Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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About virtual displacement
Thornton Marion
The varied path represented by $\delta y$ can be thought of physically as a virtual displacement from the actual path consistent with all the forces and constraints (see Figure above).
The varied path $\delta y$, in fact, need not even correspond to a possible path of moti... | Tl;DR: A virtual displacement is by definition frozen in time and hence never corresponds to an actual path of motion.
The other hallmark of a virtual displacement is that it obeys the constraints. For more information, see e.g. this, this, this & this related Phys.SE post.
| {
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Proton Electron Merger Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
| If they are simply falling directly towards each other, they can't combine. To combine, they would need to form a neutron, but a neutron has slightly more mass. The extra mass would have to come from another particle, or source of energy - for example smashing them together forcefully enough.
So as they can't combine, ... | {
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True or False: energy is conserved in all collisions Using introductory physics, how would you answer this question? (I have a disagreement with my instructor and I’m curious to hear your input)
One of us says true because the question doesn’t specify “kinetic energy,” or a “system” and all energy is always conserved. ... | Yes it is conserved, and this does not depend on the course level. The tricky part it can still be transferred to parts of the system that are not the colliding objects.
Energy can escape the system of colliding particles via sound or heat, converted to mechanical work resulting in a permanent deformation of the colli... | {
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What is the difference between circular motion and rotation? I've tried so hard to understand the difference, yet no progress. There is a lot of answers here, on Quora, on Youtube,... but everyone give a different answer.
So can you please give a simple yet satisfactory answer?
Someone says that rotation is only about ... | This is semantics, not physics. Whether you call it “rotation,” “circular motion,” “circular rotation,” “circulation,” “circumambulation,” “rotary motion,” or any other permutation/synonym, the key is to clearly define what you mean. That way, everyone can be clear about the physics, regardless of their semantic opinio... | {
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Addition of velocities vs. Addition of forces Imagine two strings tied to a box.
Case 1: Two strings are pulled with the same $u$ velocity. The box will also move with velocity $u$.
Case 2 : Tension along $\text{a}$ string is $T$. Therefore total force acting on the box is $T+T=2T$. (Box is accelerating)
I think my... | You are walking down the street with your friend. Now you hold hands. Are you now moving twice as fast?
If addition of velocity worked like that, you would get total nonsense. Whenever two moving objects would stick to each other, they would move faster.
Another, more mathematical way of looking at it. The energy of an... | {
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Doubt concerning biot savarts law Why do we calculate $dB$ for an infinitesimal part of a wire instead of a point?What is the reason behind that?Why can't we determine the magnetic field of a point with respect to a point of the wire instead of an infinitesimal part?
Also why is $dB$ proportional to $dl$ where $dl$ is ... | As already mentioned by @Lili FN in the comments, "points" of a wire do not give rise to a magnetic field. But a small length of wire does.
This makes sense intuitively since it's actually the current (density) $\vec{j}(\vec{r})$ that gives rise to a magnetic field $\vec{B}$ (Ampere's Law).
And in the $1d$ case (infini... | {
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Why is the gravitational potential energy lost not subtracted from the required work done in the given problem?
An elastic string of natural length $l \;\text{m}$ is suspended from a fixed point $O$. When a mass of $M \;\text{kg}$ is attached to the other end of the string, its extension is $\frac {l}{10} \;\text{m}$.... | You are 100 percent correct when you say that additional GPE loss got stored in EPE and actually the question requires you to only calculate this change i.e. from initial $l/10$ extension to additional $l/10$ extension.
Just consider the EPE initially for an extension of $l/10$. This will give you a value $Mgl/20 \text... | {
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Why doesn't charge escape from capacitor? A charged spherical capacitor kept in air do not loose charge because air is a bad conductor and increase in charge results in Corona Discharge. Is it because the nucleus of air molecule repels the charge in sphere and after a limit the repulsion is less than the attraction by ... | It does escape - via a quantum tunnelling effect.
| {
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Does gravity get stronger the higher up you are on a mountain? So I saw this article stating that gravity is stronger on the top on the mountain due to there being more mass under you however I have read some questions other people have asked and most of the responses state that the mass is concentrated at the middle o... | If you are a satellite 6870 km above the center of the Earth, and directly below you there is flat land, you will experience some gravity. If you move on to another point, also 6870 km above the center, but this time there is a huge mountain below you, then this time you will feel a gravity which is slightly larger.
If... | {
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In 2D space, how to calculate the direction to hit a moving projectile from a position? Imagine a 2D space. A is where our missile is, and B is where our target is currently moving with a velocity of $v_{2}$. B will come close to A in a certain time and then move away like a comet to earth. Our missile can travel at a ... | If I understood the question correctly, there is a point $\vec A_0$, from which a mass point is launched at time $t_0$ at some constant velocity $\vec v_1$ which should hit another mass point launched from $\vec B_0$ at the same time with velocity $\vec v_2$ and $v_1 := |\vec v_1|$ is known, but not the direction.
The ... | {
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Why does water contract on melting whereas gold, lead, etc. expand on melting? My book mentions that water contracts on melting, but the book doesn't give any reason why it does so. It is mentioned that:
$1\,\mathrm g$ of ice of volume $1.091\,\mathrm{cm}^3$ at $0^\circ\mathrm C$ contracts on melting to become $1\,\ma... | The reason is attributed to the hydrogen bonds that determine the structure of ice. The molecules of water in ice are arranged in a cage-like fashion, with rather hollow spaces in between them, thanks to the hydrogen bonds shown as dotted lines:
When ice melts, the energy supplied helps in breaking these hydrogen bond... | {
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Why does twisting a cork make it easier to remove from a bottle? When we want to remove a cork from a bottle first we turn the cork. Turning in one direction makes it easier to remove in the axial direction.
Does anyone know something more about this?
| Let me take a shot:
The cork has made chemical bonds with the glass. These are the same for all dS of the cork surface: the difference is that in rotating the cork because of the circular motion, a small d(theta) brings the surface unstuck, the resistive forces will not add( different directions). For the axial directi... | {
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How strong is the force of ice expanding when freezing? Why does water contract on melting whereas gold, lead, etc. expand on melting? reminded me about something I've been wondering myself for some time.
We know that water expands as it freezes. The force is quite formidable - it can cause solid steel pipes to rupture... | The other answers are excellent in explaining the theory.
There is a good Youtube video "Can You Stop Water From Expanding When It Freezes Into Ice" showing a practical experiment trying to contain freezing ice in a steel pipe, and then explaining the pressures required to contain freezing ice.
I don't have the reputat... | {
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What's the difference between a perfect fluid and an ideal gas? This is how I understand it at the moment:
*
*A perfect fluid is a collection of non-interacting particles, which are as a whole characterised by energy and pressure.
