Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is the torque produced by 2 rotating bodies with a clutch I am trying to simulate a car engine etc, but I have failed to find any equations governing the torque created by $2$ different constant velocity shafts of different angular momenta joining together with some given slip or friction factor. I know $I_1w1 + I... | A clutch has two sides and a degree of freedom between them. Let's call one side the engine side with known torque $\tau_E$ and unknown speed $\omega_E$. On the other side, the transmission side, the speed is known $\omega_T$, but the transmitted torque $\tau_T$ isn't.
The clutch itself has a critical torque $\tau_C$ w... | {
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Would the existence of a universal wave function automatically mean the Many Worlds Interpretation? If the Universal Wave Function definitely existed, would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?
| The concept of "wavefunction"is inherent in the definition of Quantum Mechanics,in the same way the concept of mass is inherent in the definition of classical mechanics: it is a mathematical function which is used to model data and predict physical behavior of matter at small dimensions .
Present physics modeling assum... | {
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Expansion Postulate Quantum Mechanics How does the expansion postulate allow predictions to be made about measurement outcomes?
I understand the postulate as:
$$
ψ =\sum_{n} a_n φ_n
$$
with coefficients calculated by:
$$
a_n =\int φ_n^*ψdτ.
$$
I think that:
$$
|a_n|^2
$$
is the probability of the system being in state... | Yes, $\vert a_n \vert^2$ is not the probability of the system being in the state $\phi_n$. It is the probability that the system (which is with $100\%$ probability in the state $\psi$) will be found in a state $\phi_n$ upon a measurement of an operator whose eigenstates are $\{\phi_n\}$.
| {
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Why exactly do we feel a shock when we place our hand into a conducting solution? I have a very naive question.
Suppose you have pure water in a flask, and you place two ends of a copper wire (which are connected to a battery) into the water.
If you were to place your hand into the water, you would not feel any shock, ... | when you immerse your hand into the conducting water, your skin is connected to the conducting medium. The charge being transported through the water is then faced with a choice, as follows.
Your hand and the water surrounding it represent two resistors in parallel. If your hand is more conductive than the water, the e... | {
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Does it make sense to say that something is almost infinite? If yes, then why? I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length.
As someone who hasn't studied very much math, "almost infinite" sounds like... | Almost infinite can make a lot of sense in physics. There isn't a precise definition but I would interpret it as the following: when something is 'almost infinite' the properties we are considering will barely change when we make the system actually infinite.
Examples:
*
*In thermodynamics the particle number is ofte... | {
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Continuity equation in QM I found this question in a quantum mechanics exam:
What is the physical interpretation of the continuity equation $\frac{\partial\rho}{\partial t}+\frac{\partial j}{\partial x}=0$? Here $\rho(x,t)$ is the probability density and $j(x,t)$ is the probability current.
I assume they want a one lin... | You're actually right, it stems from the "conservation" of probability, or the fact that probability sums to 1. It is literally the equation that says if $\rho$ changes, then that must be due to $j$.
Consider the integral version of this equation. In 3D the space derivative is a divergence,
$$\int \left[\frac{\partial ... | {
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What is a Topological Twist? I have come across topological twists on numerous occasions but I have never actually seen them explained in an understandable way. So, I was wondering
*
*What does it physically mean to topologically twist a theory?
*What does it mathematically mean to topologically twist a theory?
*Wh... | So, I think I've found an answer to my own question. One can take a supersymmetric theory defined on $\mathbb{R}^n$ and topologically twist it by redefining the rotation group of the theory into a mixture of the (spacetime) rotation group and the R-symmetry group.
Physically, this is just making one sector of the theo... | {
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Could light from the Sun be used to power the Breakthrough Starshot microships? The Breakthrough Starshot initiative aims to accelerate a swarm of 16m$^2$-area solar sails to 15% of $c$ using Earth-based lasers in the order of 100GW power in 10 minute bursts. Considering loses from various medium densities and temperat... | Because of its angular width (low spatial coherence), the sun's light cannot be focused to a small (meter-sized) spot at large distances. Any kind of lens arrangement can at best form an image of the sun.
However, large arrays of photovoltaic cells could certainly be used to power a laser array for Starshot. A laser b... | {
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Describing forces in rolling Consider a wheel on a frictionless horizontal surface. If we apply a horizontal force (parallel to the surface and above the level of the center of mass), what happens to the wheel? Does it roll or slide forward or rotate only or does any other phenomenon happen? Please guide me. Also draw ... | Consider the Free Body Diagram:
where:
*
*$F$ is a driving force
*$mg$ the weight of the wheel
*$F_N$ a reactive force, called the Normal force
*$F_f$ a friction force
We can now establish some force/torque balances.
In the vertical ($y$) direction, there no motion because with $\text{N2L}$:
$$\Sigma F_y=F_N-mg=... | {
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Why is total kinetic energy always equal to the sum of rotational and translational kinetic energies? My derivation is as follows.
*
*The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $\bf{ω}$ and with the $i$th particle rotating with velocity $ \textbf{v}_{(rot)i} = \textbf{r... | You're right that the third term does not generically vanish. The key element in decomposing the kinetic energy into rotational and translational parts is that you calculate the rotational kinetic energy about the center of mass.
If the center of mass of the object is at the coordinate origin, and $\mathbf r_i$ is the ... | {
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What is happening when magnetic field lines snap or break? In discussions of sun spots and auroras on Earth, magnetic field lines are often described as "snapping" or "breaking", with the result of releasing charged particles very energetically.
My understanding is that field lines are just a visualization tool. I don'... | You are right: magnetic field lines can't snap or break because they are not physical objects. They are more analogous to elevation lines on a topographical map, or more precisely to lines perpendicular to elevation lines: to the fall lines on a ski slope. However, they do describe something physical, which is the ma... | {
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Why use virtual displacement to make constraint forces vanish? Why do we use virtual displacement to vanish work done by constraint forces instead of the actual displacement?
| *
*In a nutshell, d'Alembert's principle states that a certain vector should be perpendicular to a constraint surface, i.e. perpendicular to all its tangent vectors, i.e. perpendicular to all infinitesimal virtual displacements. See also e.g. this related Phys.SE post.
*Note that at this stage, we are just trying t... | {
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What is the energy of a (conduction/valence) band? I'm trying to figure out what determines the energy of the bands, either conduction or valence band. Mostly I can read about the bandgap energy, which is mostly just the difference between $ E_C $ and $ E_V $ but there are also more concise expressions like $ E_g(T) = ... | Really it depends how deep you want to go! I hopefully will keep it fairly simple.
