Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Does the path of the centre of mass of two planets in a solar system change before and after collision? Does the centre of mass of two planets keep following the same course before and after a collision of two planets in a solar system?
Is it possible to use conservation of linear momentum even though there is an exter... | Lots and none at all and what did your own calcs show?
Until they collide, no two bodies share either a centre of mass or a path, except by irrelevant co-incidence. To suggest they did would bring us perilously close to the three-body problem…
Consider two billiard balls and first, explain how it matters whether both, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691684",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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"answer_id": 4
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Is kinetic energy relative or absolute? I only can think of kinetic energy as absolute. I know velocity is relative but I can't see kinetic energy as being relative because that would violate energy conservation. For example, if in some reference frame, the loss of kinetic energy is $60\mathrm{\ J}$, how can, in anothe... | The confusion may be a result of a very common misconception about the conservation of energy:
People often think that the energy conservation states that potential energy equals kinetic energy ($E_{\mathrm{kin}} = E_{\mathrm{pot}}$).
But this is only a special case, where the reference frame and the reference point fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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A planet with a square orbit? To understand how gravity influence objects, time and space, I have been thinking of how a planets shape would change the orbits of its moons.
More specifically: can I design a planet whose moon move in a square orbit?
Below is a diagram of my first intuitive try. For simplicity I imagine ... | If you just want a body to have a stable-ish square path relative to a parent system's barycenter, this can easily be done with a retrograde orbit. Illustration of concept:
I drew this as a planet in a binary star system, but it doesn't necessarily have to be— Be warned that the body the green planet or moon is orbiti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692338",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "55",
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Is the time interval between two events at different points in the same rest frame the proper time? For example, if an observer in the rest frame of a room measures an explosion on one side of the room and then at a time $\Delta t$ later observes another explosion on the opposite side of the room, is this time interval... | Suppose we have two events $(t_1, x_1)$ and $(t_2, x_2)$, where $t$ denotes the time the event happened and $x$ denotes the place the event happened, then the proper time, $\tau$, between the points is given by:
$$ c^2 \tau^2 = c^2 (t_1 - t_2)^2 - (x_1 - x_2)^2 $$
It is convenient to write $\Delta t = t_1 - t_2$ and $\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692537",
"timestamp": "2023-03-29T00:00:00",
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Do perpendicular lights interfere on a surface? In the following experiment, we have an observer looking at a material illuminated by a light.
Imagine that the lights are similar to a laser (coherent?) so that all of the photons follow the direction of the coloured lines, and the observers have to be in the correct pla... | Ok here is an advanced explanation but it is fairly easy to follow. Firstly the word "interference" is from like 200 years ago but we still use it today because it is very good at getting across the basics. In truth 2 photons never interfere with each other or cancel as that would be violation of conservation of ener... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692673",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Resistance-capacitance (RC) circuit
My textbook says: "This continues until the voltage across the capacitor matches the emf of the battery"
If I were to have a resistor in series with a capacitor, would the voltage across the capacitor still be equal to the emf of the battery?
My thinking process: The voltage across ... |
My question: If I were to have a resistor in series with a capacitor,
would the voltage across the capacitor still be equal to the emf of
the battery?
In an ideal circuit theory context, the answer is no except in the trivial case that the initial condition is just that.
That is, for the ideal RC circuit drawn, the v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/692950",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Speed of heat through an object According to the Heat equation (the PDE), heat can travel infinitely fast, which doesn't seem right to me. So I was wondering, at what speed does heat actually propogate through an object?
For example, if I have a really long iron rod at a constant temperature (say 0 Celsius), and one en... | Here it is with no math:
Heat in a solid is not transferred at infinite speed, it diffuses through the solid the way that the molecules in a spoon of sugar syrup diffuse slowly into an unmixed drink. This is a relatively slow process and there are equations you can use to solve for the amount of time it takes for heat ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693112",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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$I$ proportional to $V$ or vice versa? I am confused whether Voltage depends on current or the vice versa. I always thought that the vice versa was correct. I tried to find the answers of some of my other conceptual doubts on the web but I was not able to understand the answers as people were saying things beyond schoo... | Ohm's law, like many (most?) physical laws, does not involve the idea of cause and effect.
I admit that I usually think of V as causing I, but an electronics engineer might put a resistor in a current-carrying circuit in order to produce a pd which can be applied across (say) a voltmeter. The current causes a voltage d... | {
"language": "en",
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Casimir effect without a quantum field outside of the plates? In the usual example of the Casimir effect we have two metal plates seperated by some small distance and a quantum field that lives both outside and inside of these plates. The boundary condition for the field inside constraints the allowed modes and thus al... | My best guess (please correct me if I'm wrong, I'm just learning):
If the absolute value (not relative to in-between the plates) of the quantum field energy outside the two plates can be assumed to be zero, then a net outward force would be exerted on the plates via the Casimir effect.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693349",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Finding deflection of an electron through 2 charged plates when given initial velocity I've been trying to relate the initial velocity of an electron to the deflection created based on the electric field between 1 pair of plates. The 2nd half of page 3 of this pdf is what I'm concerned with. Now, I was trying to derive... | What you did here was take the time that the charge moves from start of the plate to the end of it, which you had as $\frac{L}{v_x}$ But the the time of flight of the electron to the screen is $\frac{L+D}{v_x}$ because $v_x$ stays the same from the point where the electron is released until it reaches the screen (not ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/693502",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Magnet A exerts an magnetic force $F_1$ on magnet B, B exerts a Reactive force $R_1$ on A, B exerts an magnetic force $F_2$ on A, is $R_1=F_2$? Let's suppose there are 2 magnets, A and B, that are within the magnetic field of each other. Then A will exert a magnetic force on B (let's name it F1), and, due to the 3rd la... | A nontrivial result from electromagnetism is that the electromagnetic field carries energy, momentum, and angular momentum. So it’s possible to construct a system where Newton’s Third Law is violated if you consider only the forces on the magnets themselves.
In practice the momentum carried by the electromagnetic fiel... | {
"language": "en",
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What would happen if you left Earth and then it was destroyed? (Potential energy and thermodynamics) So I did some research on magnetic generators and what kind of energy magnets loose when they move something. Turns out magnets loose potential energy (you need to expend energy to get the object moved closer to or furt... | "Deleted" and "blew up" are not the same thing. If you could cause the Earth to explode into a symmetrical, expanding cloud of countless billions of fragments (i.e., if you "blew it up,") then that cloud still would have the same mass as the original Earth, and it still would have the same center of mass. So long as yo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694021",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If force depends only on mass and acceleration, how come faster objects deal more damage? As we know from Newton's law, we have that $\mathbf{F} = m\cdot\mathbf{a}$. This means that as long as the mass stays constant, force depends solely on acceleration. But how does this agree with what we can observe in our day-to-d... | The force we care about is not the force of gravity, but the force between the coin and the persons head.
If the coin and the persons head were both rigid bodies, then the force involved would be infinite. That is clearly unrealistic though.
