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. I

    How does magnetic moment transform due to relativity?

    Hi, I have seen textbooks model how an electric field of an electron changes when viewed from another frame of reference. In these models, the electric fields seems to "compress" along the axis of motion. What happens to the magnetic moment in these situations? Does the magnetic moment also get...
  2. E

    Welcome to the Moment Calculation Discussion Forum

    Hi, I was thinking of something: How are one supposed to calculate the moment needed for a scoop to scoop up a sample of e.g. sand? Does the classical p=mv work? Any ideas or comments?
  3. T

    Shear force and bending moment diagrams question

    Homework Statement So in my notes we have the following example: So I decided to try to solve it another way, this time I flipped the figure and here is my attempt: I got the correct moment but then the signs on my shear is flipped. Does anyone know why?
  4. F

    3D Moment with force and couple

    Homework Statement The special-purpoise milling cutter is subjected to the force of 1040 N and a couple of 211 N·m as shown. Determine the moment of this system about point O. (Let's laugh at the text's typo)Homework Equations Mo = R x F + (Couple)The Attempt at a Solution I'm having a little...
  5. S

    Magnetic Moment Of Steel and Iron Wire

    Hello all, i would like to ask which is the magnetic moment of a steel and a iron wire with a length of 10,20 or 30cm! Is there any equation from which the magnetic moment can be derived? Thanks in advance :)!
  6. F

    Finding the Moment of Point B: Is it Largest?

    Hi can anybody tell me if my working for finding the moment of a b c is correct? Taking clockwise as +ve Ma+1.2k x 3 +0.7 x 7 = 0 Ma= -8.5Knm Mb-8.5+1.9k x 3=0 Mb=2.8kNm Mc=1.2k x 4 +1.9k x 7 -8.5k=0 Mc=-117.85Nm Hence Point B has the biggest moment am I right? However the...
  7. W

    Dipole Moment Integration Question

    In "An Introduction to Electrodynamics", Griffiths gives the following equation for the dipole moment: p=\int r' \rho(r') d\tau'. My question is, in general, what volume am I integrating over? It seems a bit arbitrary to me. I assume I'm integrating over whatever volume is enclosing the charge...
  8. W

    Moment produced by a fluid of varying density

    Homework Statement Find F, the force acting at the top of the gate. The gate is 2m high and 2m into the page. It is hinged at the bottom (red dot in the diagram) Density of fluid varies linearly. 1000 kg/m3 at the top and 1600 kg/m3 at the bottom (depth of 4m) Homework Equations...
  9. Y

    Finding the magnitude of the moment on a pipe wrench

    Homework Statement A force of 56 pounds acts on the pipe wrench shown. find the magnitude of the moment about O by evaluating || OA x F || Homework Equations || OA x F || The Attempt at a Solution First I tried to find my vector component for Force which I got -56 [ cos(30)i +...
  10. G

    Hollow Sphere Moment of Inertia

    I need to find the moment of inertia of a sphere of radius ##r## and mass ##m## about an axis through it's centre. I've already done it and got the correct answer of ##\frac{2}{3}mr^2## however I have tried doing it using a different method to see if I get the same answer, but I don't, and I...
  11. F

    Shear and bending moment diagram problem

    Homework Statement I have attached a diagram Homework Equations 14 + Va -32 + Vb -15=0?? or Vb=-15? The Attempt at a Solution The reason why I cannot attempt this problem is that I'm not sure whether it is valid that there can be a point load at Support B or whether they are...
  12. P

    Calculating Mass Moment of Inertia in a Two Stage Planetary Gearbox

    hi everyone, help me, To calculate the mass moment of inertia at output shaft with respect to input shaft in the two stage planetary gearbox. Torque at input = 15 Nm input speed = 1440rpm stage I zs=14 zp=23 zR=61 fixed stage II zs=21 zp=40 zR=102 fixed
  13. G

    Moment of Inertia: Kinetic Energy, Momentum & Conservation

    I read that for a rotating body the kinetic energy ##E_k = \sum \frac{1}{2}mv^2 = \frac{1}{2}{\omega}^2∑mr^2 = \frac{1}{2}I{\omega}^2## where ##I## is the moment of inertia. If we did the same thing for momentum then ##P = ∑mv = \omega\sum mr## So why is angular momentum ##I\omega=\omega\sum...
  14. B

    What is the Relationship Between Moment of Inertia and Relativity?