*An ideal gas is also a collection of non-interacting particles, but here the ideal ga... | Contrarily to the existing answers, and to the citation in one of them, the terminology is not uniform. According to the answer to a previous similar question and to Landau&Lifshitz textbook on Mechanics of Fluids, a perfect fluid is a fluid described by the Euler equation, continuity equation, without viscosity and th... | {
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Why can't the speed of gravitational waves be greater than the speed of light if the universe can expand faster than the speed of light? Since the expansion speed of the universe can be greater than the speed of light, why can't gravitational waves, which also uses space as the medium, travel faster than the speed of l... | Gravitational waves are solutions to the linearized field equations
$\Box h_{\mu \nu} = 0,$
where $\Box$ is the d'Alembertian differential operator.
They are of the form
\begin{align}
h_{\mu \nu}= \text{Re}[H_{\mu \nu} e^{i k_{\rho} x^{\rho}}] ,
\end{align}
where $H_{\mu \nu}$ is just a complex symmetric matrix settin... | {
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Wigner classification of particles vs generic Hamiltonian spectrum Wigner tells us we should associate infinite dimensional unitary irreps of the Poincaré group with particle states. His classification using eigenvectors of the spacetime generators $P^\mu$ and the method of little groups tells us particles are asssocia... | Wigner's classification looks at the quantum numbers that are associated to the Poincaré group. It says nothing about other quantum numbers.
Consider a free theory with a two particle state $|\boldsymbol p_1,\boldsymbol p_2\rangle$. Wigner will tell you that the quantum number associated to the generator of translation... | {
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Path independence and Spherically Symmetric Force
This problem is from John Taylor's Classical Mechanics.
I can't figure out how to prove that a series of paths consisting of paths moving radially or in the angular direction. I understand intuitively that it works, but I'm not sure if I know to prove that the series... | If the path went from A to B in a series of small steps like this
If we focus on one of the steps, the real path in blue can be approximated as a straight line
the work done, against $F$, going from P to R, is $PR\times Fcos\theta$ and this is the same as $F\times PQ$. Since it's true for one of the small steps it'll... | {
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Why do little chips break off so easily from strong neodymium magnets? I have some strong toy neodymium magnets. Typically after a while little chips start breaking off, unlike from most other small metal objects, like in this image.
It could of course be that neodymium is more brittle than metals used for other objec... | Magnetizing a chunk of magnet material induces stresses in the material which are relieved when the material cracks apart. When you combine this with the extreme brittleness of the magnet material, it is natural for the magnet to shed flakes and chips of itself.
| {
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Why ground water is cold during summer and hot during winter? I've heard somewhere that during summer the temperature of ground water is lower than that on the Earth while during winter the temperature of ground water is higher.
How is this possible ?
| Soil is a bad conductor of heat. So, the layers of the top surface of earth act as insulators.
During summer, they insulate the underground water and soil from the heat radiation from the sun, and from the general hotter atmosphere, hence underground water is colder.
In winter, they again act as insulating layer and ... | {
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Two point measurement statistics in Quantum systems I am reading a paper related to fluctuations in Quantum thermodynamics. I am unable to understand the math behind equation no. 10 where the probability density function for work distribution is calculated. I can't understand how delta function is arising in the equati... | The Delta function is constraining energy to be conserved.
The sum is over all transitions $n\rightarrow m$. However, the term $\delta[Q - (E_m - E_n)]$ is picking out only the terms where the heat generated ($Q$) is equal to the energy lost in the transition ($E_m - E_n$).
| {
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How to deduce existence of photons by applying quantum mechanics to Maxwell's equations Watching this video lecture of Peter Higgs https://youtu.be/QtudlGHoBQ8?t=372, he says (roughly) at one point that Paul Dirac applied quantum mechanics to Maxwell's field equations and deduced the existence of photons (previously pr... | Historically, quantum mechanics was first postulated by Planck as a way to solve the ultraviolet catastrophe that arose when trying to apply thermodynamics to electromagnetism. So, it's not so much that we have quantum mechanics and applied it to E&M, we had E&M and statistical mechanics/thermodynamic and the mismatch ... | {
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Missing complex conjugate in (1/2,1/2) representation of Lorentz group Ticciati QFT I've been working through some computations involving representations of the Lorentz group (now using the fantastic Ticciati QFT textbook).
After some work, Ticciati gives the following formula
$$D^{j_{1},j_{2}}(X_{i})=D^{j_{1}}(T_{i})\... | Check the definition of $S$ in Eq. 6.7.1, you can observe first that it is defined using the complex generators for the Lorentz group, $T_r, \bar{T}_r$, which are given before Homework 6.3.9. (where the $X_i$ and $B_i$ are defined), and second that the complex elements $\bar{T}_r$ are sent to $\tau_r$ not $\bar{\tau}$ ... | {
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What are the degrees of freedom of a dumbbell? Edit 1: May be I should modify my question after getting the answers. I see why $(X_c, Y_c, Z_c, \theta, \phi)$ are legitimate Dof's of the dumb-bell, I never had any problem with that.
Please consider now any rigid body in general. It has $6$ Dof's, two examples of which ... | For simplification I will take the 2D space .
The constraint equation is:
$$ \left( x_{{2}}-x_{{1}} \right) ^{2}+ \left( y_{{2}}-y_{{1}} \right) ^
{2}-{L}^{2}
=0\tag 1$$
thus you obtain three generalized coordinates
solving equation (1) for $x_2$
$$x_2=x_1\pm\sqrt{L^2-(y_2-y_1)^2}$$
you get two solution for $x_2$ but t... | {
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Amount of force required it to tip over a cone Say I have a cone of height $h$, radius $r$, and mass $m$.
How can I determine the amount of force required to tip it over (to have it fall completely to the other side), say exerted (horizontally) at the top of the cone? And in addition, how does the position at which I ... | You will need to start by locating the center of gravity (or mass). As the cone tips, that will move up along an arc centered on the tipping point, and the torques will decrease, and reach zero when the center of gravity is over the tipping point. For a minimum driving force, it should be applied at a right angle to th... | {
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Can nothing other than light have speed independent of source? Is it impossible for there to be some phenomenon that travels at a different speed than light to have speed independent of the source? Because if there were such a phenomenon there would be competing formulas for time dilation, correct?
To be clear, this is... | Fundamentally, the speed of light has less to do with light, and more to do with a universal speed limit, which is given by the value of $c$.
Provided an object is massless, it would move at the speed given by $c$, and would meet the criteria that its speed is independent of the motion of source or observer.
Anything w... | {
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Can a metal sheet roof be vibrated at audio frequencies? So I'm renting a cheap place for now due to certain circumstances. Problem is outside noise is excessive because there is no ceiling and the roof is only a metal sheet... Lately I play white noise to get some peace but it's not as effective as I want it to be... ... | Yes, you could make a big surface like your metal roof radiate sound. If it's effective, or how effective, depends on the details such as density, thickness, total area and geometry.
