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. W

    Decomposing angular velocity and moment of inertia

    Homework Statement See the attached image. Homework Equations ##T = 1/2 \omega^2 I## The Attempt at a Solution So ##I_1,I_2,I_3## are just the moments of inertia of the object with regards to the 3 axes. Right? OK, then I intuitively assume that the total kinetic energy must simply be...
  2. sams

    Transition dipole moment of diatomic molecules

    Hello Everyone, A little question regarding the TDMs between two different electronic states of a diatomic molecule. If I am calculating the TDM from state A to state B, is it the same if we are calculating the TDM from state B to state A? Are these two transitions the same? Thank you so much...
  3. T

    Moment of Inertia for Composite Object

    Homework Statement for this composite object, what moment of inertia needs to be used if you were to sum the moments about the centroid of the object, \sum M=I\ddot\theta Homework EquationsThe Attempt at a Solution is it the sum of the I_zfor a solid sphere and a solid cylinder
  4. J

    Dynamics Problem: Incline Block and Moment of Interia

    Homework Statement Homework Equations ∑F=ma ∑M=Iα 3. The Attempt at a Solution I used the dynamic equilibrium formulas to find the tension. The tension helps me to find the acceleration of the block. Then, I used kinematics to find the velocity. But, I'm not getting the right answer.correct...
  5. dbaliki918

    Find the Principal Axes of the Section Shown

    Homework Statement [/B] Statement: Find the principal axes of the section shown: The origin is on the top left corner. Homework Equations [/B] Centroid equations: Second moments of area: Mohr's Circle for I equations: Coordinates Centre Angle from principal axes: The Attempt at...
  6. O

    Understanding Moment of Inertia in a Ball-Rod System

    Homework Statement "a uniform steel rod of length 1.20 meters and mass 6.40 kg has attached to each end a small ball of mass 1.06 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. Find the moment of inertia of the ball-rod system." Homework...
  7. P

    Moment of Inertia of a Regular Hexagon

    A equilateral triangular lamina, has a moment of Inertia of I if the axis of rotation passes through the centroid of the triangle, perpendicular to it's plane. What is the moment of inertia of a regular hexagon(Again, through it's geometrical centre, perpendicular to the plane), provided that...
  8. L

    Moment of force and static equilibrium

    1) Problem: An individual holds a ball of mass 3 kg in his hand in static equilibrium. The biceps brachii attaches a distance of 2 cm from the centre of rotation of the elbow joint, and the muscle's line of action is directed at an angle of 115° counter clockwise from the forearm. The forearm...
  9. X

    Magnetic Dipole due to an electron's orbital motion

    Homework Statement Select all of the following which are possible combinations of Lz and θ for hydrogen atoms in a d state, where Lz is the z component of the angular momentum L, and θ is the angle between the +zaxis and the magnetic dipole moment µℓ due to the electron's orbital motion...
  10. T

    Magnetic Moment and Principal Quantum No of electron

    Homework Statement The magnetic moment of a revolving electron around the nucleus varies with principal quantum number as ? Homework Equations mvr = nh/2π The Attempt at a Solution i know μ = (qωr2 )/ 2 and after that i am substituting values for r and i get μ∝ n2 but that is wrong.Help !
  11. B

    Toppling Effect: What's the Best Procedure?

    Hello, I uploaded an image of the question so it becomes clear my main doubt is which procedure should I follow 1) total object weight*PERP. Distance to toppling point=Moment of cylinder+moment of cone 2) moment of cylinder ≥ moment of cone I tried doing method two since they asked for least...
  12. S

    Experimental value for moment of inertia - Not about c.o.m.

    Homework Statement These are the pre lab tasks for my upcoming lab. Find the theoretical value for moment of inertia for a ring with off axis rotation using parallel axis theorem and outline procedure to obtain experimental value of I. During the lab we will be using a rotating platter with a...
  13. H

    Minimizing the maximum bending moment

    Homework Statement The question is asking us to minimize the maximum bending moment by changing l3. l1=3(m) l2=6.5(m) l4=12(m) P1=1200(KN) P2=2300(KN) P3=410(KN) and we know that obviously, 6.5<l3<12 Homework EquationsThe Attempt at a Solution We made relevant cuts and acquired the equations...
  14. J

    Uniformly distributed load - Max bending moment help

    Homework Statement I have to work out the reactions at A & D. Sketch the shear force diagram for the beam and sketch the bending moment diagram. i have worked out the reactions at A=56kN and D=34kN. I have done the SFD. I am just struggling doing the bending moment diagram and don't know how...
  15. H

    What is the role of moment of inertia in rotational motion?

