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. F

    Total moment caused by an unbalanced mass on a rotating shaft

    Homework Statement [/B] The shaft connecting A to D is rotating at 1200RPM clockwise and has a concentrated unbalanced load of W2 of 8lb at a radius of 2in. in a plane midway between points A and D as shown in the figure. A constant vertical load W1 of 1500 lb is applied by means of two...
  2. A

    Why Did Ignoring the Ground Reaction Force Yield the Correct Torque Calculation?

    Homework Statement A uniform cylinder has mass m kilograms and radius 5 metres. Calculate the magnitude of the horizontal force Fthat needs to be applied on its axis to start it rolling up a step of height 2 metres, as shown in the diagram Homework Equations Anticlockwise torque=Clockwise...
  3. A

    Alternative approach -- Bicycle on a curve

    Homework Statement A bicycle of mass m is traveling at constant speed v around a curve of radius r without slipping. You can take the acceleration due to gravity as g. Calculate the angle of tilt, θ, that will enable it to balance. Homework Equations R=mg Rsintheeta (Length)=Fcostheeta...
  4. M

    Determine Mass moment of inertia about any axis given Ixx...

    Hello, I am analyzing human motion. for each body segment, I have measured values for Ixx, Iyy, and Izz in local coordinate system. I want to transfer all body properties from one coordinate system to another using a transformation matrix. My question is that, is there a way to calculate mass...
  5. Z

    A Second moment of area about Y-Y

    How to calculate Secondmoment of area about Y-Y axis A solid cylinder ?
  6. B

    How to Calculate F1 and F2 for a Balanced Beam?

    Ok here goes. It's been a long time since I've done anything like this and i just can't remember what to do. I'e got a beam 167.5mm long. It is supported at 24.5mm along the beam. 6600kgf acts at one end of the beam. F1 acts at 128.5mm along the beam. F2 acts at 167.5mm along the beam. F1...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. arpon

    I Four-vector Dipole Moment: Electric & Magnetic

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  12. 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...
  13. 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...
  14. G

    Moment of Inertia: Definition & Physical Meaning

    What is the physical meaning and definition of moment of inertia?
  15. I

    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!
  16. Pbaseball

    Conservation of momentum and Moment of Inertia

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  17. 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...
  18. 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)...
  19. 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...
  20. 9

    Total moment density of electromagnetic fields

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  21. Diptangshu

    Are Moment Arm & Common Perpendicular Different?

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  22. harpazo

    MHB What is the concept of moment of inertia?

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  23. 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 ?
  24. 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?
  25. 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...
  26. 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
  27. 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} \\...
  28. 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 ?
  29. F

    Understanding Fixed End Moments in Beams: AE vs EA

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  30. 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?
  31. top12eaper

    Moment of inertia of cylinder with a rectangel shaped hole

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  32. 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##...
  33. 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
  34. 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...
  35. 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...
  36. 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?
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  49. 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...
  50. 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
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