Regarding the cancellation of external noise, I doubt it. Maybe you could add some layers, like a thick curtain, to add disipation for me... | {
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Do the quark types differ from each other in ways other than charge and mass? I've read things online here and there that seemed to hint that there's more to quark type than mass and charge. Is this true?
For clarity's sake, I'm not asking about properties individual quarks have other than mass and charge, such as spin... | Yes, that is true, and well-known.
Quarks come in 6 different families, called flavors: up, down, top, bottom, charm, and strange. Each has a corresponding antiquark family, each of which has the opposite electric charge of the quark family.
Each quark in turn comes in three color charges: red, blue or green, which are... | {
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Question about instant axis of rotation The given question is:
A man is rotating a stone of mass 10 kg tied at the end of a light rope in a circle of radius 1m. To
do this, he continuously moves his hand in a circle of radius 0.6 m. Assume, both circular motions
to be occurring in the same horizontal plane. What is th... | If the motions are in the same horizontal plane, then the 1250 N is the maximum horizontal centripetal force. Knowing this, you can find the corresponding tangential speed.
| {
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How do geodesics explain two identical balls thrown up at the different speeds? As stated in the title, two identical balls, both thrown directly upward, but at different speeds. The slower ball will reverse direction at a lower height than the faster ball. But the curvature of spacetime that they are passing through... | Two worldlines starting at the same event in spacetime but having different velocities are going in different “directions” in spacetime, even if they are going in the same direction in space. So their geodesics are different.
Remember, most worldlines here on Earth are nearly parallel, since they travel at very small f... | {
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Electric field above a ring of charge To find the electric field at a point $p$ which is at a distance $h$ above the center of a ring of total charge $q$ with radius $r$, one can integrate the charge density over the circumference of the ring and get:
$$E = \frac{qh}{4\pi\epsilon_o(r^2+h^2)^{\frac{3}{2}}}$$
Another app... |
Firstly the first method you have shown is correct and the second is wrong .
As you can clearly see in the diagram the force due to each elemental charged particle makes an angle $\theta$ with the axis so the net force is $F\cos\theta$ along the axis due to each particle and the net force due to 2 diametrically oppos... | {
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Why does a fluid follow the wing? When air is moving above and under a wing that is curved, why does the air at the top of the wing follow the wings shape and go downwards when it could just go in a straight line? It doesn't make sense to me.
| When a wing flows through air, if the air strikes the the top surface of the wing, and then moves off in a straight line, there would be lower pressure on the top surface of the wing. For this not to happen, the wind must flow around the surface of the wing.
You can also think about it as if the air above the wing has ... | {
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Are there any quantum mechanical systems where the position vector lives in a finite dimensional Hilbert Space? I don't have much to add to the title. Are there any quantum mechanical systems where the position vector lives in a finite dimensional Hilbert Space? If so, please provide example(s).
| We know that for any system, the position and momentum satisfy the commutation relation
$$[\hat{x},\hat{p}]=i\hbar $$
Take the trace of the both hand side
$$\text{Tr}(\hat{x}\hat{p}-\hat{p}\hat{x})=i\hbar\text{Tr} (I)$$
$$0=i\hbar \text{Tr}\ (I)\ \ !!! $$
It's clear that such a commutation relation can't be satisfied ... | {
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Can we feel heat in outer space? Is there air outside of earth atmosphere? If not, could we feel heat coming from sun?
| We can most definitely feel heat in space.
As @aystack said, on earth heat transfer is through contact, convection or radiation. Convection relies on the movement of air or some other fluid, so that will only work inside a spacecraft or spacesuit. Transfer of heat through contact means that, if you touch something that... | {
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Conservation of Angular Momentum when potential energy is function of position I have read that the angular momentum $(L)$ of a body is conserved if its potential energy is a function of solely its position vector. For example, the motion of planets on their orbits. I have two questions regarding this concept:
*
*How... | Angular momentum is conserved if your system is invariant under any arbitrary rotation.
To prove that angular momentum is conserved, note that if you calculate the force from the potential, the force itself will be parallel to the position vector.
\begin{equation}
\mathbf{F}(\mathbf{r}) = -\mathbf{\nabla} \Phi(r) =- \f... | {
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Will a stone released from an accelerated train retain the velocity the train had at the instant of release? My books says that since the 2nd law is a local relation, when a stone is released from an accelerated train, there is no horizontal force or acceleration on the stone, if air resistance is neglected. The stone ... | Yes, the stone's horizontal velocity (which will match that of the train's when it is thrown) will be conserved, so long as no horizontal force is acting on it.
If the stone is thrown up while the train is accelerating forwards, then an observer in the train will witness the stone appearing to accelerate backwards in t... | {
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How can spacetime be expanding faster than the speed of light? How can spacetime be expanding faster than the speed of light when the speed of light is the speed limit of the universe?
| The speed of light is the speed of causality. It is defined by the geometry of spacetime itself, and every observer will agree on its value (except for experimental issues that may arise when measuring it).
However, when trying to measure velocities between distant observers you must compare vectors (the four-velocity ... | {
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How to predict the photoelectric effect with modern quantum theory? In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. We are told that one can solve the problem by only allowing the light to have d... | The photoelectric effect indicates that either energy levels in matter or light is quantized. Willis Lamb and Marlan Scully authored a relevant paper in 1968, entitled "The Photoelectric Effect without Photons.".
There are several phenomenon, particularly spontaneous emission (which is used in lasers), that require qu... | {
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What is the effect of normal reaction at round corners? Should we consider the case of collision at corners? or it is a kind of circular motion? $A B C D$ is a rhombus shaped tube with rounded corners (Fig). It lies in a vertical plane. A ball is made to roll from $A$ to $B$ to $C$. Next the same ball is made to roll f... | The answer is that the path ADC will be the quicker, because the ball undergoes the higher rate of acceleration first, and therefore completes the DC section at a relatively high speed compared with the speed at which it would have completed the corresponding AB section had it taken the other route.
There is no informa... | {
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Deriving the equivalent capacitance in a series circuit formula When we derive the formula for the effective capacitance in series, we say:
$$Q/C_{eqv} = Q/C_1 + Q/C_2 + Q/C_3$$ (if there were 3 capacitors in this case). We would then cancel $Q$ to obtain the formula.
I understand why each capacitor has the same charge... | Let's imagine a series of three $0.6F$ capacitors, being charged by a $120V$ battery. From this website
Each capacitor will end up with $40V$ across it and a charge of $24C$, from $Q=CV$.