In reality neither the coin nor the persons head is able to remain rigid in th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694736",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Time constant versus half-life — when to use which? In some systems we use half-life (like in radioactivity) which gives us time until a quantity changes by 50% — while in other instances (like in RC circuits) we use time constants. In both cases the rate of change of a variable over time is proportional to the instan... | I think the main reason why time constants are used in the first place is that this causes the least probability of nuisance constants in calculations. It is the same reason why $\exp(x)$ is more popular than $2^x=\exp(x\ln 2)$: if you derive the latter (which is done very often), you get the natural logarithm of 2 cre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/694850",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Differential equation of the free falling object with air resistance I'm puzzled by the result I get when I try to solve the differential equation for an object that is falling subject to air resistance. Suppose the $y$-axis is directed upwards, then $\vec{F_a}=bv \hat{y}$ and $\vec{P}=-mg\hat{y}$, where $b,v, g$ are p... | You have missed a minus sign: Your velocity is the downward velocity ($\vec v =−v\hat y$), so there is an extra minus sign on the lhs of your differnetial equation. Then, you get $v(t)=mgb(1−e−bt/m)$ as expected.
In general, you can write $\vec v= v_x \hat x +v_y \hat y$) and solve the equation of motion ($m\dot{\vec v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695003",
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On Bell's Spaceship Paradox I am facing trouble in understanding Bell's Spaceship Paradox.
I understand the explanation for the rope breaking in the stationary observer's frame well. I do not understand how to explain it with respect to the spaceships.
One of the explanations I read involved the idea that leading cloc... | Let's say the spaceships use bombs to accelerate. Front ship detonates one bomb every hour, measured by a local clock,rear ship does the same.
Now we can see that in the ships' frame:
*
*Delta v caused by one explosion is same for both ships according to the crew. (except when the ships have gained a very large speed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695511",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How are sidebands generated in an AM signal? I can't understand how sidebands get generated, even after reading this wikipedia page: https://en.wikipedia.org/wiki/Sideband#Amplitude_modulation
This is how I picture Amplitude Modulation in its simplest form.
There is a LC circuit. A an inductor plus a capacitor work tog... | All three tones (lower sideband, higher sideband and carrier) are transmitted in so-called double sideband amplitude modulation (AM-DSB). It is possible to transmit and receive/demodulate only one of the sidebands, this is called single sideband (AM-SSB not using the other sideband nor the carrier that are not transmit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695777",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Are reciprocal lattice basis vectors parallel to their corresponding real lattice basis vectors? So I had a question asking to find the angle between b* and (113) plane normal in a tetragonal unit cell. I know that the angle between two plane normals are given by:
My thinking was that if I know a direction that is par... |
The reciprocal lattice vector g with components (h,k,l) is
perpendicular to the plane with Miller index (hkl).
Yes.
Suppose $3$ non orthogonal vectors a, b and c, like $3$ lines from one of the vertex of a tetrahedron. Each $2$ of them determine a plane. In a bravais lattice, this is a cristallographic plane, with a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to check if a curved metric satisfies Einstein's equations? So I have come across threads on how to check the vacuum solution of Einstein's field equations. But say if someone give me an AdS-like metric, or the AdS C metric for example. If I by inspection don't recognize the exact form of the metric, how would I be... | In general you need to plug the metric in Einstein's equation
$$G_{\mu\nu} +\Lambda g_{\mu\nu} = T_{\mu\nu}$$
that arises from the variation of the action
$$ S = \int d^4x \sqrt{-g} \left(\frac{R-2\Lambda}{2} + \mathcal{L}_{M}\right)~,$$
where $T_{\mu\nu}$ comes from the matter lagrangian $\mathcal{L}_{M}$.
If your spa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/695998",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can black holes evaporate into photons if they contain no anti-matter? Hawking theorized the evaporation of black holes. Photons are pictured to slowly radiate their mass away. The higher the mass the longer it takes (due to smaller tidal forces).
Which makes one question, how can the inside matter, composed of nor... | A black hole has no net electric charge and the photon has none either So charge is conserved and there is no problem
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/696293",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 5,
"answer_id": 4
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Where do electrons flow inside a battery? What happens inside a battery? Sorry, if this sounds silly, but I have had this doubt from a long time. Please help me, I'll forever be grateful to you.
I'm a student of 10th grade. This is my doubt:
*
*What happens when electrons from the negative terminal reaches the positi... | If you have no external connections to a battery then due to the electro-chemical reaction inside the battery electrons move from the positive terminal (making it more positive) to the the negative terminal (making it more negative).
This creates an electric field within the battery from the positive terminal to the ne... | {
"language": "en",
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How does turbulence arise from Navier-Stokes? I would like to know how turbulence arises from the standard Navier-Stokes equations, both mathematically and also physically. At least I suspect this is the case as many of the "vanilla" Navier-Stokes simulations seem to develop turbulent.
I am a mathematician who does not... | The Navier Stokes equations are non-linear in velocities, and thus have multiple solutions, some of which are time-dependent turbulent solutions. In practice, the most stable solution prevails. In turbulent flow, the fluid velocity and pressure vary rapidly with time and spatial position, even for so-called "steady f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/696839",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Euler-Lagrangian equation of motion of quantum fields in QFT A canonical way of doing quantum field theory is by starting with some Lagrangian, for example, that of free scalar field
$$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi-\frac{1}{2}m\phi^2$$
Then by employing the Euler-Lagrangian equation, i.e. $\delta L... | No, we don't start by assuming EL equations for the quantum fields. We start by assuming the action of the quantum fields. The job that the EL equations do in classical field theory, i.e., predicting the time-evolution of the field configuration, is done by evaluating the propagator $\langle \phi(x)\phi(y)\rangle$ via ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is positive rotation direction of a pulley in the Atwood machine? In the Atwood machine the mass $m_1$ hangs on the left and $m_2$ hangs on the right, with $m_2 > m_1$. When released from rest the system accelerates clockwise which we define to be the positive direction.
The pulley has non-negligible mass and also... | Consider the following diagram of the pulley with some axes added.
Torque, $\tau = \vec r \times \vec F$
The torque about the centre of the pulley due to force $\vec T_1$ is $\vec \tau_1=(-r\hat i)\times (-T_1 \hat j) = +r\,T_1\,\hat z$ which with the right hand convention corresponds to an anticlockwise rotation.
Th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Making Lorentz equation dimensionless for simulations \begin{equation}
\frac{dv}{dt}=\frac{e}{m}(E+\frac{v}{c}\times B)
\end{equation}
I'm making a numerical simulation and I need to make the equation dimensionless. I'm having trouble in doing so.
