Moment Definition and 1000 Threads

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...

Hello! I have to calculate the deflection of a beam at at given point (C). The books says the should be a moment which plays a role in this deflection. How does this moment occur? I have drawn a FBD but couldn't find a moment? Should I divided the beam into separate parts or so? What am I...

I used the parallel axis theorem to solve the question but my answer is still wrong. Any ideas where I slipped? I can't seem to figure out the problem?

hi guys I have read the other day about how the nuclear quadruple moment descries the deformation of the nucleus, however i can't get my head around how is that!, I am familiar with the multiple expansion in which we can describe the potential of an arbitrary charge distribution by the following...

Some more details on the system are that L1 is very long (close to 100ft) and L2 is close to 30ft (the vertical pipes). The piping is all schedule 40 1/2" OD. Moment of inertia is roughly 10^-8. Components are about 2kg each. The distance of the pipes horizontally is small (around 2ft). Pressure...

* The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...

I am sure you are all familiar with the cross product in 3D space. i cross into j gives k. Cyclic Negative, if reversed, etc. I am sure you are all familiar with the definition as: norm of the first vector, norm of the second, sine of the angle, perpendicular (but direction using right hand...

Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex. Can I split the rotated square to two squares in the x-z plane and y-z plane to find...

Part of a project I am working on (part #3…see description below) is asking us to find the internal loads (shear and moment) and draw the corresponding shear/moment diagrams of the control arm shown below. It’s a little tricky to me, because all of the members associated with these type of...

This was the question (The line below is probably some translation of upper line in different language) For disc it was ma^2/2 For ring it was ma^2 For square lamina it was 2ma^2/3 For rods It was different Please explain Thank You🙏

My solution is now I am asked for the same result but in this form but I don't know where to start.

This isn’t a HW problem per say, but it’s an example shown in my statics textbook that is used to try an explain that you need to add a couple moment to move a force to a point not on the line of action, and I’m just not seeing how the direction of the couple moment is correct. See the image...

Hello! I tried to solve a) see figure below, is it correct? b) so what I think I can do is to solve ## M_{12} ## from the equation of the magnetic flux then I will get ## \frac{\Phi}{I} = M_{12}## Then I can even use the equation får the magnetic flux and the magnetic field $$ \Phi = \int \vec...

I tried to solve it and I got the following is it correct? and 2 My solution... is a negative distance?

This is the image of the problem: I tried to solve it and I got the following is it correct? derive and equal to 0 because it is between an angle of 0 and 180° is this statement correct?

Hi guys, I don't really know how to cope with this problem, maybe just because I can't properly understand the data. In the figure we have a beam with its loading(plus a force of 15kN), a pivot O and support at the rightmost point. I would say that in order to find the equivalent system, I...

Is it still true that under the Copenhagen Interpretation the standard theory of QM tells us that a measurement apparatus gets into superposition of possible measurement outcomes and does not tell us how and when we get a single decisive outcome? (The so-called "Measurement problem")

Apologies if this is in the wrong section as it isn't particularly medical in nature despite it being about the body. I am currently conducting a rapid review with outcomes of knee muscle strength. This is measured by biodex dynamometry, which assesses numerous values including Peak moment...

Good morning everyone! I am an aerospace engineering working on my thesis and i am trying to solve a little problem. In the picture you can see an "aeordynamic" body. The CFD analysis gives me the forces and the moments acting on this body. How can i calculate the momentum acting on the body...

Hello! Are there any experimental measurements or theoretical calculations of the electric dipole moment of any Rydberg state for CaF or BaF? Thank you!

Hi! I would like to calculate (roughly) how much torque is needed bringing the blue plateau in movement. Assume the blue plateau is loaded with 7.5 kg. The radius of the blue circle is 100 mm.

