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.
I am stuck on part b) i). I understand that there is no normal force from the ground as the bin is on the point of being lifted off the ground, that is all fine. That leaves R, F and W.
I know W is 40g, and I am required to calculate F, therefore it makes most sense to take moments about the...
This formula works for a beam with one uniformly distributed load... How would I apply the same technique to get the bending moment equation in terms of x for the same type of scenario with a point load before R1 and after R2 at each end of the overhangs? Would I simply add a term for each the...
A current current loop is running through this figure.
How do I design integration surfaces to find the magnetic dipole moment?
In the solution the three following figures were designed for integration surface, and they prove that they all give the same answer of ## m= 2IRd \hat{z} ##.
For...
Hello, I am curious to find the moment of inertia of an insect.
My guess is that I use the formula
to find the moment of inertia.
I would appreciate any help.
If a circular rod is allowed to rotate freely and a moment (M) is applied to one end of the rod. A moment acting in the opposite direction, with magnitude (M/3), is applied to the other end of the rod. What is the maximum moment in the rod that would be used to calculate the maximum torsional...
Hi,
Can I someone please explain to me, the moment behaviors of having something fixed on CG vs on Tail in a rocket? are there any benefits of having a Sensor on CG than fixed on the tail?
Thank you
So I have a system in which there is a disc with a moment of inertia of 1248.68. this system can rotate this disc from zero RPMs to 36 RPMs and approximately 2 seconds. How would I go about determining how much power is exerted to do said work? Many thanks
from the partition function - am trying to show that ##\langle \mu \rangle = \beta^{-1} (\partial \log Z / \partial B)## where ##Z## is the canonical partition function for one atom, i.e. ##Z = \sum_{m=-j}^{j} \mathrm{exp}(\mu_0 \beta B m)##, and ##\mu = \mu_0 m##. The average...
Two rotating cylinders are held in contact by a force F1. The force is applied through the center of one of the cylinders. One cylinder is the driving cylinder and the other is the driven cylinder .
Does the moment of inertia of the system depends on the force contact force F1? Why?
And...
a=2/3*g*sin(25*(pi/180))=>a=2.8507 m/s^2
vf=vi+at=>vf=0+2.8507*1.50=>vf=4.2760 m/s
So the translational motion of the cylinder is 4.2760 m/s.
4.2760=R*w
w=134.04 rad/s
PE=mgh=>PE=215*9.8*.108=>PE=227.56 J
PE = KE at the end of the roll because of energy conservation.
227.56 =...
Hi,
I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?
Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##
It seems like the right hand side is the magnetic dipole...
Hello all,
I'm trying to understand the maximum moment on a free beam. Consider a tail sitter drone that is simplified into being a beam with two motors fitted with propellers on the end of the beam (see the photo below), let the payload be estimated as two, 2 newton loads going downwards. If...
If two plates of Aluminum (both are 2" tall, and 1/2" thick) were placed over each other (see photo 1) and then welded together all around the perimeter of the second plate (the blue one) as indicated by the yellow lines in photo 2, then would the moment of inertia be calculated as if the local...
Every time when you increase RPM on longitudinal placed internal combustion engine, car shake to side in oposite direction of crankshaft rotation.
This is reaction moment for change in RPM of crankshaft/flywheel.
How this reaction moment transfer to engine block/car if crankshaft is separated...
hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...
Hi,
unfortunately, I am completely confused about the task
It is about the task part a
I have now defined the two rotations as follows:
The thin disc rotates around the ##z## axis, red in the picture, and then the rod to which the disc is attached rotates around the ##z_I## axis, in the...
Hello! Assume I have a 2 level system, where the 2 levels have opposite parity. If I apply an electric field, I will get an induced dipole moment. For now I want to keep it general, so the induced dipole moment can be very large, too. Let's say that I start rotating this electric field in the...
What I did was plug in the outer radius time the force into the torque and then the mass moment of inertia is equal to m*ro^2 so then I plugged in the mass times the radius of gyration squared into I and solved for a but this is not right.
A possible estimate for the third central moment is the product of the skewness and the standard deviation raised to the third power. Is it also true that a possible estimate for the fourth central moment is the product of the kurtosis and the standard deviation raised to the fourth power?
In engineering statics I've learned the concept of bending moment, which in some way indicates an applied load that tends to bend the object, and it seems that it can move around freely in the reference frame. (I understand moment in engineering is not quite the same concept as torque in physics...
TL;DR Summary: Finding maximum bending moment on a boom
I am trying to solve the problem stated in the picture below.
The answers are given.
I've manage to find the Normal and Shear Forces but I'm stuck at the bending moment.
According to my analysis the maximum bending moment is +7208,1...
Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point...
How do I interpret physically what dipole moment is ? The explanations that I received were "two charges seperated by a small distance " ,"it talks about ability of a dipole to rotate under the influence of an Electric Field " ,"Second term of the Multipole expansion" ,I get that these terms...
Hi all,
Why was the thickness of the beam considered when moment was being calculated and why was the horizontal component of the 600 N force used in calculating the moment? That part is unclear to me. Please explain it. Am I looking for the logic behind using the horizontal comp. and the...