If you consider an atom, the energy levels are determined by the orbital the electron is in, calculated from the Schrodinger wave equation. It is a similar concept for a material, albeit complicated by there being a large number more ato... | {
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Is it possible for two observers to observe different wavefunctions for one electron? Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=x) while the other observes the wavepacket localize... | I will confess that this I am not certain on this, as this is a quite odd question. but I have formulated what seems like a very reasonable answer. Also the very first thing to mention is that one cannot physically observe the wave-function, we can only predict how it evolves, and then measure a property of a particle,... | {
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'Why' is the Schrödinger equation non-relativistic? The transition amplitude for a particle currently in one spacetime point to appear up in another point doesn't respect causality which becomes one of the main reasons to abandon non-relativistic quantum mechanics. We impose the relativistic Hamiltonian $H=\sqrt{c^2p^2... | The Schrödinger equation is non-relativistic by construction. It follows from the nonrelativistic classical energy expression by applying De Broglie's idea to replace $(E,\vec p)$ by $-i\hbar (\partial_t, \vec \nabla)$.
| {
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Isn't the disturbance in quantum field an interpretation of quantum wave function? In quantum mechanics, a particle is neither a wave nor a particle but is described by a wave function which does not have a physical interpretation. But in quantum field theory, a particle is a disturbance in the associated field. Isn't ... |
In quantum mechanics, a particle is neither a wave nor a particle but is described by a wave function which does not have a physical interpretation
Note the bold a particle. The quantum mechanical equations , Dirac, Klein Gordon, quantized Maxwell, all describe a single particle.
The postulates of Quantum Field Theor... | {
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What is the difference between a force and a net force? I read in Newton's first law, it states that an object will continue to have a constant velocity unless acted upon by a force whilst for other articles, it states "unless acted upon by a net force." Which one is correct? Are they both interchangeable? Is there any... | Besides the answers already given, you can think of Newton's first law as a special case of Newtons second law. For Newton's second law the "force" is explicitly stated as a "net force", or
$$F_{net}=ma$$
Assuming constant mass, if the net external force acting on an object is zero, then the acceleration of the object ... | {
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How does the Brownian motion of air molecules compare to the threshold of human hearing as a function of frequency? This fantastic question essentially asks what is the noise floor of air? Both the answer given on that thread and the value stated by Microsoft are around -23 or -24 dBSPL.
However, overall loudness is on... | It depends.
*
*The threshold of human hearing is adaptive and varies depending on the preceding noise level (for a couple of hours). After a shift in an anechoic chamber, engineers start hearing how their own blood goes through veins, food being digested, etc. The threshold can not be assigned a "fixed" value. The "u... | {
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Is it always the case that the square root of a lagrangian gives the same equations of motion as the lagrangian itself? Inspired by the Phys.SE post Geodesic Equation from variation: Is the squared lagrangian equivalent? I was wondering if it is always the case that the square root of a lagrangian gives the same equati... | That is rarely$^1$ the case. Sufficient conditions and examples are given in this duplicate Math.SE post.
--
$^1$ An instructive example is perhaps this Phys.SE post: The coefficients of each squared term in the Lagrangian have been carefully fine-tuned to make it work. It is not just $(T-V)^2$.
| {
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What does the uncertainty principle tell us about the harmonic oscillator? For the harmonic oscillator we have $\sigma_x \sigma_p = \hbar(n+1/2) $ and by the uncertainty principle $\sigma_x \sigma_p \geq \frac{\hbar}{2}$.
In one of the exercises I was doing I was asked to comment on this result. This makes me think tha... | I cannot read the mind of the person who asked you to comment, but my guess is that they were looking for something like "In this case, the uncertainty principle doesn't tell me anything beyond what I already knew because it's obvious that $n+1/2\ge 1/2$."
| {
"language": "en",
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On the Application of the Einstein-Brillouin-Keller (EBK) Method Consider the Born-Sommerfeld quantization condition (modified) [see Einstein–Brillouin–Keller (EBK)]
$$I_{i} = \frac{1}{2\pi}S_{i} = \frac{1}{2\pi}\oint p_{i} dq_{i} = \hbar \left(n_{i} + \frac{\mu_{i}}{4} + \frac{b_{i}}{2} \right),\tag{1}$$
when applied... | Hint: Eq. (1) is for a closed orbit, i.e. the particle traverses the interval $[0,a]$ twice, i.e. forth & back. This explains the factor 2.
| {
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Is a capacitor a dipole? A few more questions about understanding dipoles I recently learned about dipoles, according to its definition I was wondering if a capacitor can be considered also as a dipole?
Also I was wondering what is the physical meaning of the dipole moment $\vec{p}=qd$?
And my last question is what is ... | No capacitor is not a dipole it is combination of oppositely charged plates so that electric fireplace within then is zero . The value of electric for any other system is different from that a dipole . The basic motivation for it's study is to understand the change in values of electric field and potential when a sys... | {
"language": "en",
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Error in equations for harmonic spherical wave? I am currently studying Optics, fifth edition, by Hecht. In chapter 2.9 Spherical Waves, the author says the following:
$$\dfrac{\partial^2}{\partial{r}^2}(r \psi) = \dfrac{1}{v^2} \dfrac{\partial^2}{\partial{t}^2} (r \psi) \tag{2.71}$$
Notice that this expression is now... | It's no error. $k$ has dimensions of inverse length, $r$ has dimensions of length, $v$ has dimensions of length per time, and $t$ has dimensions of time.
What you propose is dimensionally incorrect, as $kr$ is dimensionless and $vt$ has dimensions of length. On the other hand, $k(r\mp vt)$ is a valid operation, and it ... | {
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Do atoms absorb the same amount of light? I'm currently working on a project on my own where I'm interested in finding information about an object based on a spectrum. Namely, I want to use the spectrum that I input into my program to be able to analyze what atoms are present in the analyzed object. (I know this is pro... | The amount of light is not a precisely defined quantity here. For your purposes it may be safe to assume that each atom may absorb only one photon, however these photons would have different frequencies. The number of photons of different frequencies absorbed is then proportional to the number of atoms absorbing this f... | {
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Baryon number vs electromagnetic charge, what is the difference? What exactly is a Baryon number? I looked up definition from wikipedia and still struggle to understand this. And how does this differ than the
electromagnetic charge?
My textbook did the following computation:
It is calculating the electromagnetic charg... | Baryon number ($B$) and electric charge ($q$) are different quantities.
Both quantities are useful because both obey their own conservation law.
To make this more clear consider the proton ($p$), the neutron ($n$),
their constituent quarks ($u$ and $d$), and the electron ($e$).
Proton and neutron have the same baryon n... | {
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In metals, the conductivity decreases with increasing temperature? I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.2 Material equations says the following:
Metals are very good conductors, bu... | In a metal, the number of charge carriers is almost unaffected by temperature. There is an enormous number of free electrons per unit volume (compared to a semiconductor like germanium), so Fermi Dirac statistics applies.
As the temperature increases, the scattering events of the electrons with the phonons increase bec... | {
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Does a book get lighter if you rearrange the letters? I'm wondering if the information lost by rearranging the letters of a book is measurable as a difference in its initial and final mass.
Choose a long, random string over an alphabet, say $\{0,1\}$, of length $N$. It should be random in the sense that it is incompres... | Well if you compress the more ordered book into code and write the code in a new book. Yes, the new book will be lighter.