This can happen by charge (electrons) leaving one capacitor, e.g. the right plate of the left capacitor and ending up on the left p... | {
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Issue about rotational and translational kinetic energy of a pendulum Let’s say we have a pendulum that consist of a light string hanging a disk-like object. It is allowed to undergo simple harmonic motion with small oscillations.
My question: Is the energy of the disk pendulum at anytime written as
*
*(a) $$E_\text{... | Using the parallel axis theorem, a disk pendulum that is allowed to rotate around a fixed point with a distance $l$ from it's center, has total rotational kinetic energy $$E= \frac{1}{2}\omega^2(I_{cm}+ml^2)=\frac{1}{2}I_{cm}\omega^2 +\frac{1}{2}m\omega^2l^2$$ and since we can write the angular velocity in terms of the... | {
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Where does pseudo force act at? It is known that, to apply Newton's laws in a non-inertial frame, we use the concept of pseudo force. We also know that force is a bound vector. Hence, is there a general way to determine where the pseudo force vector would be located at?
| Like gravity, pseudoforces apply at all points in a body. In mechanics, when we say that a distributed force "acts" at a single point, we mean that performing such a replacement does not change the torque acting on the body as a whole. Whether this is possible depends on the pseudoforce.
*
*In a uniformly acceleratin... | {
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A bowling ball on an infinitely long track We knew that a after a bowling ball is threw out with a certain velocity to a non smooth track, it first rolls and skids as the translational velocity (decelerates due to friction) of the center of mass is greater than tangential velocity of the point of contact of ball with t... |
How does translational kinetic energy decrease while rotational
kinetic energy is increase by torque due to friction?
Since, you are asking about the situation AFTER rolling without slipping has been achieved, i think it is incorrect to say that rotational KE increases.
Once rolling without slipping has been achieved... | {
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Confusion about friction during pure rolling Friction comes into play with the relative motion between the surface and the points of the body in contact with it. In a perfectly rolling sphere, the instantaneous velocity of the bottommost point is zero, which means there shouldn't be any friction.
But if there is not f... | Zero velocity doesn't mean no friction. The friction acting on a stationary object is called static friction. Friction arises when there is a relative motion or a tendency for the relative motion. So there is a tendency for the relative motion at point of contact in rolling motion. Therefore there is friction, which he... | {
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Do we hear sound at pressure or displacement antinodes? I have read from Young & Geller (2007), College Physics 8th Edition, Pearson Education Inc. (pg 385) that we hear sound at pressure anti-nodes rather than displacement anti-nodes as microphones sense pressure variations.
When we have 2 speakers facing each other ... | If you realise that our ears are pressure sensors you can easily reach the answer that we perceive the sound to be louder at pressure anti-nodes.
One more thing to consider is that no speaker or any other physical system is a good candidate for the idealised (and rather simplified) models used at an introductory textbo... | {
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Is entropy of planets and others bodies proportional to the area? Is entropy of planets and others bodies proportional to the area? If yes, how do I prove that? I know it works for a black hole but, and for others? If no, then the entropy is really proportional to the volume in some cases? I have seen this proportiona... | The total entropy is an integral of the entropy density over the body volume. I do not know if it even makes any sense for planets, though.
Black holes are exotic (thoeretical) objects with non verifiable properties.
| {
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Cauchy sequences through examples in Quantum Mechanics (at the level of the rigor of physicists) I have just read the definition of a Cauchy sequence:
A sequence ($\psi_n$) is a Cauchy sequence in a vector space $V$ when $||\psi_n-\psi_m||\to 0$ when $n,m\to\infty$. The limit of every Cauchy sequence $(\psi_n)$ conver... | The most common way Cauchy sequence appear is as series. For example, if $|0\rangle, |1\rangle, \ldots ,|n\rangle , \ldots$ is an orthonormal sequence and $\sum |a_n|^2 = 1$, we expect $|\psi \rangle = \sum a_n |n\rangle$ to be a well defined state, ie we would like the limit :
$$\lim_{N\to +\infty} \sum_{n=0}^N a_n|n\... | {
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Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies I've never found a rigorous proof of this fact.
The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, then the center of mass spin... | real answer: it uses three facts:
*
*the arbirtrary movement of a rigid can be seen as a translation through any of it's points $P$, whose image is $P'$, and a rotation by some axis passing through $P'$. Valid to any point $P$ on the body. (Chasles theorem)
*the center of mass of a rigid body can be seen as a point... | {
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Internal structure of atomic nuclei When one considers the decay chain of heavy elements, alpha decay forms a significant part of the decay series.
This make me wonder about the internal structure of atomic nuclei. When atomic nuclei are created by fusion is the structure of the two combining elements “scrambled”, or a... | I think yes, because of the high binding energy of alpha particle the matter is clustered inside heavy nuclei. At least there are such models.
You can read about them here:
https://iopscience.iop.org/article/10.1088/1742-6596/111/1/012001/pdf
https://www.ggi.infn.it/talkfiles/slides/talk3742.pdf
| {
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What is the intuition behind the spacetime interval? In an article that I am currently reading (under the Lorentz Invariants sub-heading), it explains that, just as the distance between two points on a Cartesian plane are obviously invariant of the coordinate system, the “spacetime distance” is also invariant. While in... | You have two great answers, but you might find it interesting to know that it was once common for spacetime in SR to be described with an imaginary time axis. That allowed people to consider that it was a straightforward Cartesian arrangement, where the calculation of a length was through the usual Pythagorean method o... | {
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Can we define operators like $\dfrac{1}{a^\dagger a}$? I was recently reading this paper on Enhancement of Few Photon Optomechanical Effects and could not quite understand eq.(2). The author has written an operator like this:
$$\hat \xi=\dfrac{g_oa^\dagger a}{w_m-g_{cK}a^\dagger a}$$
I don't understand how I am suppose... | In general, $\frac{A}{B}$ is lazy physicist shorthand notation for $B^{-1}A$. You might rightly complain that there is an ordering ambiguity and the expression could also mean $A B^{-1}$. That's completely correct, and this notation is only meaningful if $[A,B^{-1}]=0$.
If we take $A=g_o a^\dagger a$ and $B = w_m - g_{... | {
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Newtonian vs Lagrangian symmetry Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the form $x(t) \to x(t) + const$ (we are working in only 1D). However, we cannot see this sym... | Well, it seems to me that under a translation $x(t) \to x(t) + c$, the Lagrangian goes to $$\mathcal{L} \to \mathcal{L}' = \frac{1}{2}m v^2 - mg(x+c) = \mathcal{L} -mgc.$$
So yes, the Lagrangian may appear to be different, however since it only shifts by a constant, these two Lagrangians ($\mathcal{L}$ and $\mathcal{L}... | {
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Do fermions of different types have the same quantum states available to occupy? I'm not asking whether two fermions of different types can occupy the same quantum state, cf. the Pauli exclusion principle. I'm asking whether fermions of different types would have the same options available if you had one in at a time. ... | The difference in the bound states of electrons or muons and a nucleus originates from their different masses (muons are a lot heavier than electrons). Because the Hamiltonian of the problem depends on the mass, the energy eigenvalues do as well.
