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Imagine there is a massless spring of spring constant 10 newton/metre
Now, a person's hand apply a pulling force of constant 100 newton on the spring
Now, according to Newton's 3rd law, the spring should also exert an equal amount of pulling force on the man, but right at this MOMENT/INSTANT, the spring has 0 elongat... |
I am trying to understand symmetries in the case of topological insulators. And I have a huge problem with the interpretation of symmetries. Let's say we consider quantum spin Hall state, where we consider edge states -- spin up electrons moving along one direction and spin down electrons moving opposite. And as I can ... |
In general, conservation laws can result in shock waves, i.e. locations where a variable changes quickly and a discontinuity arises. One of the most common examples that is always mentioned is the shock wave that forms when fluid or an object travels at supersonic speed, which creates a shock wave. However, are there o... |
My question is mainly related to (a).
What I`m trying to say is that considering the specimen is constructed to layer by layer and each atom on a layer is rigidly coupled with atom of up and down layer.
Then Can phonon vibration(in Debye model, as soundwave) go through up and down? or not? and why?
Should I do cons... |
I am writing a thesis about fuel cells and trying to follow the calcultion of the Gibbs free enery of the reaction of some author. I am confused because he took the higher heating value (HHV) of the hydrogen, which means that the water is in liquid form, but then continued the calculation with the standard entropy of w... |
I am browsing the materials project, and want to find which materials expand more when heated. However, expansion coefficients are not given there. There are bulk moduli, and elastic constants calculated with DFT, as well as mass densities.
Can I roughly estimate thermal expansion by an inverse of the bulk modulus? I d... |
My question arises from this post by Ashish Arora, where he asks: "If $g$ becomes zero suddenly, a body at rest on a fixed table will start moving away from it."
In the above question $g$ is the acceleration due to gravity.
Some in the comment section have stated that the body will fly away due to the loss in the centr... |
Suppose two electrons are entangled with opposite spins. Electron #1 passes through the event horizon of a black hole, together with Laboratory Assistant #1. Suppose the assistant measures electron #1's spin after they pass through the event horizon (according to #1's [proper] time) and measures a $+$ spin.
Another lab... |
I'm currently trying to understand expectation values within Quantum Mechanics. I have a few questions that I could need a little bit of help with understanding how to interpret and how to further do calculations.
Notations and other important variables for this example:
A free particle has the wave function $\Psi(\ve... |
I was doing a question in which I was able to find the charges on each capacitor in parallel by assuming that the total charge would get distributed amongst each capacitor according to their capacitance. I want to know if this assumption is true, or if I just happened to get the right answer using the wrong method. The... |
I've read in multiple quantum mechanics books that the name "continuous" of the continuous spectra is said continuous because in many examples it is an interval of values. But I couldn't find references for this...
Is the continuous spectra always "continuous"? And when the spectra is "continuous", is the continuous pa... |
When atoms are formed, first nucleus is formed and then, nucleus attracts electrons(we can call them free electrons) and we get an atom.
but in terms of Bremsstrahlung, what happens is:
In the case of an electron passing close to a positively charged atomic nucleus, the electric field of the nucleus would exert an att... |
I'd like to ask my query through 2 case examples:
Case 1) Suppose a person whirls a stone tied to a string in a horizontal circle around him such that he/she is always pointing and looking towards the stone such that the stone appears stationary.
Case 2) Suppose a person stands at the edge of a rotating disc and thro... |
Do electric field lines approaching a boundary at an angle get refracted and change direction just like light rays do?
Because will discussing electric field lines and flux associated with it we do not consider a change in direction
|
My question is about the variation of conductivity in a volume of material and its effect on measured current. A volume is comprised of two metals joined symmetrically in a cuboid shape as in the image below. These metals have different conductivities: $\sigma_{1}$ and $\sigma_{2}$. Does $A_{1} = A_{2}$ or $A_{1} \neq ... |
Suppose Lagrangian $L_1(y_1,y_2)$ is a functional of fields $y_1$ and $y_2$, and Lagrangian $L_2(y_1,y_2,z_1,z_2)$ is a functional of the fields $y_1,y_2$ and the auxiliary fields $z_1$ and $z_2$. If we solve the equations of motion of $z_1$ and $z_2$ and plug the solutions into $L_2(y_1,y_2,z_1,z_2)$, we get $L_1(y_1,... |
I am currently looking into the compactification of spacetimes as it is often done in (super-)stringtheory.