The original book will not be lighter because although you have ordered the letters according to a scheme that a given algorithm can compress well, how does the Universe know which algorithm you are... | {
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Difference between massless neutrino flavours The title pretty much sums up the the question, what's the difference between massless neutrino flavours?
I know that an electron neutrino interact with the electron and so on for the muon and the $\tau$. I also get the basic of how they enter the standard model Larangian w... | Experimentally, we can determine the "flavor" of a neutrino by colliding it with matter and seeing the products. Electron/anti-electron neutrinos collisions more commonly produce an imbalance in observable electron/anti-electron count, and similarly for muon/anti-muon and tau/anti-tau neutrinos.
On an aside, this is ho... | {
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Time evolution of the standard deviation of an operator How would I find the time evolution of the standard deviation of an operator? For example, how might I find the time evolution $\sigma_x (t)$ of the standard deviation
$\sigma_x = \sqrt{ \langle \hat{x}^2 \rangle - \langle \hat{x} \rangle^2}$
of the position opera... | In case you're planning to actually compute it, here's how:
Derivatives commute with operator averages in the Heisenberg picture (since your state is constant; alternatively in the Schrodinger picture, you can take derivatives of the state), so you can do something like this:
$$\frac{d}{dt}\sqrt{\langle x^2\rangle-\lan... | {
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What is a wavepacket without a photon? There are a lot of questions on this site about photons and wavepackets.
Relation between radio waves and photons generated by a classical current
This one lists a lot of them as reference. None of them in detail specifically answers my question.
What happens when a photon hits a ... | A wave packet is just a localized superposition of waves. In the context of QM it describes the probability of detecting a particle like any other quantum wave function.
| {
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How to infer about the volume of the body from measuring the mass of the object in 2 different liquids? While solving a problem on hydro statics subject I saw a statement that argued that if I know the weight of the object in the air and then I know the weight of the object in the water.so when I subtract between the w... | There can be two possible cases
Case 1
The statement in your book might be wrong (Though more likely possibility is that statement in the book might be correct but what you read /inferred from it is wrong).In that case you are right. We can only subtract two quantities with same dimensions. In your case it is mass.
We... | {
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Pseudo Force and Inertial and Non-Inertial frames In the figure given below is block placed on an incline $\theta$. Now the lift is accelerating upwards with an acceleration $a_0$. Now if we make our measurements from the lift frame we will have to apply a pseudo force $-ma_0$. Which will have two components one in the... | Perhaps you can see it better with this figure.
to apply NEWTON second law , you have to calculate the components of the position vector to the mass in inertial system.
$$\vec{R}= \pm\begin{bmatrix}
x_0 \\
y_0 \\
\end{bmatrix}=\pm
\left[ \begin {array}{c} s\cos \left( \vartheta \right)
\\ s\sin \left( \varthe... | {
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Is excited electrons life-time = half-life? Everywhere I read something related to excited electrons in atoms I only see the word "lifetime".
For example most excited states have a lifetime of a few nano to micro seconds and metastable states have a lifetime of a few miliseconds as far as I understand.
Shouldn't we say... | Half-life ($t_{1/2}$) and lifetime ($\tau$) are related to one another.
$$
t_{1/2} = \tau \ln(2)
$$
From the equivalent equations,
$$
N(t) = N_0 \left(\frac {1}{2}\right)^{\frac{t}{t_{1/2}}} \\
N(t) = N_0 e^{-\frac{t}{\tau}}
$$
It’s just convention; forms adopted by different fields. I would say the half life approac... | {
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Has the ballistic motion of an electron in gravitational field ever been measured? Reading this question I thought of an argument that an electron's trajectory would bend in the gravitational field despite the electron's being incapable of strong interaction; this would then disprove the conjecture stated in that quest... | EDIT: see the answer by S. McGrew. Turns out there's some clever methods of releasing extremely low energy free electrons, which makes gravitational effects just measureable.
Let's think about the size of the effect you're looking for.
Suppose you sputter off an electron with a very low energy of around 1 eV. This corr... | {
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Which force is doing the work here? My text book (Fundamentals of Physics by Halliday, Resnick, and Walker) mentions the following about the work done in internal energy transfers:
An initially stationary ice-skater pushes away from a railing and then slides over the ice. Her kinetic energy increases because of an ext... | I think I agree there is something off in that quoted section.
The purpose of that section is not practical application, the purpose is to bring an abstract concept into focus. And that means the usual simplifications for practical purposes should not be used.
There is a physics joke that goes as follows: When Arnold S... | {
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Why does water keep dripping out of the bucket even after the faucet is turned off? So I just noticed that when I filled my bucket with water until it overflowed and then I turned the faucet off, the water kept dripping for like 20 seconds. Why does this happens? Shouldn't it have stopped dripping sooner after I turned... | There are two possible scenarios here, which I don't know which it is unless I have more details.
One is where you fill slowly until overflow just begins to happen; this results in Adrian's answer, which I will elaborate on a bit:
The surface tension of water means that the water level can rise above the level of the b... | {
"language": "en",
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Why is internal resistance of battery considered outside the terminals although it is present between the terminals inside the battery In ideal battery the internal resistance is zero whereas in non-ideal battery there is some internal resistance now this internal resistance is due to the battery material (electrolyte)... | Replacing a real battery by an ideal battery (voltage $V_0$)
and an internal resistance ($R$) is just a model.
You can apply Kirchhoff's voltage law to this model and derive
a relation between the real voltage $V$ and current $I$:
$$V=V_0 - R I. \tag{1}$$
On the other hand:
You can take a real battery, and measure
the... | {
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Finding acceleration of center of mass in cart pole problem In this link about finding equations of motion of cart pole problem,
There is an equation about acceleration of center of mass of the pole.
Screenshots of them below.
I don't understand why they have more than two parts about angular acceleration - $\varepsi... | When you transfer velocity from one point to another in a rigid body you end up with an equation like
$$ \boldsymbol{v}_P = \boldsymbol{v}_C + \boldsymbol{\omega} \times \boldsymbol{r}_P $$
Acceleration is just the time derivative of the above with
$$ \begin{aligned}
\tfrac{\rm d}{{\rm d}t} \boldsymbol{v}_P &= \boldsy... | {
"language": "en",
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Is $E^2-P^2=m^2$ true only for free particles? I'm studying Friedman and Susskind's Special Relativity and Classical Field Theory and follow them in using $c=1$.
They derive the above relation by first using Lagrangian of a free particle $\mathcal L=-m\sqrt{1-v^2}$ to show that conjugate momenta are given by $P^i = mU^... | It does depend on what is meant by P, and E.
If $E^2=P^2-m^2$, even with forces, the particle would have a constant velocity.
