Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Velocity of the touching point between 2 rotating circles I'm trying to solve the following problem that I'm having a hard time with:
We have circle ${\Sigma}_1$ with center $O_1$ and radius $a_1$. The center $O_1$ is also the center of the static orthonormal coordinate system $R_0 (O_1, x_0, y_0, z_0)$. ${\Sigma}_1$ r... |
The velocity at the contact point I is:
$$v_I=\omega_1\,a_1-\omega_2\,a_2$$
thus the components of the velocity in $R_0$ coordinate system are:
$$\vec{v}_0=v_I\,\begin{bmatrix}
\cos(\varphi)\\
\sin(\varphi)
\end{bmatrix}$$
with $\varphi=\int\,\omega_3(t)\,dt=\omega_3\,t\quad $ if $\quad\omega_3=$constant
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Electric field energy density In vacuum, the energy density of the electric field is given by $\mathcal{E}=\epsilon_0\frac{E^2}{2}$ with $E$ the total electric field present. So, if you have a static $E_0$ and dynamic $e(t)$ field, the energy density becomes
$$\mathcal{E}=\epsilon_0\frac{\left[E_0+e(t)\right]^2}{2} = \... | It is correct. Note however that, when dealing with periodic electric fields, one would often be interested in the energy density averaged over a period, where the cross-term disappears:
$$e(t) = E_1\cos(\omega t),\\
\bar{\mathcal{E}} = \frac{\omega}{2\pi}\int_{t_0}^{t_0 + 2\pi/\omega}dt \frac{\epsilon_0|E_0 + E_1\cos ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Why supersymmetry can only be verified in high energy level? I'm wondering why supersymmetry can only be verified in high energy level,can we check supersymmetry in low energy physics?
| It can! The question isn't very specific, so I'll only answer broadly. Of course it all depends on what you mean by high and low energies, but many naive supersymmetric models you might write down will affect low-energy physics. If your model predicts that the proton will decay quickly, or that a new particle will be c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562961",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How is the frequency of a wave defined if it propagates on three different directions? Let's consider a wave which propagates on 2 or three directions, like for instance an electromagnetic wave inside a rectangular waveguide totally closed on two ideal conductor surfaces:
The walls of the guide force the wave to assum... | Aside from the doppler effect or relativistic dialation, the frequency of a wave is generally determined by its source. If an electromagnetic wave enters a wave-guide at an angle, it reflects from the walls of the tube. The reflections interact with each other to produce an interference pattern. Depending on the angle... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Will magnets lose strength over time when coupled to another magnet? Will magnets lose strength over time when coupled to another magnet ?
Im designing a part (c. 200g) which needs to be held in place, but also be removable, so looking into a pair of magnets (neodymium or other) to do this, the magnets will for >99% of... | My answer is, in general, no. Ferromagnetic materials usually, on a microscopic level, have domains in which the magnetic moments are all aligned in one direction. There is a famous picture from R. W. DeBlois that shows domains within a sample of nickel (the arrows indicate the domain orientation):
Kittel (Introduct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563252",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
Cavitation plus sound equals light? “If an underwater bubble is collapsed by loud sound, light is produced and no one knows why” says one of those click-bait social media posts with no citation—“light produced” and “no one knows why.” Is either true?
Not something I heard during my studies of underwater acoustics—but ... | There exist models describing sonoluminescence example
Single bubble sonoluminescence is not an exotic phenomenon but can quantitatively be accounted for by applying a few well-known, simple concepts: the Rayleigh–Plesset dynamics of the bubble’s radius, polytropic uniform heating of the gas inside the bubble during ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563372",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
How to read some certain band diagrams? I have some problems on understanding some semiconductors band diagram.
For instance, I understand quite well something like this:
I understand it because it is quite simple: there are the energy levels (Conduction, Fermi, Intrinsic Fermi and Valence) at right and left, and the ... | Both confusing diagrams show heterostructures (i.e. one device containing different materials), and the different materials can have very different properties.
In the first figure:
*
*At the left is a metal. By definition, a metal has no band gap. So only the Fermi Level is shown.
