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. George Keeling

    I Time derivative of the moment of inertia tensor

    I am completely stuck on problem 2.45 of Blennow's book Mathematical Models for Physics and Engineering. @Orodruin It says "We just stated that the moment of inertia tensor ##I_{ij}## satisfies the relation$${\dot{I}}_{ij}\omega_j=\varepsilon_{ijk}\omega_jI_{kl}\omega_l$$Show that this relation...
  2. B

    I Question about anapole moment measurement

    Hello! My questions is about this paper, aiming to measure the anapole moment in a molecule. In their derivation, starting from equation (1), they assume that the frequency of the field felt by molecules ##\omega## is much bigger than the energy splitting ##\Delta##. That basically implies that...
  3. J

    I Direction of friction of each wheel and total moment when a car turns

    Static friction is known to provide centripetal force when a car turns. Assuming uniform circular motion, my questions are 1. Is the static friction of each wheel points toward the center of turning circle or it's the combined forces of all four wheels that has to point toward the center of...
  4. entropy1

    I Is the moment of the measurement well defined?

    Suppose Alice and Bob do an experiment with an entangled pair of particles, for instance electron spin with SG magnets. Now suppose Alice her SGM is stationary while Bob his SGM is switching fast between parallel to Alice and perpendicular to Alice. So there are two possibilities: correlation...
  5. M

    Why do I have a bending moment and an axial displacement here?

    Hello, I have an flexure where the force is applied asymmetrical, I just can't visualize why their should be a bending moment instead of an bending force? How can I distinguish those? Thanks!
  6. S

    Engineering How to find the sense of rotation of a resultant moment?

    Hello, so I have a question about the sense of rotation of the body. I get the calculating part nd stuff like that. But what I don't understand is how we would determine the sense of rotation about the moment axis? Could someone explain this to me please? (to add to this, I know that it is...
  7. M

    How to take a moment into account for deflection of a beam

    Hello! I have to calculate the deflection of a beam at at given point (C). The books says the should be a moment which plays a role in this deflection. How does this moment occur? I have drawn a FBD but couldn't find a moment? Should I divided the beam into separate parts or so? What am I...
  8. M

    What's wrong with my solution? -- Area moment of inertia

    I used the parallel axis theorem to solve the question but my answer is still wrong. Any ideas where I slipped? I can't seem to figure out the problem?
  9. patric44

    Exploring Nuclear Quadrupole Moment and Deformation

    hi guys I have read the other day about how the nuclear quadruple moment descries the deformation of the nucleus, however i can't get my head around how is that!, I am familiar with the multiple expansion in which we can describe the potential of an arbitrary charge distribution by the following...
  10. rylest

    Stuck on complex pipe system bending moment hand calcs

    Some more details on the system are that L1 is very long (close to 100ft) and L2 is close to 30ft (the vertical pipes). The piping is all schedule 40 1/2" OD. Moment of inertia is roughly 10^-8. Components are about 2kg each. The distance of the pipes horizontally is small (around 2ft). Pressure...
  11. K

    I Definition of magnetic moment in quantum mechanics

    * The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...
  12. T

    A Reason out the cross product (for the moment): a skew symmetric form

    I am sure you are all familiar with the cross product in 3D space. i cross into j gives k. Cyclic Negative, if reversed, etc. I am sure you are all familiar with the definition as: norm of the first vector, norm of the second, sine of the angle, perpendicular (but direction using right hand...
  13. curiousPep

    I Resolve moment of inertia at an angle

    Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex. Can I split the rotated square to two squares in the x-z plane and y-z plane to find...
  14. M

    Engineering Statics project involving shear & moment diagram of a control arm

    Part of a project I am working on (part #3…see description below) is asking us to find the internal loads (shear and moment) and draw the corresponding shear/moment diagrams of the control arm shown below. It’s a little tricky to me, because all of the members associated with these type of...
  15. A

    Moment of Inertia of a 4 rod system

    This was the question (The line below is probably some translation of upper line in different language) For disc it was ma^2/2 For ring it was ma^2 For square lamina it was 2ma^2/3 For rods It was different Please explain Thank You🙏
  16. Tapias5000

    How to determine the same moment of inertia in two different ways?