In general, fermions (or any two particles) will be able to occupy the sa... | {
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Why is the angle between the radial velocities at two instants the same as the angle between the tangential velocities at those same instants?
While it is clear that the angle between $v_r$ and $v_r + \Delta v_r$ is $\Delta \theta$, I cannot see a clear geometric reason as to why the angle between $v_t$ and $v_t + \... | If I'm correct, this is on p37, also this book is a classic, so many people have it, referencing it properly would speed things up.
First, I'm assuming that Vt is the component of velocity tangent to the f(x) that is your objects position, and Vr, well is just radial velocity.
Before diving in, I want you to show how y... | {
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Does relativity mean that the crew of a relativistic rocket would experience less acceleration than in our frame of reference? I have been told regarding a 1 g rocket that "the amount you accelerate would be less due to relativity".
Does that mean that from the crew's time dilated perspective, they would experience les... | If a ship starts from rest in a frame S, $a'$, the acceleration in the rest frame, S', of the crew is related to the acceleration, $a$, in S, by $a'=\gamma^3 a$.
| {
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Confusion over Feynman’s description of the Wu experiment for parity violation In his lecture on symmetry in physical law, Feynman said:
Using a very strong magnet at a very low temperature, it turns out that a certain isotope of cobalt, which disintegrates by emitting an electron, is magnetic, and if the temperature ... | The electron charge is negative, so the magnetic moment is anti-aligned with the spin.
| {
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Why do icebergs flip over? Why do icebergs flip over? Are certain shapes of icebergs more "stable" than others, in that it's harder to flip them over? If so, why?
For example, it somehow makes intuitive sense, that a thick iceberg with a certain height (or depth, because 90% of it is below water) would be harder to fli... | I really don't know if this will answer your question but you have to take into account the forces acting over the iceberg. You have pressure from the sea stream, buoyancy from the Archimedes principle, pressure from wind, and weight from gravity acceleration.
Then, why would something flip? For something to flip you m... | {
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Am trying to determine the source of a low level, low pitched "rumbling" noise that appears to only be heard inside houses in our road, any thoughts? I live in the Olton area within the UK. The noise can be briefly intermittent or continuous for hours and can only be heard indoors - louder at night. One neighbour has r... | Arthur,
High frequency sound get absorbed more quickly in dense material than low frequency sound. The fact that the noise is low frequency and can only be heard indoors suggest that it's travelled some distance underground.
However the distance could be small e.g. 10m or many km if the source is loud enough.
You've a... | {
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Simplest exactly solved model displaying a phase transition? The classical example of an exactly solved model which displays a phase transition is the 2D Ising model. However, all the proofs I've seen of this have been very long and complicated.
So, I wanted to know whether there were any other exactly solved models wi... | Exactly solvable models in Statistical mechanics by Baxter is the place to look.
The other answers have already pointed the infinite range Ising model and 1D Ising model as exactly solvable (although the latter has phase transition at zero temperature). Besides the infinite and the 1D case, the Ising (and more generall... | {
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How are these two expressions for the canonical partition function equivalent? In Equilibrium Statistical Physics by Plischke and Bergersen the canonical partition function is defined (on page 37, eq. (2.33)) as
$$Z_C = \int \frac{dE}{\delta E} \Omega(E) \exp\{-\beta E\}\tag{1},$$
where $\Omega(E)$ is the accessible ph... | (2) is the canonical partition function of a classical system of $N$ particles with Hamiltonian H. The Boltzmann weight is integrated over the $6N$-dimensional phase space $(q_i,p_i)$. This integral can be cast in the form of (1) by introducing
$$\Omega(E)={1\over h_0^3}\int d^{3N}q\int d^{3N}p\ \!\delta(E-H(q,p))$$
wh... | {
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... | Here is my favorite view of what a person in the car would observe. I don't see it represented very often, for some reason.
By the equivalence principles (that e.g. general relativity builds on), the moment the car engine starts applying torque to the wheels, a person inside the car will feel a change in gravity. It wi... | {
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Find the values of $A$, $B$, and $C$ such that the action is a minimum
A particle is subjected to the potential $V (x) = −F x$, where $F$ is a constant. The particle travels from $x = 0$ to $x = a$ in a time interval $t_0 $. Assume the motion of the particle can be expressed in the form $x(t) = A + B t + C t^2$. Find ... | The Euler-lagrangian equation gives the equations of motion that once solved give you a family of solutions that minimize the action. A unique solution is given by specifying boundary conditions. It is just a case of inputing those boundary conditions.
Wlog let $ x(0)=0 $ and $x(t_0)=a $. Integrating $\ddot{x} = \frac{... | {
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How to obtain position data from acceleration without forward euler? I am doing a investigation into the Wilberforce Pendulum and in order to find the position and rotation at any time I have attached my phone onto the pendulum in order to use Phyphox, a app that finds the acceleration and angular velocity. However, wh... | Since you already have the data you just need a numeric integrator which inherently smooths the data. But if you use a forward Euler, then you are biasing the smoothing (averaging) to previous values causing a bias in the results.
I have been down the road you are going through and here are my suggestions
*
*Use the ... | {
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Why and when can the Earth be considered an inertial reference frame? The question has been asked (e.g., here and here), but I would like to get a more definitive and mathematically formal answer.
The Earth rotates around its axis, around the Sun, and participates in larger scale motions as a part of the Solar system. ... | Motion near the Earth is basically inertial if an object is not being "pushed" by anything! If you throw a stone it is in inertial motion (apart from air resistance) until it hits the ground.
Motion of the Earth around the Solar System, Galaxy etc. is irrelevant if you are not being pushed, and is completely dominant ... | {
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Mandl & Shaw QFT chapter 1 question Page 3 of Mandl & Shaw claims that, given a vector $\pmb{A}(\pmb{x},t)=\pmb{A}_{0}e^{i(\pmb{k}\pmb{\cdot} \pmb{x} - \omega t)}$, $\pmb{\nabla} \pmb{\cdot} \pmb{A} = 0$ (eq. 1.6) implies $\pmb{k} \pmb{\cdot}
\pmb{A} = 0$ (eq. 1.7).