*In the middle (circled in green) i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Instantaneous power for a variable force I know that instantaneous power is defined as the time derivative of work done. For a constant, it is easy to prove that this is just the dot product of force and velocity.
However, is Instantaneous power even equal to to F.V for a variable force, and if so, how do I prove it.
I... | Given that work is the area under the Force-Distance curve
$$W = \int F(t)\,{\rm d}x$$
and power is the time derivative of work, and for each small-displacement increment ${\rm d}x = v\, {\rm d}t$
$$ P = \tfrac{\rm d}{{\rm d}t} W = \tfrac{\rm d}{{\rm d}t} \int F(t)\,v\,{\rm d}t = F(t)\,v $$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563569",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Magnetic permeability of a mixture How do you calculate the magnetic permeability of a mixture of two substances (e.g. alumina powder and boric acid) knowing the permeability of each one of them?
| This is a very difficult theoretical problem and to illustrate its inherent difficulty consider the following two idealized cases:
*
*take a set of infinitely long but magnetizable ($\mu_r$) cylinders of arbitrary cross sectional shape. Assume that they fill the space at a fraction of $p$ and there is a bias field pa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Emission of radiation by a charged particle undergoing acceleration An electron is travelling along the x-axis. It then changes its direction by 45 degrees. Will it emit an electromagnetic wave?
| How does the electron change its direction? Something must be responsible for the distraction from its geodesic orbit.
The electron in a wire as part of an electric current collides with the subatomic particles of the metal and moves in a zigzag manner. Any acceleration of the electron, be it a stop (negative accelerat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564094",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why torque on current carrying circular loop in uniform magnetic field is differs from results of $\mu \times \vec{B}$ if we apply calculus method We have a current carrying circular wire kept in uniform magnetic field $\vec{B}$, as shown, I tried to derive the torque $\vec{\tau}$ acting on it
For 2 elemental parts on... | There are actually two cross-products, and you've ignored one of them.
I'm going to assume that the magnetic field is in the plane of the loop, pointing along $\mathbf{\hat{y}}$, while the loop is in the $xy-$plane.
The infinitesimal torque is given by $$\text{d}\boldsymbol{\tau} = \text{d}\mathbf{F}\times \mathbf{r}.$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564297",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
On Validity of the formula for gravitational potential energy The formula for gravitational potential energy,
$$-G\frac{m_1 m_2}{R},$$
is found by using the fact that the change in potential energy is equal to negative of the work done ( by conservative forces). One of the assumptions is that the 2nd larger mass remain... | Suppose the (spherically symmetric) bodies are identical and initially separated by distance $R$. We will now take both bodies to infinity synchronously (that is keeping the midpoint in one place – relative to the fixed stars!) If we measure distance $r$ from the centre of mass of the system, that is midway between the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564413",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
How does one (physically) interpret the relationship between the graviton and the vielbein? One can naturally think of the vielbein $e_\mu^a$ as a gauge field corresponding to local translation invariance. Moreover, the metric may be written
$$g_{\mu\nu}=e_\mu^a e_\nu^b \eta_{ab}.$$
I have always seen the graviton $h$ ... | The linearized metric, also known as the Pauli-Fierz field $h_{\mu\nu} =: \frac{1}{\kappa}\left(g_{\mu\nu} - \eta_{\mu\nu}\right)$ can be shown (for example see here: Boulanger et al.) to self-couple perturbatively (to each order in $\kappa$, starting with the cubic one) to the Hilbert-Einstein action expanded in terms... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564544",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
} |
Why does glass, in spite of being amorphous, often break along very smooth surfaces? When a crystalline material breaks, it often does so along planes in its crystalline structure. As such this is a result of its microscopic structure.
When glass breaks however, the shapes along which it breaks are typically very smoot... | Stress gets concentrated at the tip of a crack or at an inside corner. See this video and this video. Note that in these simulations the crack does not propagate in a perfectly smooth path. In the second simulation, inhomogeneities in the medium affect the propagation direction.