I was thinking to use the fundamental units:
*
*setting the time as in... | Wikipedia provides a good process of nondimensionalization:
*
*Identify all the independent and dependent variables;
*Replace each of them with a quantity scaled relative to a characteristic unit of measure to be determined;
*Divide through by the coefficient of the highest order polynomial or derivative term;
*Ch... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Having trouble understanding Re-derivation of Young’s Equation I was going over a section 2.1 of this article (regarding Young's Equation and for some reason I wasn't able to derive E10 from E9 (see image below). I know it is more about the trigonometry of the problem, but when I tried to derive it myself it became cum... | If you are having trouble in simplifying the trigonometric equations, you can use the symbolic calculator in MATLAB/python. Using the symbolic code in MATLAB (shown below), you get
G = (1 - cos(theta))*(2 + cos(theta))/(1 + cos(theta))
F = (gamma_sl - gamma_so)*(sin(theta)^2 - cos(theta)*G) + gammma*(2*(1 - cos(theta))... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Understanding this quote by Feynman This might be more of a question on semantics and interpretation and if this doesn't meet community guidelines, feel free to let me know and I'll delete it.
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's... | There is a difference between "in a specific limit we need another theory" and "the theory disagrees with the experiment".
*
*Newtonian mechanics works pretty well for all experiments and more which it was created to explain.
*We still use wave description of light (and it works pretty well in certain limits)
What ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Relation between divergence of unit normal and radius of curvature I don't understand how does the divergence of a unit normal vector to a curve at a point gives the local radius of curvature. For simplicity consider a 2-D curve.
$$\nabla.n=\frac{1}{R}$$
I want to understand the mathematical proof for the expression an... | I'm really bad at drawing but have a look at this:
The bottom part can be seen as a segment of the original surface $S_o$ all points on it flow according to the surface normal, so after some time $t$ they from the top face. If we were to integrate the surface normal over this this cube and divide it by it's volume, we... | {
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"timestamp": "2023-03-29T00:00:00",
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How to express $|m\rangle\langle n|$ in terms of ladder operators? Let us consider the Hamiltonian of a single harmonic oscillator, which is expressed in terms of creation/annihilation operators as
$H=\hbar \omega (a^{\dagger}a+1/2)$. The eigenstates of this Hamiltonian are the number states ($n\geq 0$)$$a^{\dagger}a|n... | Although an answer has already been given which includes $| 0 \rangle \langle 0 |$, it is indeed possible to write an expression for $|m \rangle \langle n |$ purely algebraically in terms of $a$ and $a^{\dagger}$. This certainly must be possible in principle, since $a$ and $a^{\dagger}$ furnish a representation of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/698166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Position vector vs polar coordinates In cartesian coordinates we have the coordinates x,y,z, and the position vector is described by r(x,y,z) = $x\hat{x}$+
+$y\hat{y}$
+$z\hat{z}$
However, in polar coordinates, we have the coordinates $r$, $\theta$ but the position vector is r=$r\hat{r}$ and not $r\hat{r}$ + $\theta \... | Your $r$'s are playing multiple roles.
Instead, let $\vec R$ be the position vector ($\vec R=R\hat R$), and let $r$ be the radial coordinate in (say) $(r,\theta,\phi)$.
So, now, the position vector $\vec R$ and its time-derivative is the velocity $\vec V=\frac{d}{dt}\vec R$,
which could be expressed in any set of coord... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/698290",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Conformal symmetry and cluster decomposition? I would expect a conformal field theory would not satisfy a cluster decomposition of correlation functions. This may be due to my lack of understanding of conformal symmetry, but I would think a theory which is scale invariant would have interactions which do not get weaker... | Correlations do get weaker at long distances in unitary CFT. The unitarity bound on the scaling dimension of operators forbids the existence of correlation functions that are constant or get stronger with the distance.
And then there is the operator product expansion that tells you that if you have a bunch of operator ... | {
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"source": "stackexchange",
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Can sound waves deform (curl brake) like water waves? As far as I understand, both water waves and sound waves are mechanical waves, in the sense that both are created by the relative movement of particles in a certain medium. Sound is propagation of waves in air (relative movement of air molecules), and water waves pr... | Water waves have both transverse components, where the oscillations are perpendicular to the direction of wave motion, and longitudinal components, where the oscillations are in the direction of wave motion.
In fact, water molecules follow a circular path (orbits) in water waves. When ocean waters reach shallower parts... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the electromagnetic wave propagation direction and significance of $\vec{k}$-vector? Consider the electric field of electromagnetic wave to be of form $\vec{E} = E_°\cos(ax+bz) \hat{{i}}$ at $t= 0$ seconds. How to see in which direction wave is propagating? Does the value of $\vec{k}$ have a special signific... | The equation of a plane sinusoidal wave propagating in the direction given by the unit vector $\mathbf{\hat k}$ is
$$\mathbf E = \mathbf E_0 \cos\left(\frac{2\pi}{\lambda}\mathbf{\hat k} \cdot \mathbf r -\frac{2\pi}{T} t+\phi_0\right)$$
Here, $\mathbf{\hat k}$ is the unit vector at right angles to the wavefront, whose ... | {
"language": "en",
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How is electric field arising from photons? This question has nothing in common with the question it is proposed to be duplicate e.g about virtual photons. The question is about a real radiation field where is known that no virtual photons exist.
The electric field E moving up and down (in its value) as a sinusoidal w... | A photon is not a particle in the classical sense of the word.
A photon is a quanta of the radiation field.
Suppose you've got your sinusoidal Electric field, Suppose as you fix the energy say, hv, then the phase is maximally unknown.(Quantum Mechanics)
In a way a photon is much more similar to a field than a particle.... | {
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Determining the equations of motion for a 2 DOF in 2 directions I'm having trouble understanding a 2DOF system that moves in 2 directions. The problem asks me to determine the EOM for a system shown in the attached image:
My first idea is to transform this system into a simpler one in which the two masses move in the ... | If the pulley has negligible moment of inertia or the string slides around it without friction then you can ignore the rotation of the pulley.
It will simplify the problem if you measure displacements and extensions of springs from the equilibrium position when mass 2 hangs freely. Neither mass is accelerating in the e... | {
"language": "en",
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Conservation of momentum + conservation of energy + Newton's second law = Contradiction? When a body with a mass of 1 kg moves at constant velocity of 1 m/s and collide (elastic collision) with a body with the same mass that's at rest, we know from conservation of momentum and conservation of energy that the first body... | The solution is that energy is stored in the deformation of the objects. To maintain your argument you could assume incompressibility. However, in this limit the time interval during which both objects move simultaneously goes to zero. In this limit your argument therefore no longer holds. This limit would also requir... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can objects move during a collision-elastic collisions? Can two objects move together during an elastic collision before moving apart? Or would this be considered an inelastic collision since during the time in which the objects were stuck moving together, the kinetic energy was reduced.
| Note that terms elastic collision and inelastic collision are just abstractions to indicate certain properties of a collision. To determine if a collision is elastic or inelastic you have to observe kinetic energy just before and just after the contact. If kinetic energy is preserved the collision is said to be elastic... | {
"language": "en",
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Who makes the work, the force or the field? This is a bit of a semantic question.
According to the definition of work:
In physics, work is the energy transferred to or from an object via
the application of force along with a displacement. In its simplest form,
it is often represented as the product of force and displa... | A force without a field does not exist.
A field exists from itself. A field is real exactly if a material source exists which generates the field.