So, say I start with a ten-dimensional Lorentz manifold $(N, g)$, where $N$ denotes the underlying smooth manifold and $g$ denotes the Lorentzian metric on $N$.
Compactification would then lead to a ten-dimensio... |
For instance, if we have a general two-qubit state $$|\psi\rangle=\frac{1}{2}(|0\rangle+e^{i\varphi_a}|1\rangle)\otimes(|0\rangle+e^{i\varphi_b}|1\rangle)=\frac{1}{2}(|00\rangle+e^{i\varphi_b}|01\rangle+e^{i\varphi_a}|10\rangle+e^{i(\varphi_a+\varphi_b)}|11\rangle,$$ is there a way to create a Bell state simply by arra... |
The following question is from Heat and Thermodynamics by Zemansky and Dittman: prove that isentropic curves do not intersect for a system of two independent variables, and for a system of more than two independent variables, they do generally intersect.
My attempt: for the first part, I can take any two independent va... |
I know that when two unlike charges brought near, they will attract and cancel out each other.
So my question is what does cancel each other mean? Does they combine and form a neutral charge? I mean now they are neutral together so any of them should not be able to exert any force on a 3rd charge brought near them thou... |
The text below describes the TikTok video here.
Suppose you have 1L of blue water at 10C and 1L of red water at 55C. Assume you can pour water into a special jug with two compartments with 1L capacity each. Water in the two compartments of the jug can reach thermal equilibrium through the walls of the jug. You can also... |
On a hot summer day, dishes dry outdoors almost immediately. At other times, a cool wind with an overcast sky will sometimes also dry dishes outdoors after a while. I am aware that some heat still gets through the clouds on overcast days, but I'm guessing a significant factor on such occasions would be the speed of a c... |
I think I have a gap in how the Maxwell's equations describe the electric and magnetic fields. At first glance I used to think that the Maxwell's equations particularly the Faraday's law and the Ampere's law are about how the electric fields and the magnetic fields can and actually do generate each other. So in this f... |
On one of the string theory notes I read that the conformal symmetry of the bosonic string theory is implied by virasoro constraints. Could someone explain what is the relationship between conformal symmetry and the virasoro constraints?
|
here is my body diagram:
he have the two weights two normals and two frictions however I think I am missing something becaused I only have cosine components when analysing the torque eq with respect to the left point:
$$\Sigma \tau = -0.5lcos\theta W_1-1.5lcos\theta W_2+2lcos\theta F_{f2}+2lcos\theta N_2$$
I think i a... |
Here is a picture of the experimental setup. The electrometer shows the potential difference between plates A and B. But why? Shouldn't it show the potential of the plate A to which it is connected? Please explain why this is happening?
P.S. The question may seem silly, but I really want to understand the physics of th... |
I already asked the question very clearly in the topic, so I will use this place to explain the context for which I present this question.
Normally, since I have been doing electrostatics, I have become familiar with
$$V_{AB} = V_B - V_A$$
I am now dealing with a circuit diagram in which a $6\Omega$ and a $2\Omega$ res... |
On my QFT lecture note there is a comment that says 'Non-abelian gauge theory is extremely unique in 4-dimensional spacetime'. However, I didn't really catch what that means. Why is it extremely unique? Could someone give me some examples for that?