If you examine the exposed surface of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564751",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "38",
"answer_count": 3,
"answer_id": 1
} |
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... | One of the the big differences between work and torque:
Work - work is involved when a force is exerted through a distance and some component of that force is parallel to the displacement of the object that the force is acting on. The SI units of work are Newton-meters.
Torque - torque is a force whereby a component o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564843",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Do Maxwell's equations contain any information on the time evolution of the current density $J$? The answers to Can the Lorentz force expression be derived from Maxwell's equations? make clear that Maxwell's equations contain only information on the evolution of the fields, and not their effects upon charges; the Loren... |
Does this imply that any arbitrary time evolution of current density can be defined beforehand, and the corresponding fields always found that satisfy Maxwell's equations?
Yes, given a charge density $\rho(\mathbf r,t)$ and a current density $\mathbf J(\mathbf r,t)$, you can find fields $\mathbf E(\mathbf r,t)$ and $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564983",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
} |
Newtonian Limit of Schwarzschild metric The Schwarzschild metric describes the gravity of a spherically symmetric mass $M$ in spherical coordinates:
$$ds^2 =-\left(1-\frac{2GM}{c^2r}\right)c^2 \, dt^2+\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2+r^2 \,d\Omega^2 \tag{1}$$
Naively, I would expect the classical Newtonian limi... | If $\frac{2GM}{c^2R}<<1$ both expressions are valid as approximations.
But the second one presents the expression $dr^2 + r^2 d\Omega^2$ detached. And that is the square of a generic path element in spherical polar coordinates.
Being an elementary spatial path, it can be then replaced by: $dx^2 + dy^2 + dz^2$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
} |
Are there any quantum effects which we can see in every day life? I am wondering if there are any natural phenomenon in every-day life that cannot be explained by classical physics but can only be explained by quantum mechanics. By classical physics, I mean Newtonian mechanics and Maxwell's electromagnetic theory.
I kn... | Polarized light is a decent candidate for this, because it is relatively easy to produce and stays coherent over large distances when passing through air.
For a demonstration, you only need a laser or LCD monitor and three linearly polarizing filters. Let's say, the light emitted by the monitor is diagonally polarized.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565248",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 9,
"answer_id": 5
} |
Validity of a differing frame of reference than that used in Landau and Lifshitz's solution For the following problem, first problem in chapter 2 (page 16) of Landau and Lifshitz's Classical Mechanics text:
I am trying to see whether the picture I drew when originally solving the problem before looking at the solution... |
Solution
The momentum component is to be constrained constant along the Plane$(x)$ and not the Normal$(y)$. This is because the potential energy is independent of $x$.
$$U=\begin{cases}U_1&y<0\\U_2&y>0
\end{cases}$$
So, we have the equations
\begin{align*}
v_1\sin\theta_1&=v_2\sin\phi_1\tag{1}\\
\frac12mv_1^2+U_1&=\fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565341",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Probability current density confusion As we all know, the probability current density in quantum mechanics is defined as: $$\textbf{J}=\dfrac{\hbar}{2mi}(\Psi^* \nabla \Psi-\Psi \nabla \Psi^*)$$ For simplicity let us work in one dimension and let us suppose a wave function $\Psi= A\ \text{cos}\ {kx}$. Applying the abov... | The continuity relation holds for solutions of the Schrodinger equation. $A\cos (\omega t - k x)$ is not a solution.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565449",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Understanding the derivation of the formula for change in internal energy of a gas in an enclosed cylinder The derivation:
Let, there is $m$ mole of gas, $p$ amount of pressure, $v$ amount of volume, $T$ amount of temperature, and $U$ amount of internal energy. Now, $dQ$ amount of heat is supplied to this gas so that ... |
We derived the equation considering the volume constant or $dV=0$, so
we can't use this equation when the volume is changing. Am I
incorrect?