The force is the strength of the field at the point where it is applied. So it is not the field itself, but a part of the field, expressed as a force, that determines the wo... | {
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What is the difference between these two falling rope motion? Here are two falling rope problems in Marion's Classical Dynamics Textbook and both equations of motion given by manual solution.
(There is a typo in the third line of solution 9.15, one of the terms of velocity derivative should be time derivative of mass.)... | In 9.15 only the part of the rope below the table is accelerating, so the equation of motion is
$m g = m \dot v + \dot mv$
where $m(t)=\sigma x$ is the mass of the rope below the table at time $t$.
In 9.21 the whole rope is accelerating, so the equation of motion is
$mg = M \dot v$
where $m(t) = \frac {Mx} L$ is the ma... | {
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Why are non-Newtonian fluids called non-Newtonian when they follow Newton’s third law? To my understanding, Newton’s third law states that for every action there is an equal and opposite reaction. Therefor if I punch the non-Newtonian fluid harder, there will be a harder reaction force stopping my hand. So why is the f... | Newtonian fluids are named after Isaac Newton, who first used the differential equation to postulate the relation between the shear strain rate and shear stress for such fluids.
For Newtonian fluids there is a direct proportionality between the two quantities and so for fluids which that is not so are called non-Newton... | {
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How can satellites change direction without any medium in space? How can satellites change direction without any medium in space? How do spaceships move in space if there is no medium?
How does Newton's third law of motion work in space?
| If you are in space, floating at zero g, and you throw a heavy ball in one direction, you'll float in the opposite direction (action/reaction, conservation of momentum). You don't need any medium. Once you're moving, you don't need to do anything to keep moving (law of inertia). If you want to change direction or speed... | {
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Is it possible to built a variational principle for this first-order system? Imagine there is a mechanical system described in unitary units by the equation:
$$\dot{x} = -\text{sgn}(x)\sqrt{|x|},\quad x(0)=1 \tag{Eq. 1}$$
such it has a finite duration solution:
$$x(t) = \frac{1}{4}\left(1-\frac{t}{2}+\left|1-\frac{t}{2... | *
*A 1st-order ODE $$\dot{x}~=~f(x,t)\tag{A}$$ cannot be a Euler-Lagrange (EL) equation if we are only allowed to use a single real variable $x(t)$, cf. e.g. this Math.SE post.
*With several variables it is easy. We can e.g. use a Lagrange multiplier
$$ S[x,\lambda]~=~ \int_{t_i}^{t_f}\!dt~ \lambda(\dot{x}-f(x,t)) \... | {
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Why does the incline angle not affect how high a launched object will slide up a frictionless ramp?
I am seeing a problem with the solution given in this book. How did the height of the box have nothing to do with the incline of the ramp? Intuitively it would seem the higher the incline the higher the box would go. Es... | The box is slowed down by the component of the weight parallel to the plane. If the plane is steeper (angle is larger) the acceleration is larger and the box stops after a short time. If the angle is small the acceleration is small and the box travels longer before it stops. But, on the other hand, you have to travel f... | {
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Uncertainty Principle in 3 dimensions I'm trying to understand how to write Heisenberg uncertainty principle in 3 dimensions. What I mean by that is to prove something of the form $f(\Delta p_x,\Delta p_y,\Delta p_z,\Delta x,\Delta y,\Delta z) \geq A$.
This is what I got:
The unknown volume that a single particle can b... | There is no need for a 3D uncertainty principle.
The operators commute between dimensions:
$$[\hat{x}^i, \hat{p}^j] = i \hbar \delta^{ij}$$
Momentum in one dimension and position in another can be measured with arbitrary precision simultaneously (at least there is no restriction from QM).
The closest thing I can think ... | {
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What does Leggett mean by quantum states like $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$? In his article (p. 1986) Legett uses the notation $|\psi\rangle=(a|\psi_1\rangle+b|\psi_2\rangle)^N$ to classify "macroscopic quantum phenomena". Does the "$^N$" mean "$\bigotimes_{l=1}^n$" (tensor product)?
| Yes, it does.
Some people use the notation $|\psi\rangle^{\otimes N}$ to make that extra clear.
| {
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Instantaneous eigenstate and time dependent Schrodinger equation Instantaneous eigenstate $\psi(t)$ is defined as
$\hat H(t)\psi(t)=E(t)\psi(t)\tag{1}$
But in the lecture notes of Quantum Physics III MIT (in the section of adiabatic approximation), it is written that $\psi(t)$ may not be the solution of time dependent ... | I think the easiest way to see this is with an example. Consider a Hamiltonian that changes suddenly at $t=0$
\begin{align}
H(t) = \begin{cases} H_1 & t \le 0 \\ H_2 & t > 0 \end{cases}
\end{align}
Now the instantaneous eigenstates will, correspondingly, change suddenly at $t=0$ from eigenstates of $H_1$ to eigenstate... | {
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How do you find the final velocity when acceleration is changing between two values over some distance? How do you calculate a final velocity of an object when given its initial velocity and the object is accelerating between an initial and final acceleration over some given distance?
| As others have said, if you have an acceleration function given explicitly as a function of distance you can use mathematical tricks to do it, or use the
relation between work and kinetic energy
$1/2mv^2 = \int F(x) dx$
$1/2v^2 = \int a(x) dx$
However given that you actually have acceleration as a function of time, we ... | {
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Green function dependence on temperature Consider the retarded Green function for fermions
$$
G_{ij}^r(t)=-\frac{i}{\hbar} \theta(t)\langle[c_i(t),c^\dagger_j(0)]_{+}\rangle
$$
They can be understood as the $(i,j)$ entry of the matrix $G^r(t)$. The operators evolve in time as they are in the Heisenberg picture. The ope... | In the Heisenberg picture, the operators evolve according to the Heisenberg equation
$$i\hbar \frac{d}{dt} A = [A, H]_-$$
This governs the time evolution of the annihilation operator
\begin{align*}
i\hbar \frac{d}{dt} c_j(t) &= [c_j(t), H]_- \\
&= \sum_{mn} H_{mn} [c_j(t), c_m^\dagger(t) c_n(t)]_- \\
&= \sum_{m... | {
"language": "en",
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Will I get a shock holding a superconductive wire? Assume a current carrying superconductive wire is in front of me, with no voltage source attached.
If I hold it, will I get a shock? Forget for a minute that the superconducting wire will be too cold to touch.
My initial instinct was a maybe, for a second but ultimatel... | Another way of thinking about Bob D's answer: when you grab a superconducting wire in two different places (e.g. with both hands), you can think of your body and the wire as being wired in parallel. There is zero resistance along the superconducting wire but positive resistance through your arms, so all of the current ... | {
"language": "en",
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Circles to squares I always get lost in my thoughts on the mechanical physics of how things work or how it would work. Well I have my coffee cup here full of coffee, I flicked it and watched the waves close into the centre almost perfectly. So I took a video and was surprised to see the circular waves from the edges of... | The perturbation you gave to the coffee cup in order to start the waves on their way towards the cup's center was not perfectly radially symmetric. This means the waves themselves weren't either (and will contain some higher harmonics that contain deep nulls at certain angles), but their non-circularity isn't obvious t... | {
"language": "en",
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What does the surface integral tell us, and how is it different from surface area? In the context of Faraday's Law of Induction,
Will a paraboloid with the same cross sectional area as a major portion of the sphere (Spherical Cap), have the same magnetic flux, when put in an uniform magnetic field ?