|
Let’s say an observer is travelling at 5% the speed of light. In the opposite direction a projectile approaches the observer at 99.9% light speed. According to the formulas for time dilation and length contraction, this is almost negligeable at 5% light speed. Since this is the case, shouldn’t the observer see the proj... |
The device could be a telescope, microscope, camera, or anything that zooms in with great clarity. I'm pretty sure that lots of dust together in one place in a sunbeam can have this effect (please correct me if I'm wrong) but can a single mote produce it? Also, what causes this effect and what circumstances must be pre... |
Say we want to calculate $\langle f(t_2)|O|i(t_1)\rangle$. Where $O$ is an arbitrary operator. We can treat the states as stationary and then evolve the operator
$$\langle f(0)|O(t)|i(0)\rangle\\O(t) = U^{\dagger}(t_2)OU(t_1)$$
Or we can split the unitary operator into a free part and an interacting part $U(t) = U_{f}(... |
Say for the sake of this question we have a microscopic 3D sphere of radius $r$. This disk has a charge $q$ which is uniformly distributed.
What is the electric field within the sphere? Does it vary as a function of radius?
Edit: I've spent of bit of time on this over the last few days, trying to extend the approach th... |
Often when we go hiking, we encounter two kinds of paths whenever we have to cover elevation. We either go up via stairs or via walking up a ramp. Sometimes both are available side to side. And it's often got us wondering, what takes more energy?
I know that potential energy depends on the height alone. So, from potent... |
Thank you for helping with this question and I'm sorry if it's kind of stupid.
TLDR: In many textbooks and other derivations deriving the Lorentz Transformations, they omit coordinate axes orthogonal to the velocity vector between the inertial coordinate systems for brevity. (E.g. If $I'$ is moving (in frame $I$) with ... |
We know that a charged glass rod can positively charge a neutral object when it goes into contact with that object. But wouldn’t the glass rod become electrically neutral by gaining electrons from the object in contact? Is there a limit to the number of neutral objects that can be charged by a charged object through co... |
So I am kind of confused with Ampère's theorem, specifically when you have to use a square loop. Let's say I have a cylinder centered on the $z$ axis and there is a uniform surface current in the $\hat{\phi}$ direction. I want to find the magnetic field inside the cylinder.
What I would do is use a square amperian loop... |
Many podcast apps allow you to listen to podcasts faster than the speed at which they were recorded (typically at x1.25, x1.5, x1.75, and x2 speeds).
If these apps are simply replacing the sound's waveform $A(t)$ by $A(k t)$, where $k$ is the nominal speed multiplier, than the Fourier transform $\tilde{A}(\omega)$ chan... |
I've frequently seen two different explanations for why, in SR, it's impossible for an massive object to reach $c$:
As a massive object approaches $c$, its kinetic energy starts being converted to mass and so if it keeps getting more and more energy from somewhere, it will also just keep gaining more and more inertia... |
In the derivation of a formula for magnetic field due to a current in a straight line, I have come the across the following,
Since we considered the current element to be at a distance $l$ from the foot of perpendicular from $P$, and we took the element to be $dl$, we were able to differentiate $l$ to get $dl$, but ho... |
Imagine this scenario:
Mike lives on a massive planet, so massive he experiences time going slowly.
Le petit prince lives on a small planet ( not much time dilation )
After millions of years (making a significant time gap between the two frames of reference), the little prince sees a supernova, but it is going to happ... |
Let's imagine this scenario. An object that can be treated as a particle is already moving at constant speed that tends to zero (but I guess it can be said that it's not exactly zero). There are two forces with equal magnitude but opposite direction acting over it so that its velocity will never change. I know that the... |
The Hawking effect is induced by the causal horizon of a black hole, which separates the interior and exterior modes such that asymptotic observers at infinity see thermal radiation flux. What can we say about the physics of interior modes? Can we think of them as interior Hawking radiation at some temperature? Do any ... |
Since the Higgs boson was found in 2012, at a mass around 125 GeV, it has often been remarked that this is curiously close to "criticality" or "metastability" or a false vacuum, if one supposes that the standard model is correct up to very high energies. A Higgs mass of 126 GeV was in fact predicted in 2009, by making ... |
(Here, by ”thermal energy” I mean the energy associated with chaotic motion of molecules.)
Preface
In a textbook “Principles & Practice of Physics” by Eric Mazur, I came across two things, which make me ask this question.
First, on the picture below the author lists possible energy conversion processes.