I think that the canonical forms are more commonly used, so
$(E-V)^2=({\bf P}-q{\bf A})^2+(m+S)^2$, with $\bf P$ the canonical momentum,
and $(V,{\bf A})$and S vector and scalar potentials.
| {
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The average velocity of a SHO is 4 times the maximum velocity? I am looking at simple harmonic oscillators. The maximum potential energy is equal to the maximum kinetic energy:
$k {x_{max}}^2 = m {v_{max}}^2 \rightarrow x_{max}=v_{max}\sqrt{\frac{m}{k}} = \frac{v_{max}}{\omega}$
Also, the time to find the average speed... | You made a simple mistake converting time period to angular frequency: $\omega = \frac{2\pi}{T}$, so $\frac{1}{T} = \frac{W}{2\pi}$.
I will not work it through for you, but you should get the answers you are looking for.
If you are interested in working out max velocity and average velocity in general, i.e. not just a... | {
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Work Equals Torque? Horsepower, Pulleys While reading one definition of torque, I saw its units are Newton-meter, which is the same as work. But sources usually make it a point to emphasize "even though both work and torque units are the same, they should not be confused, they are very different". One is like an objec... | You can still do work by applying a torque, but that is not the same thing as torque being equivalent to work. An easy way to see this is that you can apply a constant torque, but the work done by the torque depends on the angle through which the torque rotates the object.
In your wrench example, assuming maximum torqu... | {
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Energy of a rotating wheel Why does a rotating wheel have kinetic energy $K=\frac{1}{2}mv^2$ associated with its movement?
I will clarify.
Let's say I have a rotating wheel in an empty void which has an angular velocity $\omega$, then its total energy will be $E=\frac{1}{2} I \omega^2$, as the wheel is not moving. Now ... |
Find the rotational and translational kinetic energy of a ball with rotational energy $\frac{1}{2} I\omega_0^2$ initially if put on a slant.
\begin{align*}
\frac{1}{2} m v^2+ \frac{1}{2} I\omega^2&=\frac{1}{2} I\omega_0^2\\
\frac{1}{2} m v^2+ \frac{1}{2} \alpha mR^2\omega^2&=\frac{1}{2} \alpha mR^2\omega_0^2&(\text{d... | {
"language": "en",
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Does entanglement of a bipartite PPT state $\rho$ imply entanglement of $\rho + \rho^{\Gamma}$? Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As separability of $\rho$ is ... | I believe this is not true, based on https://arxiv.org/abs/quant-ph/9903012, Eq. (8), where a given $\rho\in\mathcal{M}_2(\mathbb{C})\otimes\mathcal{M}_N(\mathbb{C})$ can be always written as
$$\rho=\frac{\rho+\rho^{T_A}}{2}+\frac{\rho-\rho^{T_A}}{2}=\rho_s+\sigma_y^A\otimes B,$$ i.e., a separable part $2\rho_s=\rho+\r... | {
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Are there any quantum effects which we can see in every day life? I am wondering if there are any natural phenomenon in every-day life that cannot be explained by classical physics but can only be explained by quantum mechanics. By classical physics, I mean Newtonian mechanics and Maxwell's electromagnetic theory.
I kn... | The way the question is phrased, specifically: what is not explained by Newton or Maxwell, there are 2 obvious candidates:
*
*The stability of matter: atoms governed by Maxwell's equations and Newtonian mechanics decay immediately due to EM radiation.
*The lack of an Ultraviolet Catastrophe: thermal radiation has i... | {
"language": "en",
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In the generation of X-Rays, why the incoming electron generated from anode knocks out the K shell electron rather than outer shell electrons? When the high energy beam of particles or photon hits the cathode, electrons from $K$ shell are knocked in the generation of characteristic x-rays. Why do inner electrons get kn... | Well, The story begins by the physicist C. Barkla. He noticed that atoms appeared to emit two types of X-rays. The two types of X-rays differed in energy and Barkla originally called the higher energy X-ray type A and the lower energy X-ray type B. He later renamed these two types K and L since he realized that the hig... | {
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Right vs Left Derivatives Let $\theta$ be a fermionic quantity and $f(\theta)=f(0)+\theta\frac{\partial f}{\partial\theta}=f(0)+\frac{\partial_r f}{\partial\theta}\theta$. Under a variation $\theta\mapsto\theta+\delta\theta$ we have
$$f(\theta)\mapsto f(\theta)+\delta\theta\frac{\partial f}{\partial\theta},$$
using the... | *
*Yes, by definition the Grassmann parity $|\delta z|$ of a variation $\delta z$ of a supernumber $z$ (of definite Grassmann parity) is the same as the Grassmann parity $|z|$ of the supernumber $z$ itself:
$$|\delta|~=~0.\tag{1}$$
*Perhaps OP is wondering about the following question.
Question: How does an infinite... | {
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To what precision is the heat capacity an extensive quantity We know that heat capacity is an extensive quantity, basically meaning for double the amount of substance you need double the energy to increase temperature. To what extend is this actually true, like:
*
*Are there e.g. (measurable) surface effects?
*Have ... | Classically, the heat capacity of all substances would follow the law of Dupont and Petit with the same value per atom, so then there are no surface effects.
In the quantum regime, at low temperatures, one would expect a surface effect because the vibrational modes are different at surfaces. For measurements one would ... | {
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Why are there no operators in classical mechanics? I have been wondering to find the answer of some fundamental questions in quantum mechanics and the answer to the above question will help me to clear doubts of quantum world
| Yes, there are operators in classical mechanics; one can formulate classical mechanics in terms of Hilbert space and operators, the only difference with quantum operators is that classical operators is that the former commute, see https://en.wikipedia.org/wiki/Koopman%E2%80%93von_Neumann_classical_mechanics for more in... | {
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Locally flatness in general relativity My professor made following statement:
The spacetime of GR is curved in the presence of strong gravitational fields. The effects of curvature
manifest themselves at large distances. Locally, one can choose a flat Minkowskian metric.
I dont get it:
I... | I think now I understand my confusion:
One can choose riemann normal coordinates to get the canonical form of the metric (which can be the minkowski metrik). So locally we can choose a flat metric.
I thought, this implies that spacetime is locally flat without curvature.
But the curvature is described by the riemann te... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Impulse operator on real wave function The impulse operator in quantum mechanics is given by
\begin{align}
\hat{p} = \frac{\hbar}{i}\nabla
\end{align}
As a Hermitian operator, the expected value of this operator $\langle{p}\rangle = \langle \psi|\hat{p}\psi\rangle$ should be real. However, for a real wave function $\ps... | The possibility that is not accounted for in the question is that the integral may be zero. In fact, it can be shown that a wave function corresponding to a stationary state can always be chosen real, and the momentum of a stationary state is definitely zero.
Another insight may come from considering wave function
$$\p... | {
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In a Parallel Radioactive decay , what is the ratio of sum of stable nuclei of the two products? Here is the full Question
The question gives you two Rate constants and asks for what time will the ratio of "sum of stable nuclei of Ca:Ar" be equal to 99.But what is this ?If i think of number of nuclei in terms of conce... | You're misreading the problem.
Let the numbers of potassium, calcium, argon nuclei be $N_\text{K}$, $N_\text{Ca}$, $N_\text{Ar}$, all of which are functions of time.