If it does have the... | In the equation $$\Phi=\int_{\mathbf{s}}\bf B\cdot dA$$ there is a dot product between the magnetic field and the normal area vector. This is evaluated at all points on the surface $\mathbf{s}$ and each one of these dot products depends on the angle between $\bf B$ and $\bf dA$.
For surfaces that are of different shape... | {
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Trying (and failing) to calculate baryon/photon ratio I'm reading through Modern Cosmology by Dodelson and Schmidt 2nd edition on my own, and at the start of Section 4.2 the book says that we can compute the baryon/photon ratio at the time of big bang nucleosynthesis and get
$$ \eta_{\text{b}} \equiv \frac{n_{\text{b}}... | Ahh, I see what I did wrong. At the first bullet point, I invoked (4.5), which is an approximation. It involves an approximation of the distribution by a Boltzmann distribution for a classical dilute gas. This is not what we need for photons.
What we need instead is the Bose-Einstein distribution. In that case, we have... | {
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Mathematical Definition of Point Source Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating".
The usual definition in Physics describes it just as a source whose dimensions are negligible in comparison to another variable you're relating it to, which le... | A point source is described by its math, period. And since you can meaningfully calculate fields from a charge distribution that is infinitely tall at a single point (which is represented by a mathematical distribution, aka delta-function), there is nothing more to that. It is an idealization, and may or may not repres... | {
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How are photons arranged in a light ray? Title, or more specifically, if a constant light source is directed onto a flat surface, would the photons spread equally on said surface? In addition, say, at the beginning, 10 photons reached the surface, would it still be 10 photons reaching the surface after a split second?
... | Well, I think your question is in fact about flux of photons, namely, a number of photons reaching a certain cross section during a certain time interval. Say, million of photons reaching one square meter surface in one second.
Back to your question, the answer actually depends on how intense this flux of photons is. I... | {
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Would our orbit really remain the same if the sun were a black hole of equal mass? There seems to be an idea floating around that the sun could be replaced by anything of equal mass with no consequence to our orbit.
It seems to me that if the mass of the sun were confined to a single point that the local geometry of sp... |
There seems to be an idea floating around that the sun could be replaced by anything of equal mass with no consequence to our orbit.
I have to correct my former answer. That idea is correct!
Let's assume the earth is orbiting in the static spherically symmetric spacetime shaped by the sun (we neglect the earth contri... | {
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How can light produce electric and magnetic field when there are no accelerating charged particles? If we see light as a wave, especially in vaccum, there is nothing there, no particles, yet light has an electric and magnetic field. How can this be possible?
| Light is merely a manifestation of electromagnetic fields, i.e., light itself is the electromagnetic field. What we understand as light is just the propagation of electromagnetic waves, which are eventually detected by something (our eyes, a camera, etc). These waves were generated by some kind of source, such as the n... | {
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If frequency of photons is a continuous spectrum, wouldn't the chance of a photon having the exact right frequency to excite an electron be zero? As far as I'm aware, the energy needed to excite an electron to a different orbital is discrete. Since the frequency of light is continuous, wouldn't it be impossible for a p... | There is a natural line width which is determined by the lifetime $\tau$ of the excited state. This means that you only need to be within some frequency interval of $\approx 1/\tau$ about $\omega_{\rm res}$ to have a chance of exciting the state.
| {
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Understanding the derivation of the Newtonian limit of GR I'm having difficulty understanding some of this derivation. The relevant information, as I understand it is:
We've let the lorentzian metric be a perturbation of the minkowski metric:
$$g_{\mu\nu} = \eta_{\mu\nu}+h_{\mu\nu},$$
where apparently if $h_{\mu\nu}$ i... |
I'm just struggling to figure out the working behind the last step
Note that $\overline{h}=h-\frac12h4=-h$ in $4$-dimensional spacetime, so $h_{\mu\nu}=\overline{h}_{\mu\nu}+\frac12h\eta_{\mu\nu}=\overline{h}_{\mu\nu}-\frac12\overline{h}\eta_{\mu\nu}$. What's more, $\overline{h}=\overline{h}_{00}=-\frac{\kappa c^2}{2... | {
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Electric and magnetic force between two charges moving together move at the speed of light Consider the problem of two charges, one positive and one negative, both located on the $y$ axis at time $t=0$, at finite separation. Their initial velocities are exactly equal and along the $x$ axis (positive or negative directi... | Boost yourself into the rest frame of the two charges. Since the charges are not moving, the force between them is purely electric, which causes them to accelerate towards each other at some rate. Now return to the lab frame. Here, the particles have relativistic speed, which means time dilation comes into effect. This... | {
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Radial Schrödinger equation: from $R_l(r)$ to $u_l(r)$ I am in the 3-dimensional radial Schrödinger equation, in the spherical coordinates, where we try to find the separable solutions
$$\psi(r) = R_l(r) Y_l^m(\theta, \varphi) \equiv \frac{u_l(r)}{r}Y_l^m(\theta, \varphi).$$ ($\theta$ is the colatitude and $\varphi$ th... | A friend just explained me that actually, turning $R_l(r)$ into $u_l(r)/r$ made a $\frac{1}{r}$ appear everywhere, except in the $\frac{d^2}{dr^2}$ term where the $r R_l(r)$ turns into $u_l(r)$. As there was already a $\frac{1}{r}$ in front of $\frac{d^2}{dr^2}$, all the $\frac{1}{r}$ and $Y_l^m(\theta, \varphi)$ just ... | {
"language": "en",
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What gives particles mass? Also why are particles like photons considered massless when they have energy and momentum? Interested in knowing the quantum explanation for what gives particles mass, and why particles like photons are considered massless when they have energy and momentum.
| The idea that a photon is massless is a pedagogic convention, that has not always held sway. When I was taught special relativity in the '70s, there were two kinds of mass that were distinguished. Rest mass and relativistic mass. Relativistic mass was simply and always equal to momentum divided by velocity. Photons hav... | {
"language": "en",
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Could the matter-antimatter symmetry be local rather than universal? In the observable universe there is an antimatter-matter asymmetry. Are there any theories that propose that this is just a local asymmetry one fluctuation in a universe with an overall symmetry?
| The Alpha Magnetic Spectrometer experiment, installed on the International Space Station, is designed to study antimatter before they have a chance to interact with the Earth's atmosphere or deflect in Magnetosphere.