By $E_s$ the a... |
Many conclusions made in study of electrostatics of conductor assumes that conductors should necessarily reach equilibrium. The following deductions are made assuming equilibrium is always reached in any shaped conductor
1)Electric field inside conductor is zero
2)Unbalanced Charges reside on surface(proved using Gauss... |
Generalised Hydrodynamics is a theory of hydrodynamics for Quantum integrable systems. Those system are integrable in the sense that one can find an infinite number of conserved charges i.e. operators $Q_i$ that commute with themselves and with the Hamiltonian, such that $$[Q_i,Q_j]=0, \quad [Q_i,H]=0.$$ If additional... |
Is there an equation that can calculate how high a rubber ball rebounds after being dropped? I will be using the pressure of the ball as a variable. I will drop the ball from a height of 1.5m with varying pressure, and I would like to have a model to test.
|
Was reading through a physics textbook yesterday and came across a problem that I cant quite understand.
Most of the question is clear to me but for the very last equation ( kinetic energy of alpha particle = 58.5/58.5+1... ) I just can't quite understand where it comes from.
If someone could clarify where exactly this... |
People often express an idea that steam engines would be more efficient if they used a working fluid with a lower latent heat than water. I always thought that was a misconception because (so I thought) steam engines use the Rankine cycle, which is a closed thermodynamic cycle, so you get back all that energy when the ... |
I am working on a problem in introductory solid-state physics and have a question. I feel hesitant to ask my professor because I think it might be a simple question. In the problem, an electron can move on a lattice. Sites $a$ and $c$ have an on-site energy of $E_0$, while sites $b$ have zero on-site energy. The Hamilt... |
I've heard many equilibrium terms:
Translational equilibrium
Rotational equilibrium
Static equilibrium
Dynamic equilibrium
The different terminology is slightly confusing. My understanding is as follows:
Translational equilibrium refers the equilibrium position when the resultant force is 0. Rotational equilibrium is... |
Is there any particular reason for using Al/Mg Kα rays in X-Ray Photoelectron Spectroscopy?
I read that the energy of the X-Rays produced by taking these elements as the anode materials can decrease the energy of X-Rays. I would like an elaboration on this particular statement.
Moreover, does the Full Width Half Maxima... |
I understand hydrostatic pressure to arise from the weight of the column of water above. Assuming this is true, then why does the pressure act in all directions? It doesn't make intuitive sense to me.
|
This is from Noelle Pottier's book. I am unclear on how equation 15.1.10 follows from the information that she's given. Is the equation a consequence of inserting equation 15.1.9 in the commutator?
Any help would be appreciated.
|
Entropy change of a system due to heat $Q$ can be expressed by the following inequality (assuming that temperature is constant):
$$\Delta S_\mathrm{sys}\ge\frac{Q}{T} \tag{1}$$
It can be expressed more explicitly as
$$\Delta S_\mathrm{sys}=\frac{Q}{T}+\sigma \tag{2}$$
where $\sigma$ represents extra entropy generated d... |
Recently, I started learning about different flows such as Coutte, Poiseuille and Hagen-Poiseuille. When searching for the latter, I found this interesting image:
I thought that I might be able to solve it, since I've seen the derivation of the previous velocity profiles using Navier-Stokes equation. But to make it in... |
Say we apply an AC electric field at some angular frequency $\omega$ onto a metal with a scattering time of $\tau$.
How does the relation between $\omega$ and $\tau$ affect the conductivity of the metal?
While it is easy to see from the mathematical formulation that smaller value of $\omega\tau$ leads to larger conduct... |
I'm currently studying the superconformal algebra $psu(2,2|4)$, but I'm having trouble understanding its representation.