You are correct that the ratio
$$\frac{N_\text{Ca}}{N_\text{Ar}}$$
is independent of time. But the question is about the ratio
$$\frac{N_\text{Ca}+N_\text... | {
"language": "en",
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If a pendulum of mass $m$ and length $l$ is considered quantum mechanically, what will be the approximate ground state energy? I have seen that the solution of the quantum pendulum is obtained by solving the Mathieu's equation form of the Schrodinger equation and it also depends on a parameter 'q' called the energy bar... | I could not find the reference I mentioned where they perform perturbation theory starting from both the quantum harmonic oscillator limit and the quantum rotor limit and connect their solutions and energies with the exact solutions of the quantum pendulum. Here I will just briefly scheme the basics of this procedure.
... | {
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Why Einstein action is not Yang-Mills action for gauge theory of Poincaré algebra? It is well known, how to construct Einstein gravity as gauge theory of Poincare algebra. See for example General relativity as a gauge theory of the Poincaré algebra.
There are
*
*Construction of covariant derivative:
$$ \nabla_m = \p... | The YM action for the Porcare group as you write down is perfectly allowable in the effective field theory framework, as long as you double check that pathological tachyons are absent. There are tons of papers devoted to the so called $f(R)$ and $f(T)$ theories with higher-order Lagrangian terms (like $R^2$, $T^2$).
Th... | {
"language": "en",
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Optics: mirrors While drawing ray diagrams for plane and spherical mirrors, what is generally taken as the point of observation?
Eg, If a concave mirror is presented with, say a wire turned into a triangle, placed from focus towards the mirror, the image can be obtained following rules of reflection but where would the... | We can think of every extended source as a collection of point sources. So, let us only think of point sources. When we draw ray diagrams we often say that an image of a point is formed where 2 rays meet. I was just as baffled as you are but then it clicked of what i think is corect.
Image forming means seeing. Our ey... | {
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Negative energy density There are some universe models where $\Lambda < 0$. In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time? Such that, $\Lambda < 0$... | Negative energy density may exist theoretical and the closest believed real phenomenon is the Casmir effect. If it exists, it does cause repulsion of ordinary matter, though how it happens is a little more indirect.
When there are two plates, that are very closely placed in an environment that has 0 energy density, the... | {
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Choice of representation $R$ in the $\rm SU(2)$ Yang-Mills action $\frac{1}{g^2} \mathrm{Tr}_{R} (F\wedge \star F)$ Usually we write the Yang-Mills theory with gauge group $G$ as
$$\frac{1}{g^2} \mathrm{Tr}_{R} (F\wedge \star F)$$
But here we need to choose what $R$ is. There are several cases one may expect:
*
*$R$ ... | The action should be invariant under the action of gauge group, therefore, you have to construct something, that when considering the action of gauge group remains unchanged.
Assume that the field stregth tensor $F$ transform under some representation of $G$:
$$
F \Rightarrow U^{i_1 \ldots i_n}_{j_1 \ldots j_m} F
$$
T... | {
"language": "en",
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Clarifying the relationship between pressure and temperature? From the ideal gas law, we are aware that PV = nRT, which seems to suggest a direct relationship between pressure and temperature, or that as temperature increases, pressure increases.
In my geography book, however, it is written that "The equator receives d... | The ideal gas law takes no account of weather patterns over land and water; it takes no account of atmospheric circulation. So the connection you attempt to draw between the gas law and weather reporting is invalid.
Furthermore, the gas law's relationship between temperature and pressure you cite requires that the volu... | {
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Classical Wave theory and the photoelectric effect I read that according to classical wave theory, light is viewed as a wave whose intensity is continuously variable. And for this reason, it is unable to explain the photoelectric effect. My questions are:
*
*What does "continuously variable" mean?
*How does the int... |
Electrons ejected from a sodium metal surface were measured as an electric current. Finding the opposing voltage it took to stop all the electrons gave a measure of the maximum kinetic energy of the electrons in electron volts.
What does intensity "continuously variable" mean?
It means that for any frequency one ... | {
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Is the entropy of a rotating body largest when the axis of rotation passes through it's centre of mass? I am looking for an answer to the observation that a body always rotates about its centre of mass when freely tossed. It can be explained if the entropy is highest in the case when the axis passes through the com, ho... | This is easily explained by Newton's second law. If there is no net force applied to a body then the center of mass will not accelerate. it will either be stationary or move in a straight line. The only allowed motion is a rotation about the center of mass.
Changes in entropy, arise from the exchange of energy at some ... | {
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Is energy required in generating magnetic field in simple resistance circuit? Consider a simple resistance circuit with a cell and a resistor. It is stated that energy stored in cell appears as heat in resistance as current flows in ideal circuit (neglecting EM radiation) as whole.
POWER/RATE OF HEAT GENERATION = POWER... |
1.Is energy needed to create magnetic field in general?
Yes. When you are using circuit theory the mechanism for dealing with magnetism is called inductance and is usually represented by the variable $L$. The inductance gives the total magnetic field so that you can still use a lumped element approach and do not need... | {
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Are there non-constant potentials that result in eigenstates of the Hamiltonian that are all plane waves? It is commonly known that the eigenstates to the Hamiltonian of a constant potential are plane waves, aka
$$
V(r) = V_0 \Rightarrow H\psi = n \text{ with } \psi = \exp\left(\frac{ip}{\hbar}x\right)\exp\left(-i\frac... | No, there are no other potentials with the same eigenstates. (set $\hbar = m = 1$ for clarity)
Suppose there is another Hamiltonian $\hat{H}'$, such that the eigenstates of $\hat{H}$ and $\hat{H'}$ are the same, the complete, orthogonal set $| \psi \rangle$ (obtained via the spicy spectral theorem). Then, we know that... | {
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What is the point of a voltage divider if you can't drive anything with it? The voltage divider formula is only valid if there is no current drawn across the output voltage, so how could they be used practically? Since using the voltage for anything would require drawing current, that would invalidate the formula. So w... | The first and most obvious use of the voltage divider is to use your intended load as one of the resistors in the divider. This works well if the load is well approximated as a resistor.
That's how the in-cable volume regulator of the headphones work.
When the load is not linear, one can simply make it more linear by p... | {
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Exact Diagonalization of a tight-binding Hamiltonian with periodically alternating potential My question is, can we diagonalize a general Hamiltonian ,
$$H=-t\sum_i^N (c_i^{\dagger}c_{i+1}+h.c.)+\sum_i \mu_i c_i^{\dagger}c_i$$ where,
$$\mu_i=\begin{cases}
\mu_0, &\text{if mod}(i,p)=0 \\
0, &\text{otherwise}.
\end{cases... | I think this should be treated as a tight-binding model with period $p$ and $p$ states in every site. One could do it by first introducing operators:
$$a_{l, \nu} = c_{pl +\nu}, \nu=0,...,p-1,$$
and then looking for plane wave solutions $\sim e^{ikl}$.
| {
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Specific note that is not clear for me in and the derivation of maxwell equation $\oint \vec{B} \cdot d \vec{r}=\mu_{0} I_{e n c}$ I know this is not the full equation but right now in this path of the course that what we learned so far.
