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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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?
  6. 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...
  7. Buzzdiamond1

    What is the formula for calculating the moment of inertia of a double cone?

    What is the correct formula for a double cone, is it 3/10 mr^2, or 3/5 mr^2..?
  8. Andrew VanFossen

    Moment of Inertia: Non Uniform Rod

    Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...
  9. P

    Moment of Inertia of a hollow cone about its base

    Homework Statement Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)## Homework Equations ##I=\int r^2dm## where r is the perpendicular distance from the axis Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}## The...
  10. P

    Induced Magnetic Moment (vector) vs. Induced EMF (scalar)

    When I induce magnetic flux through a closed loop, I should expect the lines of flux produced by current in that loop to oppose the change of flux through that loop. But what happens when that loop, say a rectangular loop, is curved into the shape of the letter J (like a candy cane) and my flux...
  11. bluejay27

    A more direct approach in determining moment of inertia?

    is there a directly knowing the moment if the moment of inertia would be lower for an object? I am emphasizing on knowing the value of the constant value. For a sphere is 2/5 and for a cylinder 1/2, this constant values will be placed at c of cMR^2 without directly going into calculus. A...
  12. A

    Moment of inertia of a wheel: linear to angular motion

    Homework Statement You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...
  13. Sudhir Regmi

    A Spin magnetic moment in half metals.

    I read that the stoichiometric half-metallic compound has integer spin moment. For this, n(up)-n(down) should be integer. Since n(up) +n(down) is always integer, either n(up) or n(down) should be integer to make total spin moment integer. I could not understand how the presence of energy gap in...
  14. M

    Calculate the moment and the sag

    The bridge is full extend 35 meters long, and retracted 17,5 meter long. When the bridge is installed it rest on piont(375kN) and a hydraulic pomp (525kN) , the mass of the bridge is 15 metric ton. my question is how do I calculate the bending moment diagrams when it is extending and how do i...
  15. R

    If evolution is true then why there is a monkey until this moment

    it is a common arrangement that say if evolution is true then why there is a monkey until this moment . I now that evolution is correct but who i can answer this question .
  16. N

    I Resultant force after adding a force to a couple moment?

    I don't get it. Imagine there is a stick leaning aganist a wall. There is a moment couple somewhere on the stick. The end of the stick hits the wall and the wall acts against it. The sum of moment is 0 but since the moment couple forces cancel each other, the resultant force is the wall...
  17. F

    Moment of inertia in shear stress formula

    Homework Statement In the first photo , i was told that the I represent the moment of inertia about the neutral axis ... But , in the 2nd photo , i found that the author calculate the moment of inertia about the x-axis (parallel to neutral axis ) and y -axis ( perpendicular to neutral axis) ...
  18. kamhogo

    What is the force exerted by each hinge on the door?

    1. Homework Statement The door has a mass of 30 kg, is 200 cm long and 90 cm wide. The hinges are installed at 25 cm from the bottom (R2) and 25 cm from the top (R1). What are is the magnitude of the force exerted by each hinge on the door? The door is in a state of static equilibrium...
  19. deusy

    Acceleration of the end of a hinged rod in a pulley system

    Homework Statement As shown in image. 2. Homework Equations Moment of inertia of pulley = 1/2*M*R^2 Moment of inertia of rod (about end) = 1/3*M*L^2 Acceleration of end of rod in theta direction = L*α Acceleration of end of rod in radial direction = L*ω^2 The Attempt at a Solution...
  20. J

    Can a force generate rotation with moment arm=0 ?

    I wait for your thoughts on this topic... and maybe then I will give you a small surprise. edit: Ok, there was a misconception on my side that I want to clarify changing the original title by this one: If there are two planets, rotating one around the other, and only gravity is acting. Is it...
  21. T

    B The moment we observe superposition

    Hi all, I'm a computer scientist who has been getting an increasing fascination with quantum physics. I admit I am a novice in this respect. I had a question just for my own learning and understanding, not related to a class or anything like that. :) In learning more about superposition and...
  22. C

    Shape of bending moment diagram

    Homework Statement in this question , I'm asked to draw the bending moment diagram and shear force diagram Homework EquationsThe Attempt at a Solution I don't have the ans for this question , can somoene check thruough my shape of graph . I'm not confident with it . [/B]
  23. C