I'm having trouble figuring out why (1.6) implies (1.... | You can just take the derivative of the exponential. In particular:
$$
\vec{\nabla}\cdot \vec{A}(t,\vec{x})=\vec{A}_0 \cdot \vec{\nabla} e^{i(\vec{k}\cdot\vec{x}-\omega t)} = i \vec{k}\cdot\vec{A}_0e^{i(\vec{k}\cdot\vec{x}-\omega t)} = i \vec{k}\cdot\vec{A}(t,\vec{x}) = 0\,.
$$
There you go!
| {
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Bar released from upright position rotates about a lower hinge before being caught by a steel cable, how to calculate the tension on the cable? I wish to check the safety factor of a steel cable that I've designed to catch a heavy bar that rotates freely due to the gravitational force acting on it.
From the upright pos... | The cable will exert an impulse which changes the bar's angular momentum. The maximum force will depend on how much the cable can stretch. Treating it like a spring (with a high k) is not unreasonable (but measuring the k could be a problem), and there is likely to some bounce.
| {
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Spin without quantum mechanics? In Emergence of spin from special relativity some answers discuss how spin can arise in non-relativistic quantum mechanics (let's not enter into those details here). However it is also argued that you do not even need quantum mechanics as there are some relativistic constructions.
Roger ... | In general relativity textbooks, it will be mentioned that general covariance can be achieved easily if the equations are tensorial. But tensor equations are not the only equations that have general covariance. Spinor equations also satisfy general covariance. In curved spacetime, spinors are defined using fiber bundle... | {
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"url": "https://physics.stackexchange.com/questions/665371",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Riemann curvature tensor is the only tensor that you can write down that has two derivatives of the metric tensor Is the statement in the main question correct? Can someone send me a proof (link, pdf file etc.)
| You can prove this by moving to Riemann normal coordinates at a point $p$. In these coordinates
$$
g_{ij}(p) = \eta_{ij} , \qquad \partial_k g_{ij}(p) = 0 , \qquad \partial_k \partial_l g_{ij}(p) = \frac{1}{3} [ R_{ikjl}(p) + R_{jkil}(p) ] .
$$
It is then clear that anything that contains 2 metric derivatives can be r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/665496",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Mechanism of Relativistic Momentum The formula for relativistic momentum is $\vec{p}=\gamma m\vec{v}$.
To derive this formula, one analyzes a collision while assuming the principle of relativity and the conservation of momentum principle are correct:
https://www.feynmanlectures.caltech.edu/I_16.html
I'm fine with all t... | Using your arm to accelerate a block of iron 1: to low speed 2: to high speed:
Low speed: afterwards iron atoms have gained momentum
High speed: afterwards iron atoms and fat molecules have gained momentum (there also occurs a conversion of fat molecules to something else)
Extreme speed case: before the acceleration yo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How come black body have more emissivity and more absorbtivity(a) at same time? We have two definitions to look at
Absorbtivity(a): the ratio of absorbed energy and incident energy on a body
$a_{BlackBody} = 1$
so if i have a tourch light that gives red light, in a dark room I point this tourch light at this black bod... | The light that the black body emits is defined by the temperature of that body. When you shine red torchlight and the body is cold, it will still look black, but as it heats up, it may start glowing red. It still will formally be called a "black body" though, since the term is reserved for a body that absorbs all the l... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Eigenvalues of Product of 2 hermitian operators Let $A$ and $B$ be two Hermitian operators. Let $C$ be another operator such that $C = AB$. What can we say about Eigenvalues of $C$? Will they be real/imaginary/complex? What I did was to search for examples. The following were examples (in matrix representation) I looke... | TL;DR: Assuming that $A,B$ are self-adjoint, the product $AB$ does not need to be diagonalizable. And if $AB$ is diagonalizable, the eigenvalues need not be real or imaginary.
Example 1: $AB$ is not diagonalizable:
$$A~=~\begin{pmatrix} 0 & 1 \cr 1 & 0 \end{pmatrix} \quad\wedge\quad B~=~\begin{pmatrix} 1 & 0 \cr 0 & 0 ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In freestyle swimming does flutter kick recovery causes sinking? As per my understanding in flutter kick, we kick downwards and the water pushes the swimmer up. However, in flutter kick the swimmer is also actually kicking the water upwards when recovering from the kick. We can contrast this with a dolphin kick where s... | The propulsion required to move forward is created by rhythmic upward and downward movement of the legs.To answer your question ,when one leg moves up the other leg goes down hence being unable to cancel the forces.In detail there are two phases of one flutter and its recovery.
Downbeat:-
In the first half of the downb... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Confusion about Newton's third law The question:
A toy rocket consists of a container of water and compressed air.Water is pushed vertically downwards through a nozzle by the compressed air. The rocket moves vertically upwards. The nozzle has a circular cross-section of radius 7.5mm. The density of the water is 1000kg... | In this simple model for a rocket of mass M you have a constant mass flow $\dot{M}$ (i.e. the mass of the water that leaves the rocket per second) away from the rocket which you can calculate with the data given in the exercise. The matter that leaves the rocket is assumed to have a velocity $v$ relative to the rocket.... | {
"language": "en",
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"source": "stackexchange",
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If the probability of a point (photon) hitting another point (electron) is zero why do they collide? If the probability of a point (photon) hitting another point (electron) is zero why do they collide? To have a probability greater than zero almost one of them should be not a point. Correct me, please if I am wrong.
| The photon interacts with the electron, but it does not collide with it.
You can think of an electron as having a cloud of virtual particles, which are basically excitations in the quantum EM field. The quanta of this field are called photons
Take for example, this simple interaction between 2 electrons:
As shown wit... | {
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"source": "stackexchange",
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Provided a unit vector and Force, how can I calculate it's components? Say I have a $F=kQ_{1}Q_{2}/r^{2}$ and a direction vector $(x, y, z).$ How can I find the component forces $F_{x}$, $F_{y}$, and $F_{z}$?
| It's somewhat unclear from your question, but I interpreted $F$ to be just the magnitude of the force (a scalar), and you want to construct a force of that magnitude pointing along the given direction vector.
If the direction vector is a unit vector (a vector of length 1), then all you have to do is scale (resize) it. ... | {
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Why the photomultiplier experiment proves that photon is a particle, not a wave? In QED Feynman describes the photomultiplier experiment as a proof that a photon behaves as a particle. The logic is as follows: with monochromatic single photon light source a photomultiplier coupled with a speaker is either silent or res... | Term photomultiplier refers more to the principle of detection than to what we count, which is the central point of the question here. In this respect it is better to differentiate between a single-photon detector and a photon counter, which are doing somewhat different job (although the former is usually a part of the... | {
"language": "en",
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How seriously can we take the success of the Standard Model when it has so many input parameters? The Standard Model of particle physics is immensely successful. However, it has many experimentally fitted input parameters (e.g. the fermion masses, mixing angles, etc). How seriously can we take the success of the Standa... | If you have $n$ input parameters in a deterministic theory you can perfectly fit at most $n$ data points just by adjusting those parameters. In a probabalistic theory that is more subtle, but there is a similar association. Regardless of how many parameters the standard model needs, it is a lot less than what would be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/667948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
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Where should the reference point be considered during torque measurement? This is an extremely silly and wierd question.
https://en.wikipedia.org/wiki/Varignon%27s_theorem_(mechanics)
While reading about Varignon's Theorem in wikipedia I noticed this sentence,
"If many concurrent forces are acting on a body, then the... | In general, the sum of vectors gives their resultant. But, for that to be true they must be similar and related: the sum of electric fields at a point, the sum of forces acting on a mass, and the sum of torques about a point. In the case of torques, the sum produces the rate of change of the angular momentum measured ... | {
"language": "en",
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"source": "stackexchange",
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Can we bend a light ray into any closed loop? Suppose we have a medium with varying refractive index and a source of light inside that medium emitting rays. Is it possible to bend the ray into any closed loop?