No, it's not correct. The change in internal energy for an ideal gas, for ANY process, is given by
$$ dU = nC_{v}dT$$
This is a consequence of the ideal gas law and the unique ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565660",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is it possible to derive the Maxwell equations directly from the Electromagnetic tensor? The Lagrangian for ED without Gauge fixing term is given by
$$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu},\quad \text{where}\quad F_{\mu\nu}:=\partial_\mu A_\nu-\partial_\nu A_\mu.$$
I was wondering if this step, defining $F_{\mu\... | The second and third Maxwell's equations can be written covariantly as
$$
\varepsilon^{\mu \nu \sigma \tau} \partial_{\mu} F_{\nu \sigma} = 0.
$$
In gauge geometry, this equation is known as the (Abelian) Bianchi identity (not to be confused with the Bianchi identity from Riemannian geometry, which is related, but diff... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
By what mechanism is a growing tree root able to lift heavy concrete pavement? A tree root lying under several square meters of 100mm thick concrete pavement can cause the pavement to lift up as it grows.
What forces are involved in creating this lift?
I vaguely understand that the growth process is a matter of cell di... | The fundamental mechanism is hydrostatic pressure, which in a plant is called turgor pressure:
Cell expansion and an increase in turgor pressure is due to inward diffusion of water into the cell, and turgor pressure increases due to the increasing volume of vacuolar sap. A growing root cell's turgor pressure can be up... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566087",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 0
} |
Why we add the individuals quantities to find the total amount of a system's "quantity"? Is this by definition of "total"? Why to find e.g. the total energy of a system of particles (non-interacting) we add their individual kinetic energies? Is total kinetic energy defined to be that sum? It may seem obvious for scalar... | It is not always true that we do such addition to find the “total”. For example, if you have a system composed of two sub-systems, $A$ and $B$, then the volumes add as you discussed: $v=v_A+v_B$. The masses also add: $m=m_A+m_b$. But the density does not add: $$\rho=\frac{m}{v}=\frac{m_A+m_B}{v_A+v_B}\ne \frac{m_A}{v_A... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why do photons follow the geodesic curvature of the gravitational field instead of the spacetime curvature? If mass merely 'curves' spacetime, why do photons follow the geodesic path of the gravitational field (path A) instead of the spacetime curvature itself (path B)?
It seems, as if, the gravitational field exerts a... | I think the lines in the drawing describe the tidal deformation of a local cube, which is not the same as a geodesic.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566232",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 1
} |
How can multiplication rule in sigfigs make sense? I've been going through significant figures video on khan academy and it says the product of two numbers cannot have more significant digits than the significant digits in any of the inputs.
Example:
length = $301 m$
width = $2 m$
area = $301*2 = 602 m^2$
But since the... |
How can the error in area be as large as $50$ while using a $1\: \rm m$ precision ruler?
Well, because you are multiplying the reading of that "precise" ruler with a large number ($\approx 300$ in your case). So even an error of $0.5 \: \rm m$, could scale itself up and manifest itself as a $\approx 150 \:\rm m^2$ er... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566486",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What does it mean for a physical phenomenon to be "fundamentally random"? I read on Wikipedia:
Quantum mechanics predicts that certain physical phenomena, such as the nuclear decay of atoms, are fundamentally random and cannot, in principle, be predicted.
What does that mean exactly? I thought nothing can be predicte... | In you case of radioactive decay, it means that the times of decay of a sample of radioactive material occur completely randomly. The sample will have quite a lot of radioactive nuclei. When a single nucleus decays is random. Decay may occur early or late, there is no way to predict which. After an x second measurement... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566573",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Will Pascal's law apply to two immiscible liquids that have the same density? In other words, does Pascal's law apply to emulsions? As far as I know, immiscible liquids form emulsions when mixed, so will Pascal's law apply to this emulsion?
| To a good approximation yes. Pascal's law won't hold exactly for an emulsion because the interface between the two fluids will have a non-zero interfacial tension, and there will be small excess pressure inside the emulsion droplets given by the well known formula:
$$ \Delta P = \frac{2S}{r} $$
where $S$ is the interf... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566740",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Comparing a 100W and a 40W light bulb that only emits a specfic frequency I'm sort of confused by this... let's just say the bulbs only emits green light, and we compare a 40 W and 100 W bulb (identical except one is brighter than the other), since the frequency of light emitted from both bulbs are the same, does it me... | Every photon