We studied that a wire along the $z$ axis produces magnetic field $\vec{B}=\frac{\... | I don't quite understand what your instructor was telling you, but since the field due to the wire is $\propto 1/\rho$, when integrating along a hypothetical Ampèrean loop around the wire, the factor of $dr = \rho \, d\varphi$ cancels out the $1/\rho$ of the field, leaving the trivial integral $\int_\text{loop} \, d\va... | {
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Relative Velocity of two particles If two particle are neither approaching towards nor receding away from other then their relative velocity is non zero.
How is this possible??
| Turning my comment into an answer ...
The velocity can be non-zero because velocity is represented by a vector, so the vector changes when the direction changes, even if the magnitude ("speed" in this case) remains constant.
For example, consider the case of two objects in circular orbits around the barycenter. If I am... | {
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Enthalpy during compression of water What happens to the temperature of water when compressed?
Enthalpy $H = U + PV$.
$H$ is conserved in a closed system. By which I mean adiabatic and negligible external work applied.
We compress a litre of water to 10 bar (say). This requires negligible work because water is almost... | Enthalpy certainly isn't conserved in a system you do work on. However, entropy is if you do the work quasistatically and adiabatically. Thus, you seek $\left(\frac{\partial T}{\partial P}\right)_S$, the temperature rise upon isentropic compression. Applying the triple product rule and a Maxwell relation, we have
$$\le... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Doppler effect observed on pendulums I wanted to investigate the doppler effect on pendulums and set up an experiment where:
*
*The bob of a pendulum is a speaker which emits a specific sound frequency.
*Directly underneath the lowest point of the pendulum sits a microphone that observes the frequency being emitted ... | Your formula will give the velocity at any height on the swing down, and that can be used in the Doppler equation.
Recording the sound is not a problem, but measuring the (variable) frequency may be a challenge. If you can freeze (or video) the display on an oscilloscope, you might measure the period of each cycle of t... | {
"language": "en",
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Why didn't heavier elements settle at the core of the solar system? As the solar system formed, why didn't all of the heavier elements such as iron, collect where the sun is leaving the lighter elements in the outer solar system?
| That is actually somewhat the case...
The planetesimals formed in the inner Solar System were rocky planets (our terrestrial planets evolved from these), whereas the outer planets (the gas giants) in the cooler zone evolved from lighter elements such has hydrogen and helium.
This is of course an incomplete answer. From... | {
"language": "en",
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Insulator or conductor with different boundary conditions I'm studying the 1-D SSH model. It's a toy model for a topological insulator. Here's the reference I'm using. If the hopping amplitudes $v$ and $w$ are equal, then with periodic boundary conditions we have a conductor. If however, we take open boundary condition... | Are you refering to fig 1.4 in the paper you cite as evidence for an enegy gap at $u=v=1$? If so, you need to realize that in the that plot the authors are using a very small (10 site) system. The gaps between the eigenvalues are therefore due to the finite-size discreteness of the eigenvalues $E_n=\pm 2\cos k$ wit... | {
"language": "en",
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What is the probability that two chemical species of binding energy $E$ will be bound? This may seem like a very simple question, but I've been agonising over it for days. What is the probability, $p$, that two chemical species with binding energy $E$, will be bound.
My first instinct is that
\begin{equation} \tag{1}\l... | The answer is not a simple function of binding energy E. What you need to know is the equilibrium constant $[AB]/[A][B]=K=\exp (-\beta {{G}_{0}})$, where ${{G}_{0}}$ denotes the free energy difference at reference concentrations. Doubling the concentration of unbound A & B will quadruple the concentration of bound A... | {
"language": "en",
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Derivation of Schwarzschild metric I was studying the book of Hartle on general relativity. In chapter 9, "The Geometry Outside
a Spherical Star", he suddenly introduces a metric named Schwarzschild metric and then goes on describing the geometry it produces. I did not quite get how exactly this was a metric generated ... | A typical method is to make the ansatz that the spherically-symmetric metric has the form
$$ds^2=-A(r)dt^2+B(r)dr^2+r^2(d\theta^2+\sin^2{\theta}d\phi^2)$$
and determine which functions $A(r)$ and $B(r)$ make the metric satisfy the Einstein field equations, which in vacuum are $R_{\mu\nu}=0$ everywhere (except perhaps a... | {
"language": "en",
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What is the maximum deflection angle of a pendulum in a car, when the car, initially at rest, accelerates suddenly? I was doing Kleppner-D.-Kolenkow-R.J. and I came across the following problem:-
A pendulum is tied vertically to a car at rest, the car suddenly accelerates at a rate A. Find the maximum angle of deflect... | General relativity tells us that gravity is equivalent to acceleration. In this case the pendulum suddenly finds itself in a system where gravity has shifted backwards by an angle with a tangent of a/g. Being a pendulum it will swing toward this new equilibrium, and momentum will carry it an equal angle beyond.
| {
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Lagrangian potential for Newtonian gravity In the Wikipedia site for Lagrangian (field theory) the Lagrangian density for Newtonian gravity is given by
$${\cal L}(\mathbf{x},t) = \frac{1}{2}\rho(\mathbf{x},t)\mathbf{v}^2 -\rho(\mathbf{x},t) \Phi(\mathbf{x},t) – \frac{1}{8\pi G}(\nabla\Phi(\mathbf{x},t))^2$$
I understa... | TL;DR: JoshuaTS' answer is exactly right: (Minus) the 3rd term ${\cal V}_3=\frac{1}{8\pi G}(\nabla\Phi)^2$ is the energy density of the gravitational field.
*
*In total OP's Lagrangian density contains 3 terms: ${\cal L}={\cal T}_1-{\cal V}_2-{\cal V}_3$. Here ${\cal T}_1$ is a kinetic term for matter, while ${\cal V... | {
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Relativity without constancy of light speed Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive:
$$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$
$$t' = \frac{t+\kappa vx}{\sqrt{1+\kappa v^2}}$$
$\kappa = 0$ denotes Galilean and $\kappa < 0$ deno... | $\kappa > 0$ represents Euclidean geometry, in which the time axis is equivalent to (and freely interchangeable with) the spatial ones. In other words it acts like a fourth spatial dimension.
So you can for example take a left turn into the time axis and go forward, then turn around and go back in time. Many consider... | {
"language": "en",
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How do I interpret uncertainty in velocity greater than the speed of light? I just studied Heisenberg's uncertainty principle in school and I came up with an interesting problem.