If antimatter-dominated places of space existed, then the gamma rays produced in annihilation would b... | {
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What is the correct way of looking at the Dirac field? All quantum fields are operators in QFT. However, the Dirac field operator $\hat{\psi}$ has the following difference with the scalar field operator $\hat{\phi}$:
For the $\hat{\psi}$, it makes sense to define the operation $$M \cdot \hat{\psi}$$ where $M$ is any $... | To add to what hft said, $\hat \psi$ is valued in a tensor product of operator densities and the spinor bundle. If you want to get an operator, you need to pair it with a smooth section of the dual bundle and integrate. In flat space, that can be a constant section times a bump function, which corresponds to creating o... | {
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Is there a formula of heat that expresses it in microscopic work done? If I understand correctly looking at the first law of thermodynamics we have a microscopic work term (heat: $Q$) and macroscopic work term ($W$)
$$ \Delta E = \Delta Q + \Delta W$$
The macroscopic work done can be nicely expressed as: $ \Delta W = ... | Thinking of heat as “microscopic work” invites deep confusion, I suggest.
Heat is a very special type of energy transfer—that driven by a temperature difference.
Work is every other type of energy transfer not involving mass transfer.
If you wish to distinguish heat and work microscopically, consider McQuarrie’s dichot... | {
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Light as a wavelength I am learning that light is an electromagnetic wave, does this wave travel in every direction simultaneously from the source of light? I am trying to visualize this concept but I haven’t seen an explicit definition saying there are infinitely many wavelengths emitted from a source of light. Would ... | The first thing I'd recommend is to get in the mindset of how waves move. Find a still pool of water, and toss a small rock into the middle of it. Observe the waves moving outwards in all directions. Do we call this "infinitely many waves?" Or is there just one wave reaching outward?
One thing that can be confusing... | {
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Where does gravity come from? First, in my childhood, I learned that gravity is a force. Later, I learned that gravity is a property of spacetime. If gravity is a property of spacetime, then why is it one of the fundamental forces. What is gravity, really?
| if gravity is property of spacetime then why it is one of the fundamental forces.
If you replace the term "fundamental forces" with "fundamental interactions", everything becomes much more understandable.
As you correctly pointed out, "gravity is a property of spacetime". And it is not a force in the sense of mechanics... | {
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What is the difference between antenna input impedance and its radiation resistance? I got to know that the input impedance of the halfwave dipole antenna is given as:
$Z_{in}$=1/$I_m$* sin($\beta$(H-|Z|))
where $I_m$ is the maximum current on the antenna( when excited with a 1 volt supply),
H is the half-length of the... | The radiation resistance of an idealized antenna is the nonreactive (real) component of the load impedance of an antenna. The real component "looks" like a purely ohmic resistance to the power flowing into the antenna, which means no power is reflected off the antenna and sent backwards up the feedline when the the loa... | {
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Phonon, photon have chemical potential equal to zero Hi I know the chemical potential of the phonon and photon is equal to zero. And I know the reason is the number of these particle isn't conserved.
But I don't know why the number of the phonon isn't conserved? Isn't the number of phonons 3N?
Thanks for your help.
| The number of modes of the phonons is $3N$. However, for each mode, the number of phonons is not conserved.
An analog is that we have $3N$ different harmonic oscillators, and each of them can be in a generic excited state, labeled by an integer $n$. Here each harmonic oscillator is the analog of a mode of phonon, and f... | {
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Is there a law stating why a quark never decays weakly into a quark of the same weak-isospin ($T_3$)? So I read multiple articles on weak isospin and one of them stated that
"a quark never decays weakly into a quark of the same $T_3$".
If this is true, can someone please explain what law states this?
| The term in the standard model lagrangian which couples quarks of different flavors looks like
$$(\overline{u}_L,\overline{c}_L,\overline{t}_L)\gamma^\mu V_{CKM} \begin{pmatrix}d_L\\s_L\\b_L\end{pmatrix}W_\mu^- + \text{h.c}$$
where the row and columns are in flavor space. The up type quarks have $T_3=1/2$ and the down ... | {
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A rubber ball gets thrown horizontally from $H$ height find the horizontal distance of the ball till it hits the ground
There's a rubber ball that has mass $m$, it gets thrown horizontally (from $H>0$ height) with initial velocity of $\vec V(0) = V_0 \hat X$ ($\hat X$ is the axis, meaning horizontal)
in addition to th... | I think when you integrated $V_y$ something funny happened. Notice in your expression for $y(t)$, at time zero your height should be $H$. Try using an indefinite integral instead:
$$y(t)=\int V_y dt$$
If that function antiderivative is $\int V_y dt=f(t)$ then you should end up with:
$$y(t)=f(t)+C$$
Then use your $t=0... | {
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Does statistical mechanics imply that the universe is probabilistic? Statistical mechanics says that a system will evolve to a state of higher entropy (i.e. states with higher number of microstates) simply because it is overwhelmingly more probable than evolving to a state of lower entropy. Does this simply that the ev... | No. Statistical mechanics does not imply a non-deterministic universe.
When you ignore some information about a deterministic system you can still use probabilities. Consider a machine that flips a coin to the opposite side every 5 seconds. If we don't know how long since the machine was started, we can say there is a ... | {
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What is the difference between "cluster states" and "graph states"? I wonder about the difference between the cluster state and the graph state.
I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice
The concept of the cluster state and the graph state can be known ... | There's no difference really. For example Michael Nielsen's review paper discusses this terminology a little bit (https://arxiv.org/abs/quant-ph/0504097):
Note that the states we have called cluster states are sometimes also known as
graph states. Originally, the term “cluster state” was introduced by Raussendorf and
... | {
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Failure of Newton's corpuscular theory and success of photon theory of light Corpuscular theory of light States that:
Light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity.
According to Einstein,
Light is composed of small particle ... | The corpuscular theory was opposed to the wave theory, and was rejected when diffraction experiments confirmed the wave theory. The blackbody spectrum also confirmed the wave theory at low frequencies, but at high frequencies it didn't work. Thus, the photon theory emerged with its counterintuitive mix of particle and ... | {
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Dropping a mirror into a blackhole Say you dropped a mirror into a black hole while observing at a distance and holding a clock such that the clock's face was pointing to the black hole.
What is the latest time you would view on the reflection of the clock?
What time would the reflection of the clock show after waiting... | The clock will measure the proper time of an observer falling into the black hole. The observer will reach the horizon in a finite proper time; you will observe the clock reaching this value asymptotically (you will never see the clock actually reach the value it has when it reaches the horizon but you will see it get ... | {
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How does one apply the phase change of $π$ on reflection at the rigid end of a string? Consider a string, with a free end $P$ and another end $Q$ which is rigidly fixed.
Now, we start oscillating the point $P$ (with $0$ initial phase difference) and a wave starts traveling(in the positive $x$ direction) towards $Q$. L... | The Phet Wave on a string simulation is worth a look at with oscillate chosen.
You can also change the damping, tension, frequency etc to look further at what happens when there is a fixed end.
At the fixed end the reflected wave is $\pi$ out of phase as compared with the incident wave.
