∑m r2 I= ∫ r2 dm I don't know when to use the first and when to use the second rule.
  37. F

    Sign of moment in buckling of column

    Homework Statement Can someone explain why the M is assigned to be anticlockwise here ? Homework EquationsThe Attempt at a Solution When i assign it as clockwise , i will get -P(δ -v) , which is different from the author ... Can i do so ? Why ?
  38. M

    What is the Relationship Between Inertia and Moment of Inertia?

    Hi Have a look at attached formula. This is a part of a software. it is 'Inertia' which has 'Kg.m^2' unit. You know 'Kg.m^2' is 'Moment of Inertia' unit. What is your idea about this? Does it use 'Inertia' as 'Moment of Inertia'?
  39. T

    Proving generality of moment of inertia

    Homework Statement Consider a circular disc (that might be a tautology), free to rotate and translate in the xy-plane only. It has radius R, but its mass is unhomogeneously distributed in some unknown fashion. All we know is that the center of mass is displaced from the centre of the disc by...
  40. P

    MHB Moment of Inertia: Use Parallel Axis Theorem

    Use a parallel axis theorem to determine the moment of inertia of a uniform disc of mass M and radius R about the x-axis perpendicular to the plane of the disc and passing at the edge of the disc.
  41. W

    Understanding Net Force and Net Moment in Statics

    Homework Statement Homework Equations I can see how the net force is not the same but I'm not getting the net moment. The Attempt at a Solution 12mm x 10N = 120N-mm. How do these two FBDs not have the same net moments. Thanks for any help!
  42. RavenBlackwolf

    Center of Mass and Moment of Inertia

    Homework Statement A small pine tree has a mass of 15kg. Its center of mass is located at .72m from the ground. Its trunk is sawed through at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 17° angle with the...
  43. F

    B Exploring the Concept of Moment Conservation in Structural Engineering

    If the base of a column suddenly turns from fixed to pinned.. the moment (bending) would be redistributed to the top of the column or the beam. Why is that? What is the principle called? Conservation of Moments? Or what?
  44. F

    Moment of inertia about the origin for the lamina

    Homework Statement find the moment of inertia about the origin for the lamina which the surface of sphere (x^2) + (y^2) +(z^2) = 9 . z>2 . Given that density is a constant . Here's my wroking The ans is 16pi (k) , but my ans is different , is my ans wrong ? If so , which part is wrong ? I...
  45. C

    Moment of inertia of a hollow cylinder derivation

    Homework Statement Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry. Homework Equations $$dm = \rho dV$$ $$dV = (2 \pi R)(dR)(h)$$ The Attempt at a Solution I was mainly...
  46. J000e

    Understanding Maximum Moment for Moving Loads: Strength of Materials Reviewer

    Hey guys, I've been reading my strength of materials textbook and its pretty much like a reviewer that contain several problems and short descriptions of their concepts. There's this formula that computes the maximum moment for two moving loads and its: [PL-(Psmall)(d)]^2/4PL where P= Psmall...
  47. M

    Parallel Axis Theorem- Composite Areas (STATICS)

    Homework Statement Consider the beam shown in (Figure 1) . Suppose that a = 15 in. , b = 8 in. , c = 1 in., and d = 4 in. Determine the moment of inertia for the beam's cross-sectional area about the x axis...
  48. L

    How is tension in a string affected by moment of inertia?

    Homework Statement I'm in need of a more conceptual answer, rather than numerical. Say you have a block on a horizontal frictionless table (block 1). Then you have a string tied to block one and strung over a pulley that is at the right end of the table (the pulley has mass). On the other...
  49. E

    Why is "dr" not used for moment of inertia calculations?

    When calculating the moment of inertia for a rotating object, why is "dr" not incorporated into the integral? However, dm is part of the integral, isn't the distance from the axis of rotation changing as well? Hence shouldn't the integral involve both dm and dr?
  50. F

    Moment applied causing bending stress in beam

    Homework Statement From the solution , it's clear that the top part of the beam undergo tension , while the lower part undergo compression . Homework EquationsThe Attempt at a Solution But , i don't understand why it is so . When the moment is applied in the horizontal axis , the structure...
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