Confusion Definition and 1000 Threads

##\bar{\mathcal{O}}## is moving with a velocity ##v## relative to ##\mathcal{O}## along ##x^{1}## The Lorentz transformations between a Frame ##\mathcal{O}## and ##\bar{\mathcal{O}}## is given by: $$\Delta x^{\bar{0}} = \gamma\left(\Delta x^0 - v\Delta x^1\right)$$ $$\Delta x^{\bar{1}} =...

My thought process of how i do the ice melting part: (note I just ignore the copper/lead part cause I already know how to do that part) Q_ice + Q_melt + Q_liquid so, it 0.018(2100)T+0.16(4190)T+0.018(334*10^3) but on chegg they didn't use 2100 but they just use 4190 instead and I am confused...

Suppose a particle is falling under the pull of gravity, the distance it has fallen is given by s=16t^2.Suppose we wish to find the instantaneous speed at t=1. Find the average speed between t=1 and t=1+h where h is any real number except 0. Distance traveled/Time it takes to travel the distance...

My general understanding of electric flux density is 'electric flux per unit area'. This gives the SI unit N/C. But According the formula of electric flux density, D=eplison*E, the SI unit is C/m^2. How come the dimension in both cases not matching if both are true?

There is an ambiguity for me about vector components and basis vectors. I think this is how to interpret it and clear it all up but I could be wrong. I understand a vector component is not a vector itself but a scalar. Yet, we break a vector into its "components" and then add them vectorially...

x component of ##F_3## ##F_{3x}= m a_x- F_{1x}-F_{2x}## = ##ma\cos 50-F_1\cos(-150)-F_2\cos90## y component of ##F_3## ##F_{3y}= m a_y-F_{1y}-F_{2y}## =##ma\sin50-F_1\sin(-150)-F_2\sin90## And so on… My question how we can represent it in diagram ##F_1\sin(-150)##. I suppose...

https://slideplayer.com/slide/10708471/ This is the context I am talking about. What contradiction occur here? We begin by telling that there is a Turing machine H that solves the halting problem. So how does this contradicts? Can you tell me about that? What contradiction occur here? We...

https://slideplayer.com/slide/10708471/ This is the context I am talking about. What contradiction occur here? We begin by telling that there is a Turing machine H that solves the halting problem. So how does this contradicts? Can you tell me about that?

Hi I have been doing a question on Lagrangian mechanics. I have the solution as well but i have a problem with the way the question is asked regarding dimensions. The 1st part of the question says that a particle of mass m with Cartesian coordinates x , y , z moves under the influence of...

Goldstein 3rd ed says "First consider holonomic constraints. When we derive Lagrange's equation from either Hamilton's or D'Alembert's principle, the holonomic constraint appear in the last step when the variations in the ##q_i## were considered independent of each other. However, the virtual...

I am currently reading David Morin book and found this statement : ##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM" Is it really alright to choose the center of a...

If there is a spherical conductor like this with excess charges on its surface then this is the field it sets up. Each e- would have there own radial field of lines. And all the e-s would exert a force on each charge and the net field on each charge and thus net force would be zero. All the e-s...

So I was trying to get a bit better handle on the definition of the difference between an event horizon and a Killing horizon. Locally they are indistinguishable, and the key difference (to my understanding) is that the event horizon is the last Killing horizon that escapes to future null...

In this page you can see it’s written: E must be perpendicular to the surface. If it were not then the charges would move due to a component along the surface. I am assuming the field is generated due to the charges on the surface. I have a doubt. Is the author saying if it were not...

Hello everyone, I recently completed kleppner and kolenkow classical mechanics book. Next I am going to learn Electrodynamics. My brother is a EE major and he gave me his copy of "principles of electromagnetics" Matthew Sadiku 4th edition. But a lot of people here recommend Griffiths. So, 1.)...

I understand that potential energies are energies relative to reference points. For example, gravitational/electrical potential energy is relative to a point at infinity. What is the reference point for centrifugal potential energies? In the case of planetary orbits, must the reference point...