The amplitude of the wave at you... | {
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How to reduce magnetic field between two magnetic shield sheets (silicon steel sheets)? I put 2 parallel silicon steel sheets between magnetic field as below:
As silicon steel has much bigger permeability than air,magnetic line will go through 2 silicon steel sheets.
What I can do to reduce magnetic field between thes... | The best currently material for magnetostatic shielding of strong magnetic fields (high saturation value needed) is Giron:
Mu-metal material although it has a better magnetic permeability has however a relative small saturation value thus is suitable only for small magnetic field strength, less than one Gauss (i.e. μΤ ... | {
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Quantum effects on phonon transport? Phonons are the quanta of vibrations in a crystal lattice. As the name suggest, phonons are already a quantum phenomena but when studying heat transfer the phonons are mostly very classical (wave mechanics, semiclassical treatment).
Usually the quantum characteristics enter into the... | One example is a phonon-polariton, which is a coherent quasiparticle made from light and optical phonons.
| {
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Is vapor pressure conserved during an adiabatic ascent of an air parcel? Consider an air parcel with relative humidity $H$ and vapor pressure $e$ that experiments an adiabatic lifting process. Obviously the saturating vapor pressure is going to change since said process is going to lower the temperature of the system, ... | Vapor pressure (e) is NOT conserved during unsaturated adiabatic ascent. However, mixing ratio (q) is conserved during unsaturated ascent. I see this error in textbooks as well. Vapor pressure is a function of dewpoint, which in turn depends on pressure, which is decreasing during ascent, and dewpoint decreases as an a... | {
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Submerged Landau jet I am reading Landau & Lifshitz's Fluid Mechanics. On page 81, section 23, it reads
Determine the flow in a jet emerging from the end of a narrow tube into an infinite space filled with the fluid - the submerged jet. We take spherical polar coordinates $r,\theta,\phi$, with the polar axis in the di... | Since the problem has an axial symmetry then he rid off the $\phi$ angle, i.e. no dependence on the azimuthal angle $\phi$ hints to the absence of this variable in the solution in the function $F$ or $f$.
As to the $r^{-1}$ the spherical diverting waves loss their magnitude (or Intensity in other words) by this low bec... | {
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How does a sliding object stop moving by the effect of kinetic friction, if kinetic friction is constant and Fk can't be greater than Fapp on its own The kinetic friction is constant. So if say, I apply a force of 20N on an object and the kinetic friction is 13N, then how does the object stop moving after some seconds.... | You're right that kinetic friction is constant, assuming the coefficient of friction and mass of the weight don't suddenly change. It seems like your confusion is how a mass would eventually come to rest if friction isn't greater than an applied force. Let's break this down with Newton's second law:
$$m\ddot{x}=\sum_iF... | {
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Contradiction in my understanding of wavefunction in finite potential well Most things like to occupy regions of lower potential. So the probability amplitude should be higher in a region of lower potential. I denote the potential by V.
However, we also know that the kinetic energy of a particle is given by E-V - the b... | Even classically, particles with a fixed total energy spend more time near the turning points since this is where the motion is the slowest. The probably of finding the particle in a small region near the bottom of the well is NOT the largest: it is in fact the smallest.
Thus your statement that the particle wants oc... | {
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Radio Waves and the Lorentz Force? Is the Lorentz Force involved when the EM wave intersects the receiving antenna? I.e. induces EMF on electrons in the antenna conductor?
I use the RHR with index finger $\vec v$ pointing in the direction of wave propagation towards antenna, middle finger $\vec B$ perpendicular and my ... | The usual way to model a small dipole receiving antenna is as an electrostatic probe sensing the electric field. Small loop antennas are modeled as sensing the EMF due to the magnetic field.
However, you should note that the way we understand the incoming wave is that the electric field excites the magnetic field, and ... | {
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Thin layer of air between lenses in contact consider the following case for thin lenses
Case 1: lens between two different medium
applying refraction through curved surfaces two times and subtracting -
$$\frac{\mu_{oil}}v - \frac{\mu_{air}}u = \frac{\mu_{L} - \mu_{air}}R - \frac{\mu_{L} - \mu_{oil}}R $$
(note if both ... | A thin layer of air (or any other medium for that matter) will have no impact on ray trajectories, image locations or image shapes, as long as (1) the layer is sufficiently thin, and (2) the radii of curvature on both sides of this layer are the same (meaning the layer has the same thickness throughout). When we speak ... | {
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Eyes shut, can a passenger tell if they’re facing the front or rear of the train? Suppose you’re a passenger sitting in one of the carriages of a train which is travelling at a high, fairly steady speed. Your eyes are shut and you have no recollection of getting on the train or the direction of the train’s acceleration... | I don't think this question as posed is really well defined. But here's an attempt at an answer.
In the real world the answer is yes. Assuming the train is longer in the direction of motion (as is the case for any train I can think of), you could determine the direction perpendicular to the motion of the train. Then yo... | {
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Inclined plane question: Why does $F_f = Mg \cdot \cos{\theta}$?
So I was reading Morin's Book and it had this as first example.
My confusion is with the forces here, the book mentions
$F_{f}=Mg(\sin(\theta)-\cos(\theta))$ and $N = Mg(\cos(\theta)+\sin(\theta))$
but shouldn't $F_{f} = Mg \cdot \sin(\theta)$ and how co... | It is quite ambiguous in this problem, but keep in mind the horizontal force is NOT the gravitation force, but a force which equals $Mg$, let's call it $\tilde{F}$. You thus have to treat it like any other force. I don't know why you say that $F_f = \tilde{F} \cdot \sin \theta$, have a closer look at the picture:
$\co... | {
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Charge density by Gauss divergence theorem when the electric field is dincontinuous Let's say the electric field across a surface is discontinuous. Now if I want to find the surface charge density which electric field should I use in Gauss divergence theorem?
| Discontinuities on the electric field are due to a presence of charge on the surface you're looking at. This can be seen from Gauss's Law itself. If $\mathbf{E}$ has a discontinuity, then $\nabla\cdot\mathbf{E}$ has a Dirac delta contribution at the place of discontinuity, which $\nabla\cdot\mathbf{E} = \frac{\rho}{\ep... | {
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What shape does an elastic rod take when both ends are dragged to the same point? Suppose we have an ideal elastic rod of some kind, where the energy at a point along the rod is proportional to the square of the curvature, and we drag the ends of this rod so that they touch, and the rest of the rod is now making some k... | By Euler-Bennoulli Law,
$$ \kappa= \frac{M}{EI}=\frac{d\phi}{ds}=\frac{F y}{EI}=\frac{y}{c^2}$$
where $\kappa$ is curvature, $\phi$ slope, $M$ bending moment proportional to $y$ coordinate, $EI$ flexural rigidity, $F$ are two equal opposite forces applied at towards origin along x-axis and $c= \sqrt{EI/F},$ a length co... | {
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Path Integral QM and Destructive Interference In Shankar's QM book pg. 224, it was said that the contributions $Z=e^{iS[x(t)]/\hbar}$ add constructively near the classical path $x_{cl}(t)$ since the action $S[x_{}(t)]$ is stationary here.
