# Moment Definition and 85 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.

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1. ### Convert moment force at lever support

I am trying to determine if a clamp holding a lever with a mass at one end can experience zero or reduced torque either by balancing the forces or converting the rotational torque into another form such as linear, I’ve looked at counterbalance with Steadicams etc. but I believe this just...
2. ### 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?
3. ### 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...
4. ### 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:

6. ### Engineering Moment of a force about point O

G'day. I have a problem with my statics work, i understand its probably quite simple but I am having trouble in my understanding. Essentially problems make more sense to me by using the component method, although in saying that i understand this problem would be quite a lot more simple were i to...
7. ### Engineering Moment and equilibrium

Summary:: I need some help with moment when using equations of equilibrium Edit: Sorry I forgot to say what the question was! The question was to solve the value of R based on the diagram below alone. I was solving the question below and I tried to resolve R into a force that is perpendicular...
8. ### Calculating the Moment from a Different Vantage Point

Summary:: Just a simple 3d rigid dynamics question which I am trying to solve by placing coordinat system differently from original solution.Everything looks ok but results are different. Mod note: Post moved from technical section. Thats my question.As you see coordinate system was located...
9. ### Engineering Moment vs simple connection

I Think it's moment connection. Because the end plate must be able to resist the moment transferred from the beam to the column. Please correct me if I am wrong.
10. ### Determining moment (or torque) around a certain point on a wrench

Here's a diagram of the problem. There are 3 possible solutions: 163 in-lb clockwise, 163 in-lb counterclockwise, 82.7 clockwise or none of them. After attempting the problem the closest I got to was 82.7 but that was wrong so I'm still stuck.

12. ### Torque: find the force necessary for a body to be in equilibrium

The question doesn't specify whether we're talking about translation or rotational equilibrium, so I suppose it's both: In order for the body to have translational equilibrium: 60 N + F2 = 0 F2 = -60N However, in order to have rotational equilibrium: 60 N * 3m + F2 *8 m = 0 60 N * 3m - 60...
13. ### Luffing Jib Load, With and Without Sheave Pulley

Now I am working with a DIY Luffing Jib Crane. Mys subcon said that: Tension of red rope for hanging a blue box load at the tip of the boom i(A) s as the same as hanging it with pulley and tied to the motor/ground_B (System in a Static Load Condition).. Blue Rope and Pulley weights are...
14. ### Problem With a Slewing Bearing Crane

Dear All Masters I have problem with slewing bearing crane. My subcon made a crane that have a very high platform deck form slewing bearing. They said it is fine and the height is not an issue as it is in lower place. I know the higher the load from slewing bearing, the bigger the force or...
15. ### Moment of a Force About a Point

Homework Statement I'm a bit confused on when a force creates a moment about a point, and when it does not. In particular, in the attached diagram, would F be able to produce a moment about point A? I initially thought that wouldn't be possible as A lies on the same line as F, but since F does...
16. ### Statics problem (moment and equilibrium)

1. Having really hard time understanding the concept of moment and equilibrium in statics. In the following picture the man is carrying a 6kg uniform rigid board. I'm asked to calculate the amount of force the man feels on his shoulder. (at point A) Now I know I'm supposed to start by making...
17. ### Moment question

Homework Statement https://cdn.discordapp.com/attachments/373928512811302912/528638926148337704/question.PNG part a )50N I cannot answer part b. Homework Equations M=FD The Attempt at a Solution Ok so if both pivots were in contact with the beam I would just equate them with the oppposite...
18. ### I Force required to tip an object

So I need to find equations for the force required to tip over a cylindrical object. This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass...
19. ### Off-Axis Torque To A Cantilever Beam

I'm interested in understanding how to deal with a torque applied to an angled cantilever beam. The torque is being applied along a horizontal axis at the location of the end of a cylindrical beam. I am interested in how this torque will cause twist along the beam's axis, as well as any...
20. ### Dipole problem with electric fields

Dipole problem (which is solved through mirror imaging) has been troubling me with its solution. I understand everything except how the dipole moment's coordinates came to be, since when converted into x-y axis, its doesn't make sense. (problem 4.6) The screenshot contains the solution which...
21. ### Beam deflection

Homework Statement Homework Equations Singularity equations for beam deflection $$\sum M_B=0=-M_0-R_AL-M_0$$ $$R_A=-\frac{2M_0}{L}$$ The Attempt at a Solution I know how to use singularity equations and all that but my problem is calculating the force especially when moment is involved. For...
22. ### Extending an aircraft landing gear that has gotten stuck

Imagine an aircraft of which the its wing is connected to its landing gear by means of a hinge (joint), and then the gear suddenly gets stuck midway. If, subsequently, the aircraft makes a turn around its longitudinal axis (see picture), it seems to hold true that then the angle between the...
23. ### FBD of an aerogenerator (Windmill)

Homework Statement Good afternoon, I hope someone could help me with this problem, it is killing my head. I have an aerogenerator, I already find the torque excerted by the air (75.8N) and the force transmitted by the gear (1010.6N). The problem comes when I try to draw the free body diagram to...
24. ### Magnetic moment and magnetic field and dot product

Homework Statement a magnetic moment of U = 1 (i) + 2 (k) , surrounded by a magnetic uniform field of B= 3 (i) + 4 (j) - 1 (k) find the potential energy in mJ ? Homework Equations dot product of 2 vectors ( ui*bi)+(uj*bj)+(uk*bk) = or finding the module of both vector and doing AB...
25. ### Turning effect of Force

Homework Statement Homework Equations How will we find the perpendicular distance between the wall and the centre of mass of the slab? How will we calculate the total downward force exerted by the cables on the slab? I thought much over both the cases but was not able to find any solution...
26. ### Turning Effect of Force

Homework Statement Homework Equations How do we calculate the value of F? The Attempt at a Solution Since for an object to be in equilibrium, F1D1 = F2D2 so 7.2 x 1 = F x 8 F = 0.9N, I am pretty much confused with the answer I worked out. If I am wrong or if I am right, please explain me the...
27. ### Calculate the course of the Force and Moment

Homework Statement I shall determine the course of the normal force, the lateral force and the bending moment. And then sketch that as a graph Homework Equations All Moments are 0 All Fx = 0 All Fy = 0 The Attempt at a Solution here is my clear cut (is this the right Word in English ? :)...
28. ### I Spin confusion: Stern-Gerlach experiment

I have some serious issues trying to understand the idea of the spin in the context of the Stern-Gerlach experiment and would appreciate some assistance! Assuming that a homogenous magnetic field ##B## in the "North-wards" ##z##-direction, assume that there is a magnetic dipole moment ##\mu##...
29. ### Mass moment of inertia of an airplane about its main gear

Homework Statement Okay, so this isn't so much a problem as a design issue while following an example given in a book. (Relevant material is here: http://www.aero.us.es/adesign/Slides/Extra/Stability/Design_Control_Surface/Chapter%2012.%20Desig%20of%20Control%20Surfaces%20(Elevator).pdf ) Now...
30. ### Stronger or stiffer ?

I have some serious confusion regarding the title for the following issue . I have read on plethora of forums and sites, giving the explanation of why hollow tubing is stronger than solid rod of the same dia or weight by justifying as to why it bends the least . This makes me ponder ! Stronger...
31. ### Equivalent force and couple moment

Homework Statement I will post a photo of the question in the thread once I've created it. I have found the magnitude and angle of the resultant force, but I am unsure of how to proceed. I find moments and couples confusing. Homework Equations $$\vec M = \vec r \times \vec F$$ The Attempt at...
32. ### Can we say Angular Velocity is a 'moment' of tangential velocity?

If a rigid link pin joint-fixed on ground and is rotating freely about the same point with uniform ang. vel., can we say the vector form of angular vel. (omega) is nothing but moment of the tangential (perpendicular) vel. at the other end?
33. ### Help with this moments problem

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...
34. ### 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...
35. ### 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...
36. 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...
37. ### 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?
38. ### Why don't we include the kinetic moments in the summation of the moments of a rigid body?

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. ### Offset Torque Concept

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...
40. ### Finding the Moment of Inertia for a Rectangular Sheet

Homework Statement The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the...
41. ### How to determine direction of a moment

Homework Statement I am following the first problem on this online pdf: http://www.ce.udel.edu/courses/CIEG212/Homework_1_2007.pdf Homework Equations Equilibrium equations for forces and moments. The Attempt at a Solution I know how to solve the problem, that part is straight forward. However...
42. ### Find the position of equlibrium

Homework Statement From the diagram below find the position of the man (##x##) if the system is in balance. Total length is ##L## and the man is distance ##x## from one end. Homework Equations 3. The Attempt at a Solution [/B] I know that the system must be in balance if all the torque and all...
43. ### Help understanding torques and moments

Homework Statement Find the period of small oscillation of this system. Homework Equations 3. The Attempt at a Solution [/B] I understand the concept of moment of inertia but can't comprehend the first equaion here. The other two i get and they are moments of inertia of other two bodies...
44. ### Statics -- Net Moment

Homework Statement Homework Equations I can see how the net force is not the same but I'm not getting the net moment. The Attempt at a Solution 12mm x 10N = 120N-mm. How do these two FBDs not have the same net moments. Thanks for any help!
45. ### Maximum moment question

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...
46. ### 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...
47. ### 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...
48. ### 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...
49. ### Early Statics Question

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...
50. ### 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...