1. For regions that contain charge density, does the 1st uniqueness theorem still apply? 2. For regions that contain charge density, does the 'no local extrema' implication of Laplace's equation still apply? I think not, since the relevant equation now is Poisson's equation. Furthermore...

> **Exercise.** Let T1and T2be tensors of type (r1 s1)and (r2 s2) respectively on a vector space V. Show that T1⊗ T2can be viewed as an (r1+r2 s1+s2)tensor, so that the > tensor product of two tensors is again a tensor, justifying the > nomenclature... What I’m reading：《An introduction to...

Hi If i have a vector r = ( x1 , x2 , x3) then i can write r2 as xixi where the i is summed over because it occurs twice. Now is xixi the same as xi2 ? I have come across an example where they are used as equivalent but i am confused because xi2 seems to be the square of just one component of r...

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then...

I was just browsing through the textbooks forum a few days ago when I came across a post on differential geometry books. Among the others these two books by the same author seem to be the most widely recommended: Elementary Differential Geometry (Barret O' Neill) Semi-Riemannian Geometry with...

Hello all, I am trying to search for different areas to do masters which would match my interests. I am broadly interested in , fluids (aligned to general aerodynamics) especially compressible fluids , turbomachinery, rockets. I am thinking to work in some sector related to gas turbines or jet...

I don't understand, in balancing a nuclear equation, the sum of all the mass numbers and atomic numbers, given on the upper left and lower left side of the element symbol, respectively, must be equal for both sides of the equation. So why does the sum on the left side equal to 20, but the sum on...

Hello Gents, I am very confused about the working principle of gas turbines. I understand that air is first compressed in a compressor to obtain high pressure air at the inlet of turbine, but before air is introduced to the turbine, first it has to be heated to very high temperatures through...

Hello: I was reading about thin-walled members under shear force, specifically example 7-7 of Hibbeler's Engineering Mechanics, Mechanics of Materials. First, the fourth Edition: As you can see above. He starts by computing the moment of inertia on the first equation by subtracting a rectangle...

I've having trouble understanding a derivation of the speed of sound waves, which is actually similar to another derivation I found a couple days ago. Let's suppose the sound is moving through water in a long cylindrical horizontal pipe. The premises of the derivation are 1.) For a given...

Read the book and conducted research on the internet. Came to conclusion that this was an isolated system because the girl was being accelerated by gravity but answer is non isolated. Can someone please help me grasp this concept better.

Refraction has a symmetry; on going from glass to air light at the glass air surfaces refracts away from the normal. If you turn the light source around and make the former refracted beam the incident beam then its refracted angle will be the former incident angle. So at critical angle, do the...

I do not agree, this is bullocks. We can simply set up position vector of ##\vec A(t)## and ##\vec B(t)## with respect to the fixed center of the carousel, their relative velocity is simply ##\frac{d (A-B)}{dt}## or ##\frac{d (B-A)}{dt}## Since this is a pretty popular book, I am wondering if I...

DISCLAIMER: in Italy, we talk about "circuitazione" of a field through a closed loop ##\gamma##, for the physical quantity $$\Gamma_\gamma(\overrightarrow{E}) = \sum_{k}\overrightarrow{\Delta l_k} \cdot \overrightarrow{E_k}$$ but after some research, I haven't managed to find the correspondent...

Hi all, I am confused about symbols. I cannot figure out why my partial differential equations professor writes ##u## and ##\mu## in his lectures. A function ##u(x, y)## turns into ##\mu(x, y)##. His homework sets are always typed with ##u##. I also think he says MYOO during the lectures so it...

I am confuse understanding between unsteady and turbulent flow. If I look the fluid simulation in Youtube, they both look the same. What is the difference between them? Please explain for a beginner.

Hello! I was reading two things: 1) tidal locking (as explained in the Wikipedia article:https://en.wikipedia.org/wiki/Tidal_locking where it is stated that, because of internal friction caused by the body of water being attracted to the moon and deforming, the kinetic energy of the system...