As the medium has varying refractive index, is it possible?
And if possible, how will it look like if anyone s... | I think so, and not just only loops but also knots. Any optic cable tied into a loop or a knot will probably do. It's easy to imagine theoretically, but probably much more difficult to set up practically as there is the problem of getting the light into the loop into the first place.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
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"answer_id": 0
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Do electromagnetic waves contain electrons? I understand that EM waves are oscillating electric and magnetic fields. But doesn't this mean that the wave itself contains charged particles that generate the fields?
| Every body above zero Kelvin emits photons. Electromagnetic radiation is the sum of all photons emitted by excited subatomic particles. It is basically thermal radiation.
Electromagnetic waves are a special form of EM radiation. The synchronous and periodic acceleration of electrons on the surface of a conductor result... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mixed symmetry of rank $3$ tensor I have rank 3 tensor $T_{ijk}$ with following properties:
$T_{ijk}=T_{jik}$
$T_{ijk}=-T_{kji}$
Is it true that there is the only one tensor of rank 3 with those properties and it is $T_{ijk}=0$.
I'm starting from the following
$T_{ijk}=-T_{kij}=-T_{ikj}=T_{jki}=T_{kji}=-T_{ijk}$
$\Righ... | The question and accepted answer here miss the main point, which is that for tensors of mixed symmetry, the indices themselves do not obey that symmetry, which is somewhat counterintuitive. This is explained in the comments by Michael Seifert here.
Tensors of mixed symmetry are generated by applying Young symmetrizers.... | {
"language": "en",
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Is pulling a string instantaneous at both ends? Why is it or isn't it? This is a question that has bothered me for quite some time but I don't have a clue where to start in researching it.
Let's say we have a string which is arbitrarily long, light enough to not take much effort to pull but rigid enough that it would n... | No. When you pull really fast on one end of the string, that pull gets transmitted along its length to the other end at the speed of sound waves in the string. This may be several thousand feet per second, but is nowhere near the speed of light.
| {
"language": "en",
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Why do rain drops fall with a constant velocity? While reading my physics book. I came across a line that says that:
Rain drop falls with a constant velocity because the weight(which is the force of gravity acting on body) of the drop is balanced by the sum of the buoyant force and force due to friction(or viscosity ... | For intuition, think of curling (except the rain falls down, curling stones move horizontally). Once the stone is released, there are no horizontal forces on the stone (except a slight friction) yet it moves at a roughly constant speed (the slight friction slows it down over time). The player first accelerates the ston... | {
"language": "en",
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"source": "stackexchange",
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Would a pressurized container move by itself if opposite edges have different size surface area? If inside a closed container there is gas with higher pressure than outside the container, and one edge of the container has a larger surface area than the opposite side, would the container move by itself? Wouldn't there b... | Unfortunately, your thinking is not correct. If we treat the whole box as a system, then box will move if and only if $\sum F_{ext}\neq0$.
However in your setup, it's shown that internal pressure (or intenral forces) is somehow moving the box, which cannot be possible. The internal forces must cancel each other out in ... | {
"language": "en",
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Eccentricity of planets based on distance from Sun Are the orbits of inner-solar system planets more circular than outer planets? Or is it the other way around? What's the reason for this? We were taught in our high school Physics class that outer planets had more circular orbits, but some sources online and even on SE... | The degree to which an orbit deviates from a perfect circle is measured by its orbital eccentricity. An eccentricity of $0$ is a perfect circle; an ellipse has an eccentricity between $0$ and $1$ - the higher the eccentricity, the more "elliptical" the ellipse becomes; an eccentricity of $1$ is an open parabolic orbit ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Inverse Laplacian I have seen the following operator somewhere in a paper on cosmology
$$
\frac{\partial_i \partial_j}{\nabla^2} - \frac{1}{3} \delta_{ij}.
$$
What is the definition of the inverse Laplacian? What is meant by this misleading notation? Is this the inverse Laplacian? If yes, what is then $\frac{1}{\nabla^... | Let's write an arbitrary function $f:\,\Bbb R^3\mapsto\Bbb R$ as a Fourier transform:$$f(\vec{r})=(2\pi)^{-3/2}\int_{\Bbb R^3}\tilde{f}(\vec{k})e^{i\vec{k}\cdot\vec{r}}d^3\vec{k},\,f(\vec{k}):=(2\pi)^{-3/2}\int_{\Bbb R^3}f(\vec{r})e^{-i\vec{k}\cdot\vec{r}}d^3\vec{r}.$$(I've restricted to a $3$-dimensional space because... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Sustaining a current in conductor placed in external electric field Consider the following arrangement-
We have a conducting sphere and a positively charged infinite sheet on the left. The field creates induced charges and the net electric field inside the conductor is zero after a very short time. During this short ti... | There is really not much to add to the comments. Why are the charges separated on the two sides of the sphere? because there is an electric field that pushes the negative charges to the left and the positive to the right, right? This field is produced by the charge on that infinite sheet. This field exists not only in ... | {
"language": "en",
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Which topological orders described by TQFT and tensor category theories are not known to be microscopically realizable? Topological order refers to long-range-entangled phases of matter that cannot be smoothly deformed into ordinary phases characterized by Landau’s symmetry breaking theory. A large number of topologica... | Any (2+1)-D TQFTs described by a unitary modular tensor category can be realized as the boundary of a Walker-Wang model. Moreover it is believed that any such Walker-Wang model is trivial in the bulk; hence there should exist a bulk disentangling unitary. Applying this unitary will give you a microscopic 2D lattice Ham... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Graph for Coulomb Force vs $1/r$ My teacher told me that the graph for the coulomb force $F$ vs $1/r$ where $r$ is the distance between the 2 charges should be parabolic but I can't seem to understand why. I am aware that equations of the form $y^2=4ax$ are parabolic but why should $F$ vs $1/r$ graph be parabolic?
| You are right that functions like $y = ax^2$ have a parabolic graph of $y$ vs $x$.