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...

h = d1 + 0.08 d1 = h - 0.08 d2 = h + 0.08 I of the vertical portion = 1/12 m (l^2 + b^2) + md1^2 = 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2 I of the horizontal portion = 1/12 m (l^2 + b^2) + md2^2 = 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2 The moment of inertia for the whole T-shape about...

I have this moment of inertia problem and is a little confused on the semicircle part and if the rest is really right? I get over 10 if I calculate it in crew CAD but by hand I get 7,568032142. What is right and what am I doing wrong?

Homework Statement:: Anyone familiar with prokon column design ? I have no idea how the program caluculate the imperfection moment in the slender column (braced/unbraced... Relevant Equations:: I have attached an example here , it's an unbraced slender column here. Why the imperfection moment...

hi every one what is the amount of orbital magnetic dipole moment of proton? this different with the intrinsic magnetic.

I know there are more convenient differential elements that can be chosen to compute the moment of inertia of a disc(like rings). the mass of the differential element: $$dm = (M/\pi R^2) (dA) = (M/ \pi R^2) (2\sqrt{R^2 - y^2})(dy)$$ the moment of inertia of a rod through its COM is...

I have been given an answer for this but I am struggling to get to that point $$ANS = 0.430\, kg \cdot m^2$$ So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R##...

I = 2/5M R^2 + Md^2 This is analagous to Earth's movement about the Sun. Is the moment of inertia of Earth about the centre of mass of the Earth Sun system = 2/5MR^2 + Md^2, where: M = Mass of earth, R = Radius of Earth, d = distance from Earth to centre of mass of earth-sun system.

Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...

I have encountered two (?) definitions of the electric quadrupole moment. They are: $$Q_{ij}=\frac{1}{2}\int \rho(\vec{x}')x'_i x'_j\,\mathrm{d}^3x'$$ and $$Q_{ij}=\int (3x'_i x'_j-\delta_{ij}x'^2)\rho(\vec{x}')\,\mathrm{d}^3x'$$ I am trying to study radiation arising from the electric...

So I set up 3 equation for this problem. 1st was the moment equation about point G, 2nd and 3rd were from applying Newton's 2nd law to each of the blocks. I thought once I set those equations up I could solve for alpha (angular acceleration) and then find acceleration of each block but when i...

Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or...

Question: Diagram: So the common approach to this problem is using polar coordinates. The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is $$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$ whose value is...

I could do the first part of the question with ease but second part I am not sure how to proceed. Should we calculate the magnetic field at d(where the loop is) and infer something from that for it's motion?? Plz help me out Thanks in advance

On the first attached page ##\mu_z## is associated with orbital angular momentum (Eq. 41.34). On the following pages (Eq. 41.38) it is associated with spin angular momentum? Are these both part of the same thing? I tried to read further but the book does not address this. In example 41.6 it...

Hi Im a bit confused with the example Can somebody explain and show to me how they got the bending moment calculations for the diagram in the attached. i understand it up to there. I started course late and can't ask for help. Thanks

Hello: I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments. For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached? Beam...

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:

First, I calculated the number of moles of glucose. n = m / M n = 1.8 / 180 n = 0.01 moles of glucose So I checked the combustion reaction. 1 C6H12O6 + 6 O2 -> 6 CO2 + 6 H20 1 + 6 -> 6 + 6 0.01 + 0.06 -> 0.06 + 0.06 I considered the number of moles at the end of the reaction. I subtracted...

We start from the definition$$I_{ij} = \int_V \rho(x_k x_k \delta_{ij} - x_i x_j) dV \iff \dot{I}_{ij} = \int_V \rho (2 x_k \dot{x}_k \delta_{ij} - \dot{x}_i x_j - x_i \dot{x}_j ) dV$$Now since the rigid body rotation satisfies ##\dot{\vec{x}} = \vec{\omega} \times \vec{x} \iff \dot{x}_i =...

Can anyone explain why the moment of inertia for a tubular column in that textbook is like so? (take a look at the attachments). It should be (I = MR^2), as far as I know.