    In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, parabola's, hyperbola's, sphere's, ellipsoid's, paraboloid's, hyperboloid's, cones & cylinder's...
  15. A

    Moment & Distance Homework: Steel Beam & 80 kg Person

    Homework Statement A 10 m long steel beam which weighs 700 kg lies on a roof. The beam sticks out 4,5 m over the edge of the roof. How far can a person weighing 80 kg go out on the beam (on the part sticking out over the edge of the roof) without the beam tipping over? The answer is...
  16. H

    Moment and force calculation for cantilever beam

    Homework Statement A cantilever beam (prismatic, rectangular cross section) is loaded at the tip by a force P and at half its length L by a moment M. a. Calculate the reaction force and moment. b. Draw the shear force and bending moment diagrams Homework Equations ∑F=0; ∑M=0 The...
  17. N

    Couple moment problems - Calculate the distance?

    Couple moment problems -- Calculate the distance? Homework Statement http://imageshack.com/a/img691/1734/804i.jpg Homework Equations M = F x d The Attempt at a Solution M = Fxd 20Nm = 35N*x x = 0.57m cos 30 deg = x/d d = x/cos 30 deg = 0.57m/cos 30 deg = 0.66m...
  18. shinnsohai

    ShearForce & Bending Moment Exp

    Homework Statement Recently I am undergoing such experiment in school and my lecturer asked that, as if any changes in the distance(vertically) will there be changes in the force/reading of it?Assuming there is no changes in anything else except the position of the tools. (Since the "Cell...
  19. carllacan

    Moment of inertia of a cube along the diagonal.

    Homework Statement Calculate the moment of inertia of a cube which rotates along an axis along its diagonal. Homework Equations Moment of inertia definition: I = \int \rho (\vec{r}) \vec{r} ^2 dV Angular velocity vector; \vec{\omega}=\omega (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}...
  20. C

    Moment diagram with triangular load

    Homework Statement For the overhanging beam in the figure, A) draw the moment diagram indicating all critical values including the maximum moment (Value and location), and B) write the moment function, M(x), for B-C section in terms of x coordinate as shown in the figure. Homework...
  21. J

    Moment about an axis - please

    (Figure is attached) Find the tension in the cable AB such that the net moment about the hinge axis CD induced by the forces F and P is zero. The force F is applied at point A and the force P is applied at point E. The magnitude of the force P is P = 65 lb. Two coordinate direction angles for...
  22. J

    1st and 2nd moment of interia of curves and surfaces

    If I can to calculate the 1st and 2st moment of inertia of areas and volumes, I can compute for curves and surfaces too?
  23. H

    Moment of Inertia of Hollow Sphere about Center Axis x-y-z method

    Homework Statement Find the moment of inertia of a hollow sphere about a vertical axis through its center in terms of its mass M and radius R. Homework Equations I=\int r^{2} dm The Attempt at a Solution I've been curious about different methods for finding moments of inertia...
  24. D

    Change in orbit due to moment of inertia change?

    Hi, So recently I read about the massive 3 gorges dam changing the mass moment of inertia of the Earth to such an extent that the days will now be 60ns longer. Then I thought, how will this effect the orbit of the Earth about the Sun? Any thoughts?
  25. K

    Answer check please - Moment of Inertia Calculations

    Answer check please -- Moment of Inertia Calculations For question 1 I got T=mnut * r pulley * gravity For question 2 I got Isystem = 1/2 M(R23 + R24 + m (R21 + R22) First day of physics lab and I just wanted to double check that these are correct. Thanks.
  26. H

    Moment of Inertia question (dead simple)