Following arxiv:1012.4004
I know that the maximal compact subalgebra is su(2) $\oplus$ su(2) $\oplus$ su(4) (Lorentz & $R$-symmetry), and that a unitary rep is specified by the Dynkin labels [$s_1$, ... |
Why we have $\sum_k= \frac{V}{(2\pi)^3}\int d^3k$ but $\sum_r=\int d^3r$? I do not understand why the latter has not the coefficient.
|
I have an air blower and I blow this air in a cylindrical line but i dont know the velocity of air i can arrange the velocity with this blowing machine but it doesnt give me a number so i want to calculate it. I have 2 pressure instrument that means i can calculate the p0 and p1 in a specific length of in this pipe. Yo... |
Using 3D cylindrical coordinates, I get 0 as the answer.
$$ \nabla^{2} (k \hat{r}) = \hat{r} (\frac{1}{r} \frac{\partial }{\partial r}\left(r \frac{\partial (k)}{\partial r}\right) + 0 + 0) + \hat{\phi} [\nabla^{2}(0)] + \hat{z} [\nabla^{2}(0)]= 0$$
Am I correct? (Edit: I'm not)
The solution to this question in the boo... |
I apologize in advance if this is a stupid question but...
According to some scenarios about the beginning of the universe (namely cosmological inflation), in layman terms, everything was born out of a quantum fluctuation which caused a violent expansion. In this case, since an expanding universe break the time transla... |
I was recently reading about superheavy elements.
According to that article all superheavy elements currently known have only been synthesized in laboratory experiments and have a very short half-life, so they are nothing a common person could call "stable" (here I'm using the term "stable" in a rather non-technical se... |
The Achilles Twins Paradox: Proof of a Preferred Frame?
Abstract: Both Achilles and Bob spend the exact same amount of time accelerating and decelerating at the same rates. Both Achilles and Bob spend the exact same amount of time in inertial frames moving at the exact same constant velocities relative to one-another. ... |
"The Darwin term" is one of the three contributions to the fine structure of hydrogen (and other atoms). It is a perturbation to the hydrogen hamiltonian, which gives rise to a change in energy levels of $O(\alpha^4m_ec^2)$ of the form (SI units):
$$
H_D(\mathbf{r})=\frac{\hbar^2e^2}{8m_e^2c^2\epsilon_0}\delta^3(\mathb... |
I am working on a baseball pitching target. The "target" will be made of a grid of Laser emitters and photosensitive receivers. I'm wondering if I should "offset" the X axis from the Y axis so that one is behind the other and the beams never crosss.. If they are all lined up on the same plane, an X beam would cross 11 ... |
I've seen textbooks saying that for a given equation of state, for example
$$ M = \frac{C_cH}{T}. $$
Where $M$ is the magnetic moment of a paramagnetic material and $H$ is the magnetic intensity.
In this case the work is
$$ dW = -HdM.$$
But how do I derive this expression? Or the expression of work for any equation of ... |
I have a question about a passage in Polchinski's textbook [1], regarding the topological term in the Polyakov action.
In the Polyakov action for a closed manifold, we can add a term proportional to the Euler characteristic, which we can write as a local functional using the Gauss-Bonnet theorem:
$$\Delta S_{\text{clos... |
I am trying to understand the covariant/contravariant representation of the divergence in different coordinate systems.
Normally, we would get in the holonomic basis the following divergence according to wikipedia:
$$
\vec{\nabla}\cdot \vec{E} = \frac{1}{\sqrt{det(g)}}{\frac{\partial}{\partial x^i}\left(\sqrt{det(g)}E^... |
This is a common exercise in the classroom. They always check the cases when $E>0$ and $V<E<0$ for a finite negative well $V<0$.
But what about the case $E<V$. What happens here?
|
What is permittivity in an intuitive manner ?
Like is permittivity related to the resistance against charge flow ? or is permittivity related to how easily electric field lines can pass through it ?