    My solution is now I am asked for the same result but in this form but I don't know where to start.
  17. M

    Engineering Solving a Moment Vector Direction Problem: An Example from Statics Textbook

    This isn’t a HW problem per say, but it’s an example shown in my statics textbook that is used to try an explain that you need to add a couple moment to move a force to a point not on the line of action, and I’m just not seeing how the direction of the couple moment is correct. See the image...
  18. j19063dc

    Finding the resultant force, moment, and x-y coordinates

  19. A

    Magnetostatiscs: dipole moment and magnetic field

    Hello! I tried to solve a) see figure below, is it correct? b) so what I think I can do is to solve ## M_{12} ## from the equation of the magnetic flux then I will get ## \frac{\Phi}{I} = M_{12}## Then I can even use the equation får the magnetic flux and the magnetic field $$ \Phi = \int \vec...
  20. Tapias5000

    How can I solve these two physics problems? (equilibrium and moment)

    I tried to solve it and I got the following is it correct? and 2 My solution... is a negative distance?
  21. Tapias5000

    Can Derivative Methods Determine the Correct Angle in Physics Problems?

    This is the image of the problem: I tried to solve it and I got the following is it correct? derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?
  22. greg_rack

    Equivalent system (force+couple moment) of a loaded beam

    Hi guys, I don't really know how to cope with this problem, maybe just because I can't properly understand the data. In the figure we have a beam with its loading(plus a force of 15kN), a pivot O and support at the rightmost point. I would say that in order to find the equivalent system, I...
  23. entropy1

    B Copenhagen Interpretation and collapse moment

    Is it still true that under the Copenhagen Interpretation the standard theory of QM tells us that a measurement apparatus gets into superposition of possible measurement outcomes and does not tell us how and when we get a single decisive outcome? (The so-called "Measurement problem")
  24. T

    I Are Peak Moment and Peak Torque Equivalents in Biodex Dynamometry Measurements?

    Apologies if this is in the wrong section as it isn't particularly medical in nature despite it being about the body. I am currently conducting a rapid review with outcomes of knee muscle strength. This is measured by biodex dynamometry, which assesses numerous values including Peak moment...
  25. M

    Change the application pole of the moment of a force

    Good morning everyone! I am an aerospace engineering working on my thesis and i am trying to solve a little problem. In the picture you can see an "aeordynamic" body. The CFD analysis gives me the forces and the moments acting on this body. How can i calculate the momentum acting on the body...
  26. K

    I Dipole moment of Rydberg states

    Hello! Are there any experimental measurements or theoretical calculations of the electric dipole moment of any Rydberg state for CaF or BaF? Thank you!
  27. M

    Torque due to moment of inertia (?)

    Hi! I would like to calculate (roughly) how much torque is needed bringing the blue plateau in movement. Assume the blue plateau is loaded with 7.5 kg. The radius of the blue circle is 100 mm.
  28. MaratZakirov

    Rail Car with a Sail in the Wind

    I solve the following problem, there is a particle of mass ## m_p ## and velocity ## \vec{v}_p ## which collide with sail installed on rail car with mass ## m_c ## resting in the frame of reference associated with it before the collision. The cart is fixed on straight rails for which the vector...
  29. Ang09

    Moment of Inertia with varying distance from Centre of Mass

    h = d1 + 0.08 d1 = h - 0.08 d2 = h + 0.08 I of the vertical portion = 1/12 m (l^2 + b^2) + md1^2 = 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2 I of the horizontal portion = 1/12 m (l^2 + b^2) + md2^2 = 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2 The moment of inertia for the whole T-shape about...
  30. antonov

    Moment of inertia composite body

    I have this moment of inertia problem and is a little confused on the semicircle part and if the rest is really right? I get over 10 if I calculate it in crew CAD but by hand I get 7,568032142. What is right and what am I doing wrong?
  31. D

    How does Prokon calculate imperfection moments in slender columns?

    Homework Statement:: Anyone familiar with prokon column design ? I have no idea how the program caluculate the imperfection moment in the slender column (braced/unbraced... Relevant Equations:: I have attached an example here , it's an unbraced slender column here. Why the imperfection moment...
  32. A

    I Orbital magnetic dipole moment of a proton

    hi every one what is the amount of orbital magnetic dipole moment of proton? this different with the intrinsic magnetic.
  33. Hamiltonian

    Moment of inertia of a disc using rods as differential elements

    I know there are more convenient differential elements that can be chosen to compute the moment of inertia of a disc(like rings). the mass of the differential element: $$dm = (M/\pi R^2) (dA) = (M/ \pi R^2) (2\sqrt{R^2 - y^2})(dy)$$ the moment of inertia of a rod through its COM is...
  34. TheBigDig

    Determine the moment of inertia of a bar and disk assembly

    I have been given an answer for this but I am struggling to get to that point $$ANS = 0.430\, kg \cdot m^2$$ So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R##...
  35. P

    Moment of Inertia of a sphere about an axis

    I = 2/5M R^2 + Md^2 This is analagous to Earth's movement about the Sun. Is the moment of inertia of Earth about the centre of mass of the Earth Sun system = 2/5MR^2 + Md^2, where: M = Mass of earth, R = Radius of Earth, d = distance from Earth to centre of mass of earth-sun system.
  36. warhammer

    Question on Moment of Inertia Tensor of a Rotating Rigid Body

    Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...
  37. U

    Clarification on electric quadrupole moment definition

    I have encountered two (?) definitions of the electric quadrupole moment. They are: $$Q_{ij}=\frac{1}{2}\int \rho(\vec{x}')x'_i x'_j\,\mathrm{d}^3x'$$ and $$Q_{ij}=\int (3x'_i x'_j-\delta_{ij}x'^2)\rho(\vec{x}')\,\mathrm{d}^3x'$$ I am trying to study radiation arising from the electric...
  38. Pipsqueakalchemist

    Engineering Solving Moment Equations with Newton's 2nd Law: Help Needed!

    So I set up 3 equation for this problem. 1st was the moment equation about point G, 2nd and 3rd were from applying Newton's 2nd law to each of the blocks. I thought once I set those equations up I could solve for alpha (angular acceleration) and then find acceleration of each block but when i...
  39. Y

    Asymmetric bending principle of second moment of A derivation

  40. Who_w

    Moment of inertia of a regular triangle

    Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or...
  41. Leo Liu

    Computing the polar moment of inertia (calculus)

    Question: Diagram: So the common approach to this problem is using polar coordinates. The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is $$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$ whose value is...
  42. VVS2000

    Dipole moment of a rotating disk

    I could do the first part of the question with ease but second part I am not sure how to proceed. Should we calculate the magnetic field at d(where the loop is) and infer something from that for it's motion?? Plz help me out Thanks in advance
  43. R

    I General Magnetic Dipole Moment For an Electron in an Atom

    On the first attached page ##\mu_z## is associated with orbital angular momentum (Eq. 41.34). On the following pages (Eq. 41.38) it is associated with spin angular momentum? Are these both part of the same thing? I tried to read further but the book does not address this. In example 41.6 it...
  44. L

    Bending Moment for Bending Diagram

    Hi Im a bit confused with the example Can somebody explain and show to me how they got the bending moment calculations for the diagram in the attached. i understand it up to there. I started course late and can't ask for help. Thanks
  45. A

    Sign convention of internal forces in vertical bars for bending moment

    Hello: I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments. For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached? Beam...
  46. Camailee

    Engineering Statics problem: A ramp is supported by two cables

    Problem illustration: The possible answers are: I don't understand why it says Mc if it is asking for the moment at A, not C. But maybe I am getting something wrong. So with the formulas I posted above, I have this:
  47. Seibtsantos

    Pressure in a bomb calorimeter at the moment of combustion

    First, I calculated the number of moles of glucose. n = m / M n = 1.8 / 180 n = 0.01 moles of glucose So I checked the combustion reaction. 1 C6H12O6 + 6 O2 -> 6 CO2 + 6 H20 1 + 6 -> 6 + 6 0.01 + 0.06 -> 0.06 + 0.06 I considered the number of moles at the end of the reaction. I subtracted...
  48. E

    How is the Moment of Inertia Tensor Derived for Rigid Body Rotation?

    We start from the definition$$I_{ij} = \int_V \rho(x_k x_k \delta_{ij} - x_i x_j) dV \iff \dot{I}_{ij} = \int_V \rho (2 x_k \dot{x}_k \delta_{ij} - \dot{x}_i x_j - x_i \dot{x}_j ) dV$$Now since the rigid body rotation satisfies ##\dot{\vec{x}} = \vec{\omega} \times \vec{x} \iff \dot{x}_i =...
  49. S

    Tubular Column Moment of Inertia

    Can anyone explain why the moment of inertia for a tubular column in that textbook is like so? (take a look at the attachments). It should be (I = MR^2), as far as I know.
  50. C

    Moment of Inertia of a Solid Cylinder With a Wedge Removed

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