Assume an electron which is moving very slowly and we observe it with a distance uncertainty of say $\Delta x=1\times10^{-13} \text{ m}$ if... | What you've discovered is that "normal" Quantum Mechanics is incompatible with relativity. As Valter Moretti pointed out, using a relativistic expression for momentum solves this problem. There are, however, more problems that cannot be solved by simply using relativistic expression for energy and momentum. For example... | {
"language": "en",
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Need Help Understanding Why $\Delta \vec{v}$ is Perpendicular to $\vec{v}$ I am confused about the statement of how vector $\Delta \vec{v}$ is perpendicular to vector. I highlighted the statement in pink. I ended up copying the image of the right vector $\vec{v}$ in the velocity isosceles triangle and moved its tail to... | This is only true if ${\bf v}$ just changes direction but keeps the same length. If ${\bf v}$ and ${\bf v}+ \Delta {\bf v}$ have the same length, then
$$
{\bf v}\cdot {\bf v}= ({\bf v}+ \Delta {\bf v})\cdot ({\bf v}+ \Delta {\bf v})= {\bf v}\cdot {\bf v}+ 2{\bf v}\cdot \Delta{\bf v}+ (\Delta {\bf v})\cdot (\Delta {\bf... | {
"language": "en",
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Why can't photons cancel each other? The textbook argument against photons canceling each other draws upon the conservation of energy. Does this mean that energy conservation is a "stronger" principle than superposition? Waves in other media than the EM field, e.g., sound or water, do cancel out---presumably by passing... | We should be careful to distinguish interaction, correlation, annihilation and interference. Photons do not interfere. Any interference takes place at wave function level, so impacts the probability of finding a number of photons. Photons can annihilate but this requires two photons of a least 511 keV each in order to ... | {
"language": "en",
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How to derive this $\dfrac{dT}{d\tau}$? I am studying the paper "Gravitational field of a particle falling in a Scharzschild geometry analyzed in tensor harmonics" by Zerilli. The author calculates the gravitational radiation emitted by a particle falling along a geodesic into a Schwarzschild black hole.
The stress ene... | The equations of motion for a geodesic starting at rest at infinity are very simple, and as usual the key is to start with the constants of motion:
$$ -1 = \frac{d z^\mu}{d\tau}\frac{d z^\nu}{d\tau} g_{\mu\nu} = -\left(1-\frac{2m}{r}\right)\left(\frac{d T}{d\tau}\right)^2 + \left(1-\frac{2m}{r}\right)^{-1}\left(\frac{d... | {
"language": "en",
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Does dark matter follow all principles of regular physics? Is dark matter bound by all the laws of regular physics?
i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation.
What about Newton's laws of motion (since all of Newton's laws assume an interaction between particles)?
|
Is dark matter bound by all the laws of regular physics?
We call "physics" our mathematical modelling of the world's behavior, so dark matter will be covered by its laws eventually. Its behavior diverges from the behavior we manage to observe with great accuracy for matter in much closer vicinity to us, so either da... | {
"language": "en",
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Why are aerodynamic / streamlined shapes always stumpy at the front? I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:
The usual explanation is that the ... | Any speculation about what shape might be best is meaningless without specifying the flow conditions. For the keel on a boat, the main one is the Reynolds Number, a parameter that is proportional to the the length multiplied by the speed.
In most low-speed applications, a sharp leading-edge is not the best. With any in... | {
"language": "en",
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At which point in the universe history will inflation prevent galaxies feeding from intergalactic matter? It's my understanding that galaxies formed from accretion of intergalactic matter around supermassive black holes. As the universe expands the amount of matter entering a galaxy decreases, until at some point this ... | Although galaxies are moving apart from one another faster and faster, it is only at the largest scales where the average energy density of matter is smaller than the dark energy density. Clusters and superclusters of galaxies are unlikely to dissolve because they are more energy-dense than dark energy, and they will o... | {
"language": "en",
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Why is maximal kinetic energy lost in a perfectly inelastic collision? A perfectly inelastic collision is one where both of the colliding objects stick together and move as one.
My question is, why, of all possible combinations of final velocities that conserve momentum, does this one lead to the greatest loss in kinet... | If I understand your question correctly, then the answer would simply be realizing what the C.O.M frame does to a two-body problem. If you recall a two body problem can be converted into a one-body problem in the C.O.M frame. This means that equations of motion for the now new one body are equivalent to the original sc... | {
"language": "en",
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Is it possible the many-worlds hypothesis explains dark matter? To provide context for the title, is it possible that dark matter is just gravity from other 'branches' of the universal wave function that have split from ours, that are weakly interacting with the gravity in our branch? Is this an idea anyone has explore... |
Dark matter candidates arise frequently in theories that suggest physics beyond the Standard Model, such as supersymmetry and extra dimensions. One theory suggests the existence of a “Hidden Valley”, a parallel world made of dark matter having very little in common with matter we know. If one of these theories proved ... | {
"language": "en",
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Why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$? My question is in regard of the following snippet provided by my textbook.
So why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$ or $270$?
So the magnitude of the induced EMF will be determined by the rate at whic... | The field mentioned in this discussion is from an external source. The maximum flux does occur when the normal vector representing the loop is parallel to the field (The field is passing through the loop), as indicated in the diagram. The maximum “rate of change” of the flux occurs when the plane of the loop is parall... | {
"language": "en",
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How is melting time affected by flow rate and temperature of surroundings? Suppose you have a solid sphere of m, where m is an element with freezing point of 0 degrees Celsius.
In one scenario, you place your sphere in a (“static”) 25 degree Celsius environment and measure time, t, until melting. The sphere is fixed an... | The answer to this is very subtle, and is the core subject of interest in convective heat transfer. In either case, you’ll find that most engineers would model either scenario using Newton’s law of cooling:
$$Q = hA(T-T_{\infty})$$
where $Q$ is the heat transfer rate, $A$ is the surface area of the object in contact wi... | {
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Inverse metric for 3+1 decomposition I was trying to read about 3+1 decomposition of spacetime from section 12.2 of Padmanabhan's book Gravitation Foundations and Frontiers. However, other sources can also provide the context for my question.
Once the coordinate system $(t,y^\alpha)$ has been adopted on the spacetime f... | Well, maybe there is a more clear way to do this, without some guessing. I would start from the definition of an inverse matrix:
$$
g^{\mu \alpha} g_{\alpha \nu} = \delta_{\nu}^{\mu}
$$
Or more concretely:
$$
\begin{pmatrix}
-N^2+N_\gamma N^\gamma & N_\alpha\\
N_\alpha & h_{\alpha\beta}
\end{pmatrix}
\begin{pmatri... | {
"language": "en",
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What is the force required to tilt a rectangular object when exerted at 2 different locations?
I have a question to confirm if my "hunch" is correct. Assuming 2 scenarios of similar force but is exerted at different height of a rectangular object with a pivot point (shown in the pic below). Based on Torque (perpendicu... | I see you have got the definition of torque wrong. It is not just force multiplied by distance from pivot point. Torque is distance from pivot point multiplied by the amount of force which is perpendicular to the direction of point of application from pivot point. It can also be stated as the full force multiplied by t... | {
"language": "en",
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Lorentz boost expressed as Hyperbolic versors At this link https://en.wikipedia.org/wiki/Versor#Hyperbolic_versor it is claimed that an hyperbolic versor, defined as:
$$
\exp(a \mathbf{r})=\cosh a+\mathbf{r}\sinh a
$$
where $||\mathbf{r}||=1$ correspond to a Lorentz boost. But I cannot work out a proof. Can anyone help... | You can write $\mathbf s$ as a sum of parallel and perpendicular parts which commute and anticommute respectively with $\mathbf r$. Then you have $\mathbf r\mathbf s-\mathbf s\mathbf r = 2\mathbf r\mathbf s_\perp$ and $\mathbf r\mathbf s\mathbf r = s_\|-s_\perp$ and I think you'll get the Lorentz transformation.