And if it is related to how easily field lines pass,and if high permittivity means that electric filed lines can easily p... |
The derivative of four-position with respect to proper time for a light ray is undefined, as light rays move along paths of unchanging proper time. However, would the derivative of four-position with respect to an affine parameter for a light ray be:
$$
\frac{dx^\mu}{d\lambda} = \langle 0, c \rangle
$$
as $\frac{dt}{d\... |
Passive sign convention means choosing an arbitraty current direction, then assuming that current always enters the positive terminal and flows out of the negative terminal of an element. Then the following will hold true: $$ U_R = IR \qquad U_C = \frac{q}{C} \qquad U_L = L \frac{dI}{dt} $$
when we apply the KVL
And th... |
In one hand, Kubo's formula is used in linear response quantum mechanics to obtain response functions (conductivity, magnetic susceptibility, dielectric function) and so on in terms of correlation functions between an operator and the perturbation Hamiltonian (usually autocorrelations like current–current correlations ... |
The equation (62.9) of L.D. Landau's book >, we derive the retard potential
$$\phi=\int\frac{\rho_{t-R/c}}{R}dV+\phi_0$$
$$\mathrm{A}=\int\frac{\mathrm{j}_{t-R/c}}{R}dV+\phi_0$$
But in the next chapter, we derive the Lienard-Wiechert potential for a single particle
$$\phi=\frac{q}{R-\mathrm{v}\cdot\mathrm{R}/c}$$
$$\ma... |
I am writing something for school where I need to calculate the time dilation difference between Earth and Mars. First I calculated the difference from the gravity of the planets itself + that of the sun on the planets. I got 1.73 seconds in 10 years (so 1,73s slower on earth than on mars). A professor checked it for m... |
In Wikipedia, the definition starts in the following way:
"In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a weak pertur... |
From this previous Stackexchange question:
Is a detailed absorption spectrum available for carbon dioxide from 300-1100nm?
and this paper:
https://www.osti.gov/servlets/purl/1613653
as well as this Wiki article: https://en.wikipedia.org/wiki/Absorption_band
I found atmospheric absorption spectra for CO2, H2O, O2+O3, CH... |
If $10\mathrm{\ Nm}$ of torque are applied to a centrifuge with ballast and payload and we assume that the weight of the centrifuge itself is negligible (ignored), then $5\mathrm{\ Nm}$ go to the payload and $5\mathrm{\ Nm}$ go to the ballast for the duration of acceleration or time t-rev. While at speed the payload is... |
I need to study the contents of Fundamentals of Condensed Matter Physics by Cohen & Louie for grad school, but it's not very well written with regards to pedagogically or even logically motivating things (at least compared to Ashcroft & Mermin).
My research is in theoretical/computational solid state physics, so we are... |
Consider an orthonormal set $|\psi_n\rangle$ in the energy basis. Clearly $\langle\psi_n|\psi_m\rangle=\delta_{m,n}$. Does this tell me anything about $\langle\psi_n|\hat{X}|\psi_m\rangle$ or for that matter $|\langle\psi_n|\psi_m\rangle|^2$?
The logical part of my brain is saying no, but the handwavy wavy intuition pa... |
If a disc were rotating without friction or gravity could a force be applied for a time that would cause the disc for a time to rotate around a point other than the center of mass? If so how would the inertia of the more massive side of the new point of rotation affect the motion of the disc?
|
I encountered a problem asking me to calculating the contour integral to evaluate the energy of a vortex as shown in the picture. I am asked to compute the energy using the following equation.
$$E=-\frac{J}{2} n^{2} \operatorname{Re} \oint_{\mathcal{C}} \mathrm{d} z \frac{\arg z}{z},$$
I think I just need to compute th... |
I am a physics bachelor student and currently learning quantum mechanics. In my course we derived the wave function for the hydrogen atom.
I know that the quantum number L is connected with the shape of the orbital but is there a deeper intuitive explanation for that or do I just have to accept that one can just see it... |
As far as I understand, for all practical applications in GR, we would need a way to split space and time. Since, often in practical applications and understanding physical phenomena, lengths and time are quintessential. For eg, in GPS applications, an exact location in space must be given for it to work.
However, at t... |
For a non-relativistic particle of mass $m$ with a conservative force with potential $U$ acting on the particle and a holonomic constraint given by $f(\mathbf{r},t)=0$, the system can be incorporated into the Lagrangian formulation via introducing a variable additionally to the coordinates $\lambda$, called Lagrange mu... |
In hydrogen spectrum if we pass a white light through hydrogen atom it will absorb some radiation, due to which it's electron will get excited. But electron will release energy in the form of radiation again so isn't it possible to get same wavelength of light which was initially absorbed? Also if it is true then many ... |
From what I've read
The temperature of a black hole is measured by the amount of Hawking Radiation emitted.