Hello. I am trying to do a basic experiment to demonstrate I⊗β≈ƒ or current cross magnetic field results in a force perpendicular to the plane of the other two. But every time I test this out, it appears I get a force in the same direction as the magnetic field. Here is my experiment: Strong...

This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...

The test case for the block of code below is: y0=10, f=@(t,y) -0.5*y, [t,y]=euler_method_attempt(f,0,5,y0,10) This code below works and is the correct answer, but I am confused on some parts of it. When indexing the for loop it seems as if the first output for "y" would be y(2), not y(1). And...

Hello everyone! I have a course in thermodynamics this year, and there is a question about enthalpy that I cannot answer: given the definition of enthalpy H=U+PV and the integral form of the internal energy U=TS-PV we conclude that H=TS. We normally say that enthalpy equals the heat exchanged in...

Instead of talking about the simple of case of reflection interference due to a single film, this book starts off with two films with an angled air wedge between them. They talk about the "thickness", ##t##, of the wedge, but this thickness varies along the length of the films (Figure 35.`12)...

The following three equations illustrate this decomposition. Estimate separate linear wage regressions for individuals i in groups A and B: {\displaystyle {\begin{aligned}(1)\qquad \ln({\text{wages}}_{A_{i}})&=X_{A_{i}}\beta _{A}+\mu _{A_{i}}\\(2)\qquad...

Suppose there is a charged line and near that line, there is a magnetic needle lying in the vertical plane of the line. The magnetic needle is radially placed. If the charged line and the magnetic needle are moving at a same constant velocity(parallel to the line, v<<c) towards an observer. I...

I saw the information of the text at different places and when i compare it is confusing. The text is In some other section If you see the red lines i have highlighted, in the first section the book refers that the B coil is behind the A coil, but in the 2nd section it refers that in the...

1) are all Moments of forces and Moments of couples free vectors? Can I move the moment vector computed about point O to a new point "point B" without changing the system? To elaborate on the question, suppose Resultant Moment about point O is computed using several forces and the position...

I am confused about implicit differenciation in a few ways. The main confusion is why, in the equation ## x^2 + y^2 = 1 ##, when we are taking the derivative of the left side, ## 2x + 2yy\prime ##, are we adding a ## y\prime ## to the 2y but we aren't adding an ## x\prime ## to the 2x? I also...

I am writing an article about the Hubble Tension and when I was looking through the angular diameter distance I get confused over something. In many articles the angular diamater distance to the LSS defined as the $$D_A^* = \frac{r_s^*}{\theta_s^*}$$ where ##r_s^*## is the comoving sound...

As a part of a bigger problem, I was trying to evaluate the D'Alambertian of ##\epsilon(t)\delta(t^2-x^2-y^2-z^2)##, where ##\epsilon(t)## is a sign function. This term appears in covariant commutator function, so I was checking whether I can prove it solves Klein-Gordon equation. Since there's...

I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...

Should I just follow the original question? If given as ##f(x)=\ln x^4## then the domain is x ∈ ℝ , x ≠ 0 and if given as ##f(x) = 4 \ln x## the domain is x > 0? So for the determination of domain I can not change the original question from ##\ln x^4## to ##4 \ln x## or vice versa? Thanks

The charges are q1,q2 & q. P,Q,O1,O2 refer to positions only. This is a conducting sphere with cavities containing charges. I'm interested in knowing how the charge should be distributed in the sphere. I know the charges induced on the charges of the sphere should be equal and opposite to the...

The tables and Wolfram Alpha say ## \int dx/(x^2 + a^2) ^{1/2} = log~ [( x^2 + a^2)^{1/2} + x] ##. So if a=0 we get as answer ## log (x + x) = log( 2x) ## if ## (x^2)^{1/2} = x, or ## log (x - x) = log( 0) ## if ## (x^2)^{1/2} = -x but surely ## \int dx/(x^2)^0.5 = \int...