    I've been studying rotational motion for a while and I have no clue how moment of inertia plays a role in it. How would you define it? Often times, it's just described as resistance to change. Does that mean a high moment of inertia means a higher resistance to change or is it the other way...
  16. A

    Moment of inertia in plane translation

    I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...
  17. A

    Help with Bending Moment Diagram for Structure

    Homework Statement Hi I need help with drawing a bending moment diagram for this structure. All joints are rigid and it's fixed to the ground. I'm really struggling with this. I initially started with the horizontal beam (statically indeterminate) and found that the moments at the ends were...
  18. C

    Moment of Inertia of ceiling fan

    Homework Statement A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.9 kg and radius R = 0.22 m. The rods each have mass mr = 1.4 kg and length L = 0.83 m. 1) What is the moment of inertia of each rod about the axis of rotation...
  19. Greg Bernhardt

    Will You Celebrate the Ultimate Pi Moment Tomorrow?

    On 3.14.15 at 9:26:53 3.141592653 Set your alarms!
  20. R

    Moment of inertia of half disk through integration

    Hello, sorry for this stupid question. I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value. I'm pretty sure it has to be MR^2/4, but I=\int r^2 dm \\ dm=(M/A)dS With A=\pi R^2/2 I compute...
  21. W

    Area/2nd Moment of Inertia of an arc/ring

    Homework Statement I'm trying to solve for the area moment of inertia of a curved arc. To visualize this, it would be like a bent piece of cardboard (two arcs with two lines connecting them at their end points). I'm modelling the differences in area MOI with an increasingly curved piece of...
  22. A

    Moment reaction with rotation and offset CG

    Hey folks, I created and verified a model with hand calculations, and decided to re-use my same logic.. Which now is giving me false numbers. Was wondering if you guys could help me out. Setup/Verification (See attached Reaction_Forces picture): Body in motion being held down by straps...
  23. E

    Moment of Inertia of 4 Balls on Square Side

    Homework Statement There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius is r. Find the moment of inertia of the system about one of the sides of the square. Homework EquationsThe Attempt at a Solution I= 2 (two balls)...
  24. JesseJC

    Moment of Inertia about an axis at the center of mass

    Homework Statement 3.) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)...
  25. A

    Find the moment of inertia of the system

    Two rectangular objects, each 1.0 m by 3.0 m, are attached as shown. Each rectangle has a mass of 1.5 kg. Find the moment of inertia of the system about (a) axis A, (b) axis B, and (c) axis C. I have no idea what to do, any help is appreciated.
  26. A

    Bending moment Diagram for fixed-fixed beam

    Homework Statement There is a beam, say length L, with a force F UP on the left built-in support and a CLOCKWISE moment. The right side has a force, F, DOWN and a COUNTERCLOCKWISE moment i.e F up, cw moment -------------------------------------------------------------F down, ccw moment...
  27. N

    How does uncertainty apply to an electron's magnetic moment measurement?

    The electron paths in the path integral formulation of qm are in ordinary space-time. The end-points of the paths in the steady states must be in ordinary space-time as well. The electron's potential is exact or nearly exact either by measurement or by calculation. The electron's locations...
  28. P

    Can liquids be treated as rigid bodies for moment of inertia

    Consider a partially filled bottle of water. When it's tipped over and rotating about its pivot point where its edge touches the ground, it has an angular acceleration. Assuming the liquid is not viscous at all, so flows perfectly, at a given instant can it be considered to have a moment of...
  29. B

    How to Solve Moment of Inertia for a Cylinder with Varying Radii?

    Homework Statement So I generally understand how to solve the following problem. My only roadblock is that I am not sure I am solving the moment of Inertia correctly. I know that for a solid cylinder you would use I = 1/2mr^2, but I am not sure how if it has only one mass given of 10 kg, yet...
  30. J

    Statics, moment on submerged surface problem

    Homework Statement [/B] Shown below is a slew gate controlling the flow of salt water flowing into fresh water in a submarine depressurising chamber (used to measure the pressure depth and which is compared to a control signal that has been calibrated). On the inlet side, the depth of...
  31. A

    Dipole moment of a specific charge distribution

    A negative charge cloud distribute as a ellipsoid and a positive point charge situated at the centre of the ellipsoid.What should be the dipole moment of charge distribution.I mean, if the negative charge distribution is spherical and positive point charge at the centre then surely dipole moment...
  32. hdp12

    Given Moment about a Pin and a Roller

    Homework Statement For my statics homework, we are directed to: Draw the free body diagram and use the force and moment equilibrium to determine the support reactions for the following systems I'm having a bunch of trouble with problem 4.10, which is displayed in the following picture I'm...
  33. Y

    Moment of inertia and rotational motion

    Hello, I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics. I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2. However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...
  34. N

    Bending moment and shear force for screw

    Can someone help me with determining the free body force diagram, and hopefully I can go on from there. Homework Equations M = F.dI found T = 500N The answers are shear force = -62.5N , Moment = 64.4 Nm , Tension = 500N
  35. avito009

    Moment of Inertia at a point away from centre of Mass.

