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.

View More On Wikipedia.org
Recent contents Top users
  1. Andy_K

    I Twin Paradox - Observation at Turnaround Moment

    Dear All, I am doing the Special Relativity course at World Science U, and came across this question which I got wrong: When 100 nanoseconds have elapsed on traveling Gracie's watch, she immediately stops, turns around, and heads back toward George at the same speed of her outbound journey...
  2. T

    Torque on current carrying loop/Diploe moment of loop

    Homework Statement The current loop of the radius b as shown in figure is mounted rigidly on the axle,midway between the two supporting cords.In the absence of the external magnetic field,the tension in the two cords are equal and are T.What will be the tension when a vertical magnetic field B...
  3. M

    Scalar Moment around a point due to a force

    Homework Statement In two dimensions, the moment of a force can be calculated using the scalar method, MO=Fd, where F is the magnitude of the force and d is the perpendicular distance from the line of force to the point where the moment is being considered. Using the scalar method, calculate...
  4. B

    Moment Equilibrium in terms of box weight

    Homework Statement The board shown below is being held in equilibrium in the vertical plane by three smooth rods at A, B, and C Determine the magnitudes of forces at A, B, and C in terms of the weight of the body, W. Homework Equations Moment = f*r Here's a diagram The Attempt at a...
  5. arpon

    I Four-vector Dipole Moment: Electric & Magnetic

    What is the four-vector related to electric and magnetic dipole moment?
  6. S

    Rotational Motion Question, lever arm with two masses

    Homework Statement [/B] A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...
  7. F

    Bending moment diagram equation method

    Homework Statement Draw the bending moment diagram the top part is the question, the bottom part is the answer. Homework EquationsThe Attempt at a Solution There is a force at the wall in x and y direction and a moment ##F_x, F_y, M_w## Sum of forces in x : ##F_x-1000=0, F_x=1000## Sum of...
  8. G

    Moment of Inertia: Definition & Physical Meaning

    What is the physical meaning and definition of moment of inertia?
  9. Isaac0427

    Moment of inertia for a fidget spinner....

    Hi, I was just curious, how would you go about calculating the moment of inertia for a fidget spinner? I was thinking about it, and I don't know how to calculate moment of inertia for weird shapes like that. Thanks!
  10. Pbaseball

    Conservation of momentum and Moment of Inertia

    Hello everyone, I'm needing help understanding how to take the conservation of momentum equation and substitute moment of inertia inplace of mass in the equation. I understand this is a linear equation and I'm trying to incorporate angular momentum. I just want to determine the speed of the ball...
  11. M

    Moment of inertia of a cylinder?

    Homework Statement the moment of inertia of A cylinder of height 2h radius (a) and uniform mass density ρ about a line x=y=z using multiple integration. Homework Equations I=ρ∫s^2*dV where the integral is over the volume V of cylinder and s is the perpendicular distance to the axis of...
  12. fisher garry

    A Calculate the moment of inertia of H with the probability from wavefunction

    the spin, S, for an electron is $$\frac{\hbar}{2}=5.27 \cdot 10^{-35} $$ $$\frac{2MR^2 \omega}{5}=\frac{2MRv}{5}$$ It is said that the speed of an electron is 2200 km per second and can be calculated in classical manners from electrostatic and accelerating forces on the electron from (1.11)...
  13. DevonZA

    Centre of gravity, moment of inertia and radius of gyration

    Homework Statement Homework Equations Centre of gravity: X=m1x1-m2x2/m1-m2 MOI rectangle: 1/3ml^2 MOI triangle: 1/18md^2 Radius of gyration: Ixx=mk^2 The Attempt at a Solution Mass of body 1: b*l*p = 0.8*1*10=8kg Mass of body 2: 1/2b*h*p = 1/2(0.4)*0.6*10=1.2kg1.1 X=m1x1-m2x2/m1-m2...
  14. 9

    Total moment density of electromagnetic fields

    Homework Statement These is a problem from my textbook. You have an infinite solenoid with n turns per unit longitude, radius "a" and a stationary current I. In the axis there exits a uniform line charge with lineal density λ. Compute total electromagnetic momentum (lineal and angular)...
  15. Diptangshu

    Are Moment Arm & Common Perpendicular Different?

    Not only the Problem I have attached in Picture, but there are few more where I get different answer while solving by taking Moment Component and by Common Perpendicular. [NB : The problem Stated in 'Engineering Mechanics' by Ferdinand L. Singer. Process 3 is what I did, Process 1 is what is...
  16. harpazo

    MHB What is the concept of moment of inertia?

    In simple terms, what exactly is meant by moment of inertia as taught in Calculus 3?
  17. Arman777

    Magnetic moment and Minimum energy

    In exam we have a question like this , I said its false cause ##U=-\vec μ⋅\vec B## , ##U=-μBcosθ## when ##cosθ=1## it is in the most stable point.But when ##cosθ=-1## its not, since.In both cases ##\vec μ## and ##\vec B## are parallel ?
  18. I

    Calculating the moment of inertia of a rod as a point mass

    The moment of inertia of a rod with consistent density rotating about its end is M(L^2)/3. However, if you treat the rod as a point mass and try to calculate this using mr^2, you get M(L/2)^2=M(L^2)/4. Why doesn't this work?
  19. I

    Stuck on separable equation relating to moment of inertia

    Homework Statement (a) Consider a cylindrical can of gas with radius R and height H rotating about its longitudinal axis. The rotation causes the density of the gas, η, to obey the differential equation dη(ρ)/dp = κ ω2 ρ η(ρ) where ρ is the distance from the longitudinal axis, the constant κ...
  20. B

    How to measure the moment of inertia of a motor's rotor?

    Hello, I need to measure the moment of inertia of a DC motor's rotor. Any suggestion? Thanks
  21. Arisylia

    Deriving the moment of inertia of solid sphere

    So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$ \frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\...
  22. F

    Why are fixed end moments AB and BC not considered in this problem?

    Homework Statement In this problem , i don't understand why the fixed end moment AB and fixed end moment BC arent considered ? Homework EquationsThe Attempt at a Solution Is it because we are asked to find the moment at B , so only fixed end moment AB and fixed end moment BC arent considered ?
  23. F

    Understanding Fixed End Moments in Beams: AE vs EA

    Homework Statement I don't understand the fixed end moment AE and also fixed end moment EA ? shouldn't they be the same ? Homework EquationsThe Attempt at a Solution For the fixed moment AE / fixed moment EA , shouldn't it = -10(2) +5(2) = -10 , for fixed end moment , we always assume...
  24. O

    I Calculate the Dipole Moment of an object

    How would I calculate the Dipole Moment of a piece of mild steel approximately 15cm in length?
  25. top12eaper

    Moment of inertia of cylinder with a rectangel shaped hole

    i know how to calculate the inersia for the cylinder, than i have to take away the inersia of the rectangel, but i can't find an equation for the inersia for a rectangel with the plane spinning perpendicular to the rotation axis, please help !
  26. R

    Calculating the moment of inertia of a solid sphere

    Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...
  27. F

    Moment in a Beam: Consider Both Spans AB & BC

    Homework Statement In this problem , why only caluclation of span AB is considered ? why the span BC isn't required ? Homework EquationsThe Attempt at a Solution I think there's soemthing wrong with the question , We have to consider the calcilation of span BC also
  28. F

    Fixed End Moment - Clockwise or Anticlockwise?

    Homework Statement In the book (photo 1 ) , it's stated at the left span, the fixed end moment is clockwise , while on the right span , the fixed end moment is anticlockwise . But , accroding to wiki (photo2) , it's stated that at the left span of the beam , the fixed end moment is...
  29. R

    Moment of inertia of a non uniform disc

    Homework Statement A non uniform disc of radius R has a mass of M. Its centre of gravity is located at a distance x from the centre. Find the moment of inertia of mass (moi) around the axis perpendicular to the surface passinf through the centre of gravity. Homework Equations Parallel axis...
  30. AdrianMachin

    The direction of electric dipole moment of water molecule

    I was watching a video explaining how microwave ovens work when I found that there is a difference between my physics textbook and online images of the electric dipole moment of the water molecule, as well as the one shown in the video. Why do they differ?
  31. jdawg

    Shear and Moment Diagram Equations

    Homework Statement Write the shear and moment diagram equations and graph them. Homework EquationsThe Attempt at a Solution I attached my attempted solution in a pdf (I know the last section of the moment diagram is supposed to be parabolic, I accidentally drew a straight line instead). I...
  32. Z

    Understanding Kinetic Moments: Why Do They Belong on Opposite Sides?

    Why don't we include the kinetic moments in the summation of the moments of a rigid body? In other words, why are the kinetic moments on the opposite side of the equation as the moments due to external forces? I understand that the math works out but it's not making sense to me conceptually...
  33. P

    Does the moment of inertia stay the same in different positions?

    Good evening, good people of PF. I have a fairly simple question. Please see the attached drawing. My question is this: does the moment of inertia change from position one to position two (as the weight is rotating around a center line). In essence, does it maintain the same moment of inertia...
  34. ramzerimar

    How is the moment of inertia of airplanes measured?

    I know it's possible to use a trifilar pendulum to extract information on moments of inertia by measuring the period of oscillation. I've seen this test being executed on small aircraft, like in this video. But I wonder how do is the momement of inertia calculated on big aircraft, like a Boeing...
  35. M

    Moment generating functions help

    Homework Statement [/B] Let X be a random variable with support on the positive integers (1, 2, 3, . . .) and PMF f(x) = C2 ^(-x) . (a) For what value(s) of C is f a valid PMF? (b) Show that the moment generating function of X is m(t) = Ce^t/(2− e^t) , and determine the interval for t for...
  36. DevonZA

    Draw the shear force and bending moment diagrams for beams

    Homework Statement Homework Equations [/B] Shear force is calculated at each point on the beam. Downward forces are negative, upward forces are positive. Moments about points are calculated as force multiplied by perpendicular distance. Clockwise moments are negative. Anti clockwise...
  37. Jewelz

    Moment of Inertia of a Spinning Record with a Hole in Center

    Homework Statement A 45 RPM record is a disk with a wide hole in the center. The mass of such record is 45g. It is 7 inches in diameter, and the hole in the center has a 1.5 inch diameter. (Sorry for the odd units, this was the way it was given). Find the moment of inertia of the 45 RPM...
  38. F

    Understanding Carry-Over Factor in Beam Analysis

    Homework Statement I don't understand why for the first case , the 0.4 and 0.6 is used ? for the second question , we can see that in the first case , the moment from BC is carried over to CB ( highlighted part - line 4 ) ... Why for the second case , the moment from BC (6325.8) isn't carried...
  39. EthanVandals

    Moment of Inertia Ratio for Disk and Ring with Point Mass

    Homework Statement What is the ratio of inertia of a 5 meter radius disk to that of a 5 meter radius ring? How would this ratio change if the ring were replaced with a since point mass a distance 5 meters from a pivot point? Homework Equations I = mr2 The Attempt at a Solution The wording in...
  40. Jarvis88

    Why is this force considered in the moment equation?

    Homework Statement After reviewing a quiz I had in Statics, I realized I did not understand why a certain force was considered in the moments equation. If a force goes directly through the point of the moment, it is not considered when solving for a force using moments. The question is asking...
  41. S

    How Do You Calculate the Magnetic Moment and Torque of a Rectangular Loop?

    Homework Statement A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field. (a) What...
  42. J

    How do I calculate the moment of inertia for a uniform bar with attached balls?

    Hi everyone, I have just started the chapter in my Physics book that deals with calculations of Moments of momentum for various extended bodies. I have come across a problem which involves, as part of the overall problem, finding the moment of momentum of the centre of mass of the object and...
  43. Konte

    I Xt - Understanding Dipole Moment Components in Rigid and Non-Rigid Molecules

    Hi everybody, I want to ask a question about the dipole moment vector ##\vec{d}##, with components expressed in the molecule-fixed axis. By permuting identical nuclei that compose a rigid molecule, I know how ##d_x##, ##d_y##, ##d_z## change. But when dealing with non-rigid molecule, I no...
  44. P

    Moment of Inertia Calculation for Offset Mass

    Ran into a bit of a dilemma. I'm having some problems calculating the moment of inertia for an offset weight configuration. Please see the attached drawing. Basically this offset weight will be turning around an axis as labeled in the drawing. Any help would be greatly appreciated
  45. D

    Offset Torque: Solving the 1000N Problem

    Hello guys, I am doing some basic design work and can't remember how offset torques work. I am doing the sum of the torques should be equal to 0 in order to find the tipping point around either of the wheels. My problem is with the 1000N applied at to top taking the pivot point around the...
  46. A

    Moment of inertia of two cylinders placed vertically

    if i have two cylinders with same mass and radius placed over each other vertically and there is a motor inside the top cylinder welded in the cylinder itself, and connected to the bottom cylinder to rotate the bottom cylinder. assume it's the whole thing is resting on the ground and neglect...
  47. C

    I Control Moment Gyro - MOI calculation & units of measure

    Hi all, I am not a physics major and have spent some time learning via the university of Google. I would really appreciate a second set of eyes on what I am calculating and tell me if I am correct, or if I have done something wrong along the way. I am trying to calculate MOI and need results...
  48. E

    How do I calculate internal forces in a beam bending problem?

    Hello, I am having difficulties trying to work out one problem. I've attached a picture explaining the situation - the task is to determine internal forces in C but the bending moment M(x) doesn't seem to get me the correct results (I used equivalance and went from LHS). I would greatly...
  49. X

    B Why can we choose any arbitrary point to calculate the moment?

    Can someone explain, what means that we can choose any arbitrary point to calculate moment and result will always be identical? If I choose point 1 ...20kg x 1m = 20kg x 3m...seesaw right side will fall down If I choose point 2...20kg x 2m = 20kg x 2m...seesaw stay horizontal So this two...
  50. J

    I What does the magnetic moment of a particle depend on?

    Every magnetic object has a magnetic moment. From electrons to molecules, to even planets. But my question is, what determines how much of a magnetic moment a quantum object has? I'm not sure if "how much" is the right word for it. What determines the "quantity" of a magnetic moment of a...
Back
Top