As we move away from the classical path $x_{cl}(t)$, destructive interference set... | Pay attention to the word crudely. The value $\pi$ is not a precise estimate, just a typical value for phases out of phase. Shankar is implying that when the path integral sum up a neighborhood of paths $\gamma$ whose phases $S[\gamma]/\hbar$ differ by the order of $\pi$, then coherence is lost and destructive interfe... | {
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Can empty space 'press' galaxies? If gravity slows the effects of time, then empty space will see greater expansion than space inhabited by massive objects. So the space within a galaxy will be expanding more slowly than the space without. Maybe the effect is minimal, but in cosmological size and time frames, the effec... | Just to deal with these problems physicists introduced the term dark matter. In the first question the expansion rate of galaxy as you said is slowed down by celestial objects' gravity. But Hubble and ESA measured that the mass of stars and gases present in our galaxy accounting only for 16% right. So we can assume tha... | {
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Property of a wavefunction We know that a wavefunction can't be completely real, because then it would have some complex expectation values for some operators. If we let $\psi$ be a real wavefunction, then
$$\langle P\rangle= \int{\psi^*\left(-i\hbar \frac{\partial}{\partial x}\right) \psi\, dx}$$
would be imaginary, w... | If $\psi(x)$ is a "completely real" wavefunction, then $\phi(x) \equiv i \psi(x)$ is an "completely imaginary" wavefunction that is experimentally indistinguishable from $\psi(x)$. This is because multiplying a wavefunction by an overall phase of $i = e^{i \pi/2}$ does not change the results of any experiment. So any... | {
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Divergence theorem in index notation From Batchelor's book of fluid dynamics:
I guess that's an easy question for anyone having more familiartiy than me in tensor calculus, anyways.
First integral argument is the i-component of the torque and i can write it up as shown.
Im struggling understanding how the dot product ... | Maybe it helps you visualize if we expand things out. Let $A_{il} = \epsilon_{ijk}r_{j}\sigma_{kl}$, such that the first integral is:
$$\tau_{i} = \displaystyle{\int A_{il}n_{l} dA}$$
Notice that we can write $A_{il}n_{l} = A_{i 1}n_{1} + A_{i 2}n_{2}+ A_{i 3}n_{3}$, from which it is clear that $\nabla \cdot A_{il} = ... | {
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Is it possible to determine the distance between the earth and a star by only studying the light emitted from this star? I was reading about the Doppler shift and how we can measure how fast something is moving through its Doppler shift. This got me thinking is their a way/formula to measure the distance between us and... | If the star is not too far away, one can determine the distance by measuring parallax from two different points of Earth's orbit.
| {
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Electrostatic effect on neutral papers by negatively charged comb I know paper changes its dipole molecules so the positively charged side will be exposed to a negative charged comb and then attracted.
But how do a paper piece’s molecules change, if paper is a solid?
| “How do a paper piece’s molecules change, if paper is a solid?”
The paper's molecule DOES NOT CHANGE. Instead, the “electron cloud” is slightly shifted in the opposite direction of the comb. This indicates that due to repulsion, the electron in the molecule moves away from the comb. As the electron gets away, there is ... | {
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How Do We Know Electron Wavefunction Should Be Antisymmetric to Electron Exchange? As far as I know, electrons are indistinguishable particles which means that physical observables should be independent to electron exchange. Only way this can be done if the wavefunction stays the same after exchange (bosons) or flips t... | The exclusion principle came first as a physical idea to capture phenomena of atomic spectroscopy and chemistry. Exchange antisymmetry is the way that subsequent mathematical abstraction captured this physical idea. So, the phenomena gave rise to the exclusion principle, and it gave rise to the exchange antisymmetry ab... | {
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Why do clouds have well-defined boundaries? Why do cumulus clouds have well defined boundaries? In other words, what are the physical mechanisms that hold a cloud together, as an entity separate from other clouds, that prevent it from spreading, etc.
Naively, one could expect the atmospheric vapour to spread homogeneou... | Convection in meteorology is often assumed to be more or less adiabatic, and convection is what creates cumulus clouds. You can imagine clouds as bubbles rising inside a water tank, they also have a quite well defined boundary. Warm humid air rises up, cools (reduction of pressure) and condensation begins.
https://en.w... | {
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What is the origin of the inertia? Is there any explanation why it is harder to move an object with more mass than an object with lesser mass? What kind of force is opposing our force? Is it finalized currently and well known what the origin of inertia is, or not yet 100%? I read some explanations that are linked to ge... | If it is not an explanation, it is a good argument:
Suppose $2$ solids, each with a volume $V$ and the same material. They are separated, and each one receives a net force $F$. As a consequence they get an acceleration $a$. If we look at this system of $2$ objects, a force of $2F$ is being applied, resulting in an acce... | {
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Fourier Component And Resonance Wikipedia defined Resonance as the following : Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. What is meant by : ... | It means that the driving force is decomposed into sines and cosines and if one of this sinusoidal functions oscillates with frequency equal or close to the natural frequency, then the system resonates.
To see this, consider for example an oscillator described by
$$\ddot x+2\gamma \dot x+\omega_0^2x=\frac{F(t)}{m},$$
w... | {
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Isn’t natural units prone to mistakes? Suppose I am deriving a length contraction formula using natural units. If I arrive at $L = L_0 \sqrt{1 - v^2}$, I know that I should divide $v^2$ by $c^2$ to get the correct answer in SI units. But what if I mistakenly forgot to square the velocity and arrived at $L = L_0 \sqrt{1... | Natural units, philosophically speaking, are the units natural to the problem. If we are measuring the masses of atoms, we are better of measuring in atomic units rather than kilograms. Likewise, if we are measuring the masses of stars we are better of measuring in solar masses. Because we are using units natural to th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 3,
"answer_id": 2
} |
Gravity = Yang-Mills squared? What is the Lagrangian? In the following comment and references, it is mentioned that gravity can be understood as yang mills squared. What is the Lagrangian of a Yang Mills squared theory? Can anyone provide a quick primer?
In this comment:
Why are string theorist so indifferent to the g... | *
*The statement
$$ \text{(super) gravity} = [\text{(super) Yang-Mills]}^2 $$
is the punch line of the Bern-Carrasco-Johansson (BCJ) colour-kinematic duality conjecture that the perturbative on-shell scattering amplitudes for (super) gravity are the double-copy of gluon scattering amplitudes in (super) Yang-Mills theo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715593",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How to solve for the trajectory of the center of mass? I'm working on the physics engine component of a game engine I'm building, and I need some guidance with this particular situation.
Consider a square with mass M that is free to translate in the xy plane and free to rotate about any axis perpendicular to the page (... | The motion (acceleration) of the center of mass (CM) is $\vec a_{CM} = {\vec F_{ext} \over M}$ where $\vec F_{ext}$ is the total applied external force and M is the mass of the square. The rotation about the CM is ${d\vec L_{CM} \over dt} = \vec \tau_{ext\enspace CM}$ where $\vec L_{CM}$ is the angular momentum about ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715966",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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