If you... | {
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Rewriting the Laplacian on a curved manifold I guess there is a sense in which the following is true:
"The Laplacian written on a Riemannian manifold $(M,g)$ can be seen as adding a coordinate dependent mass field to the Laplacian on Euclidean space."
*
*Can someone kindly refer me to a place where this is exactly ... | *
*Recall that the quantum Hamiltonian$^1$ $\hat{H}=-\frac{\hbar^2}{2}\Delta$ for a point particle is (in the Schrödinger representation) associated with the Laplacian $\Delta$.
*The corresponding classical Hamiltonian is $H=\frac{1}{2}\sum_{i,j=1}^np_i g^{ij} p_j$.
*In flat space the Hamiltonian for a free partic... | {
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Why rotating objects stops? Sorry for asking this simple question, but really I couldn't find a good document discuss what I need exactly.
I am implementing a flight simulation, but my question is related to physics rather than aerodynamics so I find to ask the question to physics experts.
Suppose that I am having a cu... | The answer to your question is that in real life any time an object moves in air there are surface forces developing due to the boundary layer of air.
The aerodynamics of rotating objects are very complex (see the magnus effect for example), but the end result is that there is net torque applied opposing the rotationa... | {
"language": "en",
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When did the Big Bang happen? Did the Big Bang happen at a point? goes through the fact that the Big Bang happened everywhere at the same time. John Rennie's answer explains this as being a consequence of all points in space beings squished into a single point, so technically the Big Bang happened everywhere. But, when... | The real answer is that the big bang singularity isn't part of modern cosmology, in part because of the horizon problem. The big bang model is only valid back to an early era when the scale factor was nonzero; before that, something else happened. Various inflationary models are the most popular, but there are others. ... | {
"language": "en",
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Is the cosmic event horizon viewed from Andromeda different from the one viewed from Earth? If the most distant galaxies we see in deep space are in proximity of our cosmic event horizon does it mean that if we were on Andromeda galaxy and looking in the same direction we would see objects that are beyond the Earth cos... | If you're talking about the observable universe as bordered by the cosmic microwave background (which is not a true event horizon, just an opaque surface), then yes, the portion of the universe observable from Andromeda is slightly shifted relative to ours. They'd see different patterns in the cosmic microwave backgrou... | {
"language": "en",
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Frequency and intensity in photoelectric effect In the explanation of photoelectric effect it is written that intensity and frequency of radiation have different results i.e. higher intensity means greater number of emitted photoelectrons and higher frequency means greater kinetic energy of emitted photoelectrons.
But ... | Whatever you have said is right but only one thing wrong. "But according to Einstein's theory number of photoelectrons is affected only by the intensity of light not its frequency." That's is not in Einstein's theory. You can check it in any book. It is written as "The photocurrent increases if the intensity of
the inc... | {
"language": "en",
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Is my understanding of how a force is applied through a string correct? Let there be a situation where a force 'F' is acting on one end of an in extensible string which is connected to a box named 'A' resting on a friction less horizontal surface through the other end.
The Force F is transmitted through the string and... |
As the box starts to accelerate, for a very small moment there is slack in the string which makes the tension force 0 for a brief moment.
Wrong.
Tension is zero before the force is applied. Once the force starts acting and the string becomes taut, the block and string gain the same acceleration and the string doesn't... | {
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What colour would neutronium be? Everything we learn about colour in relation to matter is based on "normal" matter that has electrons around it. Absorption and emission of electromagnetic radiation is explained in terms of electrons transitioning between quantum levels with different colours being caused by the energy... | Neutrons are composed of quarks and quarks do have electric charge and so clearly photons would interact with neutrons. Light interacts with all charged particles and not just electrons. Because of its nature, neutronuim
would behave like a black body and therefore would emit light in the form of black-body radiation. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575000",
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Reason for peaks in graph of binding energy per nucleon A similar question was asked before, but it asked for a different thing. My question here is: What is the reason for spikes in this graph? The graph initially has spikes and then shows a constant decrease. Is it related to something called magic numbers as it is s... | There are two effects that lead to the presence of the small jagged peaks and valleys in the binding energy per nucleon. (The main shape of the curve is given by the semi-empirical mass formula, derived from the liquid drop model of the nucleus. The model has a positive binding energy proportional to the number of ad... | {
"language": "en",
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Energy Conservation in Rolling without Slipping Scenario
A solid ball with mass $M$ and radius $R$ is placed on a table and given a sharp impulse so that its center of mass initially moves with velocity $v_o$, with no rolling. The ball has a friction coefficient (both kinetic and static) $μ$ with the table. How far do... | I am not sure about this solution. I would set up the equations of motion as follows.
Translational motion:
there is only one force acting on the system, which is dynamic friction of modulus $F_d=\mu mg$. The motion is uniformly decelerated with acceleration $a = \mu g$. The (horizontal component of the) translational ... | {
"language": "en",
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Inconsistency in applying work-energy theorem in the classical problem of a kink on an inclined wedge Consider the typical problems of mechanics where we had to find the velocity for some mass which reaches bottom of a wedge after metting some changes in the wedge angles (kinks). The following is a particluar type of p... | The work energy theorem is alright. The problem is that you are not taking $N_x$ into account in momentum conservation
| {
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"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Lorentz Force on a Current Carrying Wire Does the Lorentz Force on a Current Carrying wire given by the equation
$$\mathbf{F} = I \int \text{d}\ell \times \mathbf{B}$$
constitute an action reaction pair? That is, if i have two arbitrarily shaped current carrying wires, is it true that force on any one of them due to th... | Newton's third law in modern terms states conservation of momentum. Electrostatic forced conserve $P_{kin}=\sum_i m_i p_i$ but magnetic forces do not , as argued by @Rohit. In the presence of electromagnetic fields the conserved momentum is $P = P_{kin} + P_{pot}$, where $P_{pot} = - \sum_i q_i \vec A_i$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Elastic moduli interrelations for homogeneous isotropic materials The classical equation for the Young modulus in elasticity theory for a homogeneous isotropic material in one-dimension is commonly given in the formulation
$$ E = \frac{\sigma}{\epsilon} \quad,$$
with $\sigma$ as the uniaxial stress, and $\epsilon$ as t... | The Bulk modulus in terms of the Lame parameters is
$$
\kappa =\lambda +\frac 23 \mu.
$$
It is not simply proportional to Youngs modulus. In stretching a wire we do not only make it longer, but we also allow its thickness $W$ to change. Young's modulus therefore needs to know Poisson's ratio, which is defined by
$$
\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575626",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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