For a photon to escape, it must travel perfectly perpendicular to the event horizon.
The larger the area of the event horizon, the more mass the black hole has.
What I do not understand is why "the larger the e... |
In any relativistic quantum field theory, we require that the spectrum is bounded from below. The typical explanation is that this condition enforces the stability of the theory. However, to me this intuition necessarily requires the existence of an external system coupled to the field theory in order for a state to co... |
This is a question raised when I was having Physics lesson (high school, not university), we were studying the circular motion of $QvB = {\frac {mv^2}{r}}$ and also straight line path $QvB = QE$. We were curious about what will happen when the charged particle experiences unequal magnetic force and electric force.
Thi... |
The trajectory of a photon in the Schwarzschild metric is given by
$$
\frac{d\phi}{dr} = ±\frac{1}{r^2}\left[ \frac{1}{b^2} - \frac{1}{r^2}\left(1-\frac{2M}{r}\right) \right]^{-1/2}.
$$
This can be solved to give
$$
bu = \sin(\phi-\phi_0) + \frac{M}{b}[1-\cos(\phi-\phi_0)]^2 + O\left(\frac{M^2}{b^2}\right)
$$
where $u=... |
Regarding the following short animation of a merger between a large and small black hole:
https://www.youtube.com/watch?v=Y1M-AbWIlVQ&feature=youtu.be
The colored surfaces are meant to be the horizons (points of no return).
I'm having a hard time understanding the reason for that tunnel that extends between the two mom... |
Here is my problem,
There are two Rooms.
Room 1 that is my living room and Room 2 that is my bedroom.
What I want to achieve, throw all the heat from Room 2 to Room 1, with Room 2 being at higher temperature (warmer) and Room 1 being at lower temperature.
Outside Temperature is lower than both of my room (Room 1 and Ro... |
I am reading Goldstein's Classical Mechanics book; I have difficulty understanding these lines. Why do the last two terms vanish? I am reading this and thinking $r'$ is a null vector, but the second term should also be zero if that is the case. Where I am going wrong? Also, If I make the center of mass as the origin, t... |
Explaining the anomalous progression of Mercurys orbit was one of the first successes of general relativity. Given that a $n$-body problem is not solvable analytically even in the Newtonian picture (I've read about one solution that apparently needs millions of terms per small time step and so is infeasible) and even m... |
A system has a Hamiltonian that depends on a few external parameters $V,X_1,X_2...$.
$$H=H(V,X_1,X_2....).$$
We can assume the dependence is continuous enough. A process is in the limit of infinite slowness when the parameters are changed in a continuous way taking a time that tends to infinity. This is often a definit... |
A cart of weight 400N is pushed up a slope by the resultant force of 50N. The cart moves a distance of 10m. By going up the slope, the change in height of the is 1m. What is the work done against friction up the slope?
The problem above is creating a slight confusion.
We can find the work done up the slope as 500J. Whi... |
When a mass particle is moving along a path $x(t)$ in the presence of conservative force, the energy is conserved, i.e., $\Delta T + \Delta V = 0$, where $T(\dot x)$ is the kinetic energy and $V(x)$ is the potential energy. Is the following straightforward derivation of the Newton’s equation meaningful?
$\Delta T +\Del... |
We have an uniform electric field E in the vertical direction andwe have a rod of superconducting material in the field. Since there is an electric field there will be a current in the material till the field inside the material becomes 0, at which point it stops.
Since the material is superconducting it should not pro... |
I am analyzing this question in the FRW universe with a perfect fluid.
The trace of the energy momentum tensor $$T^{\mu \nu} g_{\mu \nu} = \rho - 3p $$ is of course an invariant quantity. It does, however, in the case of an FRW metric, change with time as the universe expands.
Is it possible to define a quantity such ... |
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