    Homework Statement A thin disk is 100g. It's diameter is 20cm. It's thickness is 2cm. Rotation is about the central axis (ie. perpendicular to the symmetrical plane). Answer in kg*m2 Homework Equations I=(1/2)MR2 M is the mass R is the radius I is the moment of inertia The...
  27. B

    Draw shear force and bending moment diagrams

    Homework Statement For the beam shown in the figure: a) Draw necessary free body diagrams b) Calculate support reactions c) Draw the shear force and bending moments Homework Equations ∑Fy = 0; ∑M = 0; V(x) = ∫ L(x) ; M(x) = ∫ V(x) The Attempt at a...
  28. K

    How Do You Transform Electromagnetic Dipole Moments When Boosting Orthogonally?

    I just wondered how I transform electromagnetic dipole moments. For example assuming I have magnetic dipole moment μ in a frame without E dipole moment. Then I boost orthogonal to μ. Now I would like to determine the electric dipole moment. I could use the magnetic potential and transform...
  29. J

    Calculating Magnetic Moment of Nickel per Kg

    Homework Statement For nickel, which has an atomic magnetic moment of 0.61 and an atomic weight of 58.7, calculate the magnetic moment per kilogram of the material Homework Equations None given The Attempt at a Solution Do I not need density to use formula for saturation...
  30. S

    Derivation of the quadrupole moment of gravitational wave

    Hi, Can anyone give a derivation of the quadrupole moment in the TT gauge ( Equation metioned below ) of the gravitational wave ? QijTT(x) = ∫ρ(xixj-1/3δijr2)d3x Where ρ is the matter density Thanks In Advance
  31. B

    Shear and moment diagram for the beam

    Homework Statement Draw the shear and moment diagram for the beam Homework Equations ∑Fy=0 ∑M=0; ΔV=∫w(x)dx ΔM=∫V dx The Attempt at a Solution I am firstly finding the external forces as any statics problem(Ay=13.5kN upwards, By=13.5kN upwards).Then I found the equations of the...
  32. M

    Shear Force and Bending Moment Diagram

    Homework Statement This is the question that I am struggling with. http://postimg.org/image/5kb0pur3z/ I need to plot shear force and bending moment diagram of it.Homework Equations The beam is in static equilibrium so algebraic sum of forces in x and y direction equal zero. Also, moment is...
  33. binbagsss

    Moment of Inertia Tensor Cylinder.

    I am computing the \hat{I} - moment of inertia tensor - of a cylinder with height 2h and radius R, about its axis of symmetry at the point of its centre of mass. I am working in cartesian coordinaes and am not sure where I am going wrong. (I can see the cylindirical coordiates would be the...
  34. J

    Moment of inertia tensor for a laminar

    Hi, Consider a 2D laminar only rotating about the z axis, with the axis origin at the bottom left hand corner and adjacent sides coinciding with the z and x axes. so ω = (0,0,ωz) y = 0 I don't understand how the IXZ component is 0 to just leave the IZZ component?
  35. T

    Elastic postive bending moment

    Hello I just joined this forum and this is my first thread here. This is my assignment question. I'm supposed to find elastic positive bending capacities around the horizontal axes for the following cross section shown in pic. The elastic stress in tension is 10 ksi and in compression is 15...
  36. B

    Center of mass and moment of inertia of catenary

    Homework Statement A homogeneous catenary ##z=acosh(x/a)##, ##y=0## and ##x\in \left [ -a,a \right ]## is given. Calculate the center of mass and moment of inertia Homework Equations The Attempt at a Solution I started with ##x=at##, for##t\in \left [ -1,1 \right ]##, therefore...
  37. Alpharup

    Awkward Phone Call: A Scientist's Unexpected Encounter

    I once called my old high school physics tutor by phone. He was not that fluent in English. He needs to be appreciated by me because without him, mechanics would have been much difficult... Our conversation began and we spoke about some concepts, how life went on and so on...He was talking...
  38. binbagsss

    Moment of Inertia tensor - displaced axes theorem:

    Ok, so the system consists of two massive spheres, m1 and m2, of radii a and b respectively, connected by a massless rod of length R, as seen in the diagram attached. The question is to calculate the moment of inertia tensor. Sol: Set the origin at the centre of mass . So that we are in...
  39. M

    Buckling in various planes, finding moment of inertia

    Homework Statement Homework Equations The Attempt at a Solution With this problem and in general, I am having difficulties knowing what should be the cubic and what shouldn't be from visual inspection, so in this case I can't tell why I_x is 1/12ba^3, as opposed to 1/12ab^3. How can I tell...
  40. R

    Angular Moment Cube: Calculating $\vec{L}$

    Homework Statement An homogeneous cube of mass M and side 2a spins around one diagonal of the faces with constant angular velocity w. Show that the size of the angular moment in relation to one of the fixed vertexes is \sqrt{\frac{43}{3}}Ma^2w What I visualize here is a cube with one of its...
  41. B

    Derive an equation for the maximum bending moment

    The calculation for the maximum bending moment is to be verified experimentally using a strain gauge bonded to the outer surface of the beam, at the point where the maximum bending moment occurs. Derive an equation which could be used to calculate the bending moment from the measured strain...
  42. R

    Calculating Bending Moment and Microstrain in Hollow Circular Beam

    Homework Statement Hollow circular beam with outside diameter 350mm, and wall thickness of 60mm E=60 Gpa beam length 2m Force applied to beam at midpoint of beam (1m from each end) F=200KN Force applie from the Top down, Ra , and rb from bottom up Homework Equations...
  43. KiNGGeexD

    What is the Moment of Inertia of a Flywheel?

    Ok me and my friend have clashed with solutions to calculate the moment of inertia of a flywheel and I think I have it after a while but I'm not so sure about my maths! The solution he ended up with was a lot larger and more complex :) really enjoying this forum:)
  44. H

    Effective Magnetic Field in Ground-State Hydrogen Atom?

    Homework Statement A hydrogen atom in its ground state actually has two possible, closely spaced energy levels because the electron is in the magnetic field B of the proton (the nucleus). Accordingly, an energy is associated with the orientation of the electron's magnetic moment (μ)...
  45. M

    Calculating the moment along a statically indeterminate beam

    Homework Statement How could I calculate the piecewise formula for M(x)? Homework Equations The Attempt at a Solution From constructing a free body diagram it looks like up until the pin support, M(x) = -Fy*x (Fy being the force pointing upwards at the wall) but I am confused...
  46. M

    Moment of inertia of triangle about centroidal axis

    Homework Statement There is the moment of inertia about an x and a y-axis named, I_{x}, I_{y}. Then there is the moment of inertia about the centroidal x and y-axis named, \overline{I}_{x}, \overline{I}_{y}. Often we can look up these values in a table (like the figure included) and apply...
  47. A

    Exponential distribution moment generating function to find the mean

    With mean = 2 with exponential distribution Calculate E(200 + 5Y^2 + 4Y^3) = 432 E(200) = 200 E(5Y^2) = 5E(Y^2) = 5(8) = 40 E(4Y^3) = 4E(Y^3) = 4(48) = 192 E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8 E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48 is this right?
  48. 1

    Shear and Moment Function Trouble

    Homework Statement In the question (see attached images), it asks me to draw the shear and moment diagrams for the beam shown in the figure. To do this, we use the equilibrium equations. What I do not understand is why M is present in the equilibrium equation for bending. Isn't the pivot...
  49. W

    Understanding Moment of Inertia for a Beam Bending about the Y-Axis

    Homework Statement I'm supposed to solve for the maximum moment assuming the beam bends about the y-axis (not the z axis as shown in the image. Same image for different questions). I don't understand how to find the moment of inertia in this case. The solution gives the moment of inertia for...
  50. KiNGGeexD

    Moment of inertia of circular flywheel

    Hi I'm new to this forum so still getting used to it! I have to find the moment of inertia of a circular flywheel which has radius, a and mass m! But also had area density (mass per unit area) of ρ0, Where ρ0=ρa(1+r/a) I know moment of inertia is the integral of a^2 dm and in order to...
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