The force between two charges is
$$F = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$$
So the graph of $F$ vs $r$ is not parabolic. But you are not graphing that.
You are graphing $F$ vs $1/r$. You can see how the equations can be made to b... | {
"language": "en",
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Does "lifetime of up quark" have a physical meaning? I saw this question about the lifetime of an up quark.
As far as I know, free quarks are never observed in experiments. Then what is the significance of a statement like "the lifetime of an up quark is X units"?
I am looking for a physical explanation without involvi... | No, "lifetime of an up quark" is utterly meaningless (at least here, but I'd be hard pressed to find legitimate contexts for it...).
The lifetime discussed is that of a neutral pion, decaying by the F diagram (sorry)
In words, the pion "resolves" to virtual states of its valence quarks, u or d, which then couple to t... | {
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Why can basis vectors change direction? I thought that basis vectors were of magnitude one and located at the origin and were each linearly independent, so how in things like polar coordinates can the basis vectors be moving?
| "Coordinates" is a more general term that "basis vectors". Basis vectors apply only to vector spaces, while coordinates apply to any manifold (and, if one uses the term loosely enough, pretty much any space). Basis vectors provide a coordinate system by simply taking their coefficients, but not all coordinate systems c... | {
"language": "en",
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Could a non-photon massless particle travel at a speed other than $c$? The speed of light is given as $c=\frac{1}{\sqrt{ε_0μ_0}}$ which is in terms of the electric and magnetic constants.
Hypothetically, another massless particle could exist which does not interact with the electronic or magnetic fields. Postulate that... | In special relativity, the relativistic factor
$$
\gamma = \frac1{\sqrt{1-v^2/c^2}} = \frac{E_\text{total}}{mc^2}
$$
is just as closely related to the particle’s total energy as to the particle’s speed. Any object whose total energy is very much larger than its rest mass will be traveling near $c$. Objects whose rest m... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do metallic objects reflect radar? We learn that EM waves cause the electrons in a conductor to move around. For example, air to ground radar shows the ocean as having few returns compared to land. Water molecules absorb the energy. Doesn't the induced motion of electrons in the metal in chaotic eddy currents dissi... | Because metals are electrically conductive, an incoming radar pulse induces a current to flow in the surface of the metal. That current flow then radiates a replica of the original wave, moving in the opposite direction.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/671181",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why I feel cool in a region with lot of trees inspite of humidity by transporation? Today I went for a walk and entered a region with lot of trees, It feel a sudden chill, a cool feeling (comparatively)
Why, Although trees perform transpiration that cause moisture so we should feel warm but I feel cool?
| Trees draw liquid water from the ground and transport it to the leaves. This water then evaporates through the process of transpiration. Turning liquid water into water vapor requires a significant amount of energy due to water's high latent heat of vaporization. The process of transpiration absorbs heat energy from th... | {
"language": "en",
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Is the intensity of light dependent on number of photons per unit area? I was learning about the photoelectric effect of light and there it says more the intensity of light, the more number of electrons will be ejected from the metal surface given that the frequency of light is more than its threshold frequency.
Now wh... | Yes
light ray X will have more photons falling on that area dA as compared to light ray Y
(per second).
The energy of each photon depends on its frequency from $E=hf$.
If $X$ and $Y$ have the same frequency, then more photons per second are falling on the area, from light $X$.
This matches with the classical definiti... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pauli exclusion principle and antimatter Have the Pauli exclusion principle been proven to apply to antimatter experimentally?
| While CERN has created anti-hydrogen, there has never been a synthesized multi-antielectron anti-atom. So there has never been a large enough anti-atom (antinucleons with antielectrons) to experimentally test the PEP for antimatter.
But the Pauli exclusion principle applies to all spin $\frac{1}{2}$ particles (all ferm... | {
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"url": "https://physics.stackexchange.com/questions/671864",
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Pipe Open or closed from a Standing Wave Equation Here is the full question:
The part in the brackets are the answers. I am still terribly confused.
Lets say we are given an equation for a standing wave in a pipe:
$$y(x,t) = A\sin\left(\frac{3\pi x}{L}\right)\sin(\omega t).$$
Is this enough information to know whether... | The question in isolation is not well posed for a single answer; in fact, there are an infinite number of "correct" answers that could be given. Further information could be provided (or assumed by the questioner) that would lead to a particular solution.
Analysis
First, I will assume that $y$ denotes the particle di... | {
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Intuition for Stress and the Cauchy Stress Tensor I'm struggling to get an intuitive understanding of what exactly Stress is, particularly the "direction" associated with it.
In the case of a 1 dimensional bar with just uniaxial loading, the way stress was explained to me was just $\pm\frac{F}{A}$ where $F$ is the forc... |
Do each of the components describe the stress on the surfaces of some
infinitesimal volume?
Essentially, yes.
If so, which faces do they describe (there are 2faces normal to each direction)- is it the sum of the stresses on each
face?
The assumption is the volume is in equilibrium, both translational and rotational... | {
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Confused about the Pauli exclusion principle I've been struggling to understand this: Let's say I have a gas of one million electrons. Does every single one of those electrons have a different energy (up to the degeneracy from the different momentum components)?
| The Pauli principle was derived from observations of the electrons of atoms. It expresses that two electrons with the same level in the atom are distinguishable. By an external magnetic field the orientations of the spin can be manipulated.
So for an electron gas it is possible to align the electrons a bit in the direc... | {
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Matrix element and Dirac notation If
$$
T=
\left[
\begin{array}{cccc}
e^{\beta J} & e^{-\beta J} \\
e^{-\beta J} & e^{\beta J} \\
\end{array} \right]
$$
and
$$Z = \sum_{S_i=\pm 1} ... \sum_{S_N=\pm 1} \exp{\beta J(\vec{S_1}\vec{S_2}+\vec{S_2}\vec{S_3}+...+\vec{S_{N-1}}\vec{S_N}+\vec{S_N}\vec{S_1})}
$$
Then why c... | Because, with $S_i$ taking values $\pm 1$, we have
$$
\langle S_1|e^{\beta J {S}_i {S}_{i+1}}| S_2\rangle=
\left[\matrix{e^{\beta J}& e^{-\beta J} \cr e^{-\beta J} &e^{\beta J}}\right]_{S_1,S_2}
$$
where the subscript on the matrix means the appropriate matrix entry.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672697",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Confusion on molecular dynamics (MD) simulation units leading to absurd acceleration values I am trying to code up a very simple MD simulation in order to learn more about it. I am using the Leonard-Jones potential, expressed as $ V=4\epsilon (\frac{\sigma}{r}^{12}-\frac{\sigma}{r}^{6}) $
The pairwise force is therefor... | Maybe your numerical solver is instable.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/672820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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