    Lets say we are sitting on a horse at the edge of a merry-go-round. You move faster relative to a point near the centre of the merry go round. Now most of the mass of this merry go round is at the edge i.e at the horse. So the moment of inertia at the horse is less. Correct me if I am wrong.
  36. AdityaDev

    Diamagnetism and orbital magnetic moment

    For diamagnetic materials, when an external magnetic field is applied, the electrons having orbital magnetic moment in opposite directions spped up. how does this happen? The direction of magnetic momwnt is given by right hand thum rule. If there is an electron revolving in anticlockwise...
  37. M

    Mechanics Particular Wheel Problem

    http://www.uzapping.eu/upload/P3.jpg Homework Equations : Only Moment's formulas (I think) or Eventually Euler's Law[/B] The Attempt at a Solution : It's supposed to be an easy problem. But I just don't understand the mechanism and the meaning of the angle on the bottom. So I don't know how...
  38. M

    FEM, FEA, Frame, Moment, Shear, find Stiffness Matrixx

    Homework Statement Hi, I need some help analysing this frame. First of all i bellive its hard, if not impossible, to get as detailed results by hand calculations as my softwear CSI Sap2000. Becourse of shear and axial deformation. Is it possible to obtain the stiffness matrix of this frame at...
  39. fhc6791

    Dipole moment of small circular antenna - only magnetic?

    When making an extension from linear dipole antennas to small circular antennas, I am only coming across expressions for a magnetic dipole moment (as opposed to having just an electric dipole moment for a linear dipole antenna). The expression being: m = πr2I at its peak The above expression...
  40. S

    How do I calculate moment of inertia in a wheel?

    What I have are two wheels, weight assumed at 50 kg overall for both, joined by an axle. The wheels are 900 mm apart from the centre of one tire to the centre of the other. The diameter of the tire is 690 mm. How do I calculate the moment of inertia in order to find the torque in the centre of...
  41. DocZaius

    Moment of Inertia of a Square: Problem with Certain Method

    For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...
  42. S

    How to find moment at a certain point?

    I have tired it multiple times but I keep getting 228, 12 ,-8N How do in what direction the force is moving? clockwise or counter clockwise? What to do with the 20 N in the y comp? In the book it says if it moves clockwise its negative and if it moves counter clock wise its negative.
  43. H

    Moment of inertia of a solid sphere

    Homework Statement Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center Homework Equations I = ∫rρdV The Attempt at a Solution I =ρ ∫r4πr2dr = ρ4π∫r4 Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5) And...
  44. PrincessIceFall

    What is the mass moment of inertia?

    What is the mass moment of inertia about the longitudinal axis of the shape attached in this thread, but in 3 D? I found this "Handbook of Equation for Mass and Area Properties of Various Geometrical Shapes" which gives the mass moment of inertia of a regular octagon. I initially thought that...
  45. P

    How Do You Calculate Moment of Inertia for CD and FE in a Multi-Rod System?

    If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB. The question is to find the moment of inertia of the system with respect to axis AB. I managed to find the...
  46. M

    Finding mass from moment of inertia graph - inconsistency?

    Homework Statement I have a disk that can rotate about an axis at a radial distance h from the center of the disk. I am given a graph showing the the rotational inertia I of the disk as a function of the distance h from the center of the disk out to the edge of the disk. From the graph (see...
  47. Peeter

    Integration by parts, changing vector to moment & divergence

    In Jackson's 'classical electrodynamics' he re-expresses a volume integral of a vector in terms of a moment like divergence: \begin{align}\int \mathbf{J} d^3 x = - \int \mathbf{x} ( \boldsymbol{\nabla} \cdot \mathbf{J} ) d^3 x\end{align} He calls this change "integration by parts". If this...
  48. Alettix

    Determination of moment of inertia of a hollow cylinder

    Hi! I got the task to determine the moment of inertia of a hollow cylinder, however it's not about just measuring the mass and the inner and outer radius and putting it into the right formula, instead I should roll it down an inclined plane. 1. Homework Statement I'm only allowed to use the...
  49. B

    Moment Of Inertia Of Non-uniform Rod

    Hello, I am trying to find the moment of inertia of a uniform rod, that has a mass added to it at some position along it's length, which is equal to the mass of the rod itself, and the axis of rotation is at one end. 1. Homework Statement A uniform, \mathrm{1.00m} stick hangs from a...
  50. A

    How Do Collisions Affect the Moment of Inertia and Angular Momentum of a Rod?

    I am trying to learn to calculate collisions on the center of percussion of a rod. Can you tell me how to find the moment of inertia? Suppose we have a rod of length 1m and mass M = 12 kg., we know that ##I = 12 * 1^2 / 3 = 4## , if a collision takes place at the CoP ( at 0.166666 m from the...
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