    Is Torque the Same as Moment of a Force? A Confusing Semantic Issue

    I'm confused when it comes to the rotational version of Newton's Second Law: τ = Iα Is the torque τ the same thing as the moment of a force? I'm not sure if there is a discrepancy between British and American schools but I was always taught that a torque was a special case of moments and is...
  24. D

    A Dipole moment at the sub atomic level

    The following mechanism leads me to wander that a moving neutral object (compose from atoms) in vacuum may generates electric filed due to very small dipole moment. I propose that when atoms force to move in a certain direction the force propagates within the atom. A retardation in movements...
  25. C

    Replacing 10kip Load at 2ft: Understanding Forces and Moments in Beam Structures

    Homework Statement Why we need to replace the 10kip load at 2ft from D to D ? Homework EquationsThe Attempt at a Solution IMO it's wrong ... There's no need to do that .
  26. C

    Graph of bending moment doesn't return to 0

    Homework Statement I gt VA and VB = 85 N and 65 N respectively ... but , my bending moment diagram doesn't return to 0 ... Is there something wrong with the question ? Homework EquationsThe Attempt at a Solution I found that if i didnt include both the moment of 75(0.05) = 3.75Nm , the...
  27. K

    A Calculation of magnetic moment of an atom in the compound

    How is it calculated from magnetic susceptibility measurements using the mass of the sample? I know only this formula https://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_an_atom, but there is no mass, only quantum numbers.
  28. C

    Shear force diagram and bending moment diagram

    Homework Statement theoretically, bending moment should ends at bending moment = 0 , am i right ? Homework EquationsThe Attempt at a Solution Here's my sketch of SFD and BMD ,my bending moment doesn't return to 0 , which part of my working is wrong ... to find bending moment (M) , i get M...
  29. R

    Moment about a point in an incline plane

    Homework Statement Force F = 460 N acts perpendicular to the inclined plane Determine the moment produced by F about point A. Enter the x, y, and z components of the moment separated by commas. Homework EquationsThe Attempt at a Solution r(CA)=4j-3k u(CA)=4/5j-3/5k r(CB)=-3i+4j...
  30. R

    Moment about a point of a hammer

    Homework Statement In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 590 lb⋅in about point A.(Figure 1) Determine the required magnitude of force F. Homework EquationsThe Attempt at a Solution M=590lb*in -590=...
  31. R

    Moment about a point of a crane

    Homework Statement The towline exerts a force of P = 5.8 kN at the end of the 8-m-long crane boom. If θ = 30∘ determine the placement x of the hook at B so that this force creates a maximum moment about point O. Homework EquationsThe Attempt at a Solution M(max)= 8(5800) = 4.64kN*m My...
  32. Destroxia

    Quadrupole Moment and Potential

    Homework Statement Consider a physical dipole consisting of charge +q and −q separated by a distance a. • At first consider the origin of coordinates to be located in the middle of the dipole and a positive charge to be located at a distance y = a/2 and negative charge at position y = −a/2...
  33. RJLiberator

    Calculating a moment of a distribution

    Homework Statement The Lorentz Distribution is given by p(x) = \frac{1}{pi}\frac{ϒ}{(x-a)^2+ϒ^2} for -∞≤x≤∞. a) Sketch the distribution for a=0, ϒ=1, and compare the form to the Gaussian Distribution. b) Calculate the first moment of the distribution assuming again that a =0 and ϒ =1. c)...
  34. BiGyElLoWhAt

    Moment of inertia tensor calculation and diagonalization

    Homework Statement Not sure if this is advanced, so move it wherever. A certain rigid body may be represented by three point masses: m_1 = 1 at (1,-1,-2) m_2 = 2 at (-1,1,0) m_3 = 1 at (1,1,-2) a) find the moment of inertia tensor b) diagonalize the matrix obtaining the eigenvalues and the...
  35. L

    Finding Moment of Inertia of a wheel experimentally

    Hello all, and forgive me if I'm making newbie mistakes as I haven't posted here much. I realize this appears to be a homework assignment, but it is not. I am trying to develop an easy method for determining the actual moment of inertia for real wheels, for bicycles and other vehicles. I...
  36. M

    How do you calculate the moment of a spinning wheel

    What is the moment of the wheel. Dimensions: r= 1 m h= 5 cm m= 1000kg a = 4120 rad/s2 I used the formula T = I * a The moment of inertia can be calculate by Iz =(1/2)mr2or Ix=Iy= (m/12)* 3r2 +h2) wich one do i need to use?
  37. Vanessa Avila

    Statics: Finding the moment on point B?

    Homework Statement [/B] Determine the moment about point B of each of the three forces acting on the beam. Homework Equations M = F*d⊥ The Attempt at a Solution I went and found the components for each of the forces. Please double check it if I did them right: F1 : Fx = 0 Fy = 375 lb F2: Fx...
  38. Frankenstein19

    Help with Statics -- Moment of a Couple

    Homework Statement This is the problem I'm having problems with. Homework Equations M=F x r The Attempt at a Solution Let me explain what I've been doing with the practice problems before it, because I fear I may have the wrong understanding. For this exercise I just found the...
  39. C

    Calculating Moments Using the Method of Joints: A Tutorial

    Homework Statement For the moment about B , Cy(0.8) +Ay(0.8) + Cx(0.6) = 0 , right ? Why the author only give ,-Ay(0.8) = 0 Is it wrong ? Homework EquationsThe Attempt at a Solution
  40. E

    I Moment and the Larmor precession

    Hi, In the Larmor precession, we tend to define the magnetic moment as the current multiplied by the surface (for an electron rotating around a nucleus), sometimes this moment is defined (generally) as the sum of the vectoriel products of half of the position vector and the charge times the...
  41. Amru123

    About which axis the moment of inertia of A body is minimum

    I remember my teacher saying it to be the axis along the centre of mass but the centre of mass has all the mass concentrated in it and hence moment of inertia should increase as moment of inertia is proportional to mass?
  42. T

    Statics Homework: Finding Tension and Force in a Walkway Supported by Rollers

    Homework Statement Given: A 300 kg walkway supported by two rollers(at points A and B) with center of mass at G. Find: The tension T in the horizontal cable attached to the cleat at point B and the force under the roller at A. Homework Equations ∑M = 0 ΣFx = 0 ΣFy = 0 The Attempt at a...
  43. S

    Moment of Inertia for connected, hinged panels

    Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...
  44. M

    How to find the maximum moment of a force about an axis?

    Homework Statement Calculating the moment of force F about the axis isn't hard; how do I determine how to produce the maximum moment? Homework Equations Maxis = ûaxis ⋅ (r×F) F = 30N (This doesn't change at all during the problem) The Attempt at a Solution I would guess that since the...
  45. Alex Katko

    What variables are needed to find a moment?

    Homework Statement You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures. Homework Equations Mo = r x F The Attempt at a...
  46. J

    Moment effect of canoe paddle stroke

    Videos of racing canoes/kayaks show some submersion or greater draft of aft area during each paddle stroke. If we disregard entry and exit and assume power is applied straight back in direction parallel to water surface at a point perhaps 2ft below water surface please explain how and why this...
  47. JulienB

    Direction of dipole moment in e-field of another dipole

    Homework Statement Hi everybody! I'm trying to solve a problem about dipoles, but there is something I don't quite get about it. Well, first here is the problem: An electric dipole ##\vec{p}_1## is placed at the zero-point and shows in the z-direction. A second electric dipole ##\vec{p}_2##...
  48. S Aditya

    About the Orbital Dipole Moment

    I was going through the chapter Chemical Bonding in one of the books and found something about orbital dipole due to lone pairs. In each diagram the orbital dipole due to lone pair was directed from the central atom to the end of the hybridized orbital (lone pair). Why is that so?
  49. M

    MHB Moment of Inertia: Disc+Point Mass | Help Needed

    Find the moment of inertia of a disc of mass m and radius r with a point mass of m on its circumference. i can't work this out can someone help me. i can work out that the moment of inertia of the disc is 1/2mr^2 but i don't know what to do with the point mass. i think it could have to do with...
  50. T

    Does a Magnetic Moment μ exist for any closed current loop?

    I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...
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