Figure:
My attempt at a Solution:
$$\overrightarrow{TFD}=TFD\dfrac{(-0,16\widehat{i}+0,11\widehat{j}-0,08\widehat{k})}{0,21}$$
View from above:
We calculate ##D##:
$$\sigma =90-\arctan \left( \dfrac{0,07}{0,240}\right)=73,74\, \textrm{º}$$
$$d=0,16\cdot \sin (\sigma)=0,1536\, \textrm{m}$$...
This is probably a silly question, but I am really stuck. A possible senior moment, is my only excuse.
Here is an approximation:
##log(223)/log(3) \approx 10818288 / 2198026 ##
So we have:
##log(223)/log(3) - 10818288 / 2198026 = 0.0399292##
which is OK but not great -- the error shows up...
Using the equation above I get Xcm = 0.022 m. I set the origin be at the left of the vertical rod parallel to its centre of mass as in the diagram. But I’m not sure if the equation is correct for 3d.
for the moments of inertia I am using
I = Icm + md^2
= (mr^2)/2 + md^2
where d is the...
Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of...
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...
Every time I have taken moments before I have been able to solve for the required unknown regardless of what point I choose, unless there is more than 1 unknown! However I tried taking moments from the far left point load of 97.5 this time and I get the wrong answer. I don't understand why...
I am having trouble to find the moment of inertia of the second rod!
Is it related to the first rod??
At the beginning I thought It's not!
But when took those as constant,the equation had become way much simpler and there is nothing about chaos!
My approach is given below
I placed my Oxy coordinate system at the center of the square, the ##x##-axis pointing rightwards and the ##y##-axis pointing upwards.
I divided the square into thin vertical strips, each of height ##h=2(\frac{L}{\sqrt{2}}-x)##, base ##dx## and mass ##dm=\sigma h...
How can I find the maximum bending moment and maximum deflection for a spring?
It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner.
that's all, thank you very much.
We know that we need to go to 5th order in perturbation theory to match 10 decimals of g-2 for electron, theory vs. experiment. But let us not assume QED is pure and independent, but it's a lower energy limit of GSW (not Green-Schwartz-Witten from superstrings) electroweak theory. Has anyone...
I have come up with two different approaches, but I'm not sure which one is correct since they give different answers.
We use the following equation to get the total moment of inertia.
##I_o## = moment of inertia of disk about O axis + moment of inertia of road about O axis
Approach 1...
If I want to calculate the dipole moment of a dielectric cylinder of uniform polarization perpendicular to its axis, I could multiply the polarization by the volume of the cylinder, which is okay. But another method is to consider the cylinder to be a superposition of two cylinders of equal and...
Hey guys, I just numerically calculated the matrix elements for a superconducting qubit and I'm having some trouble to interpret the result.
I will include a plot of the matrix I got below:
I basically have "large" non zero elements on the main diagonal of this matrix. In previous courses I...
What kind of experiment can I design to determine the actual value of the moment of inertia. What should I instruct the sphero to do and what data should I collect?
hello, i struggle with this kind of questions and i don't understand the way of thinking and how to solve this.
in the first picture i don't understand why Moments about point Aare a*F1 because there is the 2 P forces that do moments.?
in the second problem i can't understand why there are 3...
Greetings!
As you could see the moment try to make beam to rotate in the support plane with the wall which mean for me this moment is on the Z direction but the longitudinal axis is the X direction and I know that for a moment to be torsion it needs to be in a longitudinal direction, but the...
We solved this problem in class as follows:
Net torque about the center of the pulley taking counterclockwise rotation to be positive = m1gR - m2gR = I_tot α, where I_tot is the moment of inertia of the full system.
My professor said that I_tot = I + m1R^2 + m2R^2, where m1R^2 is the moment...
I am completely stuck on problem 2.45 of Blennow's book Mathematical Models for Physics and Engineering. @Orodruin It says
"We just stated that the moment of inertia tensor ##I_{ij}## satisfies the relation$${\dot{I}}_{ij}\omega_j=\varepsilon_{ijk}\omega_jI_{kl}\omega_l$$Show that this relation...
Hello! My questions is about this paper, aiming to measure the anapole moment in a molecule. In their derivation, starting from equation (1), they assume that the frequency of the field felt by molecules ##\omega## is much bigger than the energy splitting ##\Delta##. That basically implies that...
Static friction is known to provide centripetal force when a car turns.
Assuming uniform circular motion, my questions are
1. Is the static friction of each wheel points toward the center of turning circle or it's the combined forces of all four wheels that has to point toward the center of...
Suppose Alice and Bob do an experiment with an entangled pair of particles, for instance electron spin with SG magnets.
Now suppose Alice her SGM is stationary while Bob his SGM is switching fast between parallel to Alice and perpendicular to Alice.
So there are two possibilities: correlation...
Hello,
I have an flexure where the force is applied asymmetrical, I just can't visualize why their should be a bending moment instead of an bending force? How can I distinguish those? Thanks!
Hello, so I have a question about the sense of rotation of the body.
I get the calculating part nd stuff like that. But what I don't understand is how we would determine the sense of rotation about the moment axis?
Could someone explain this to me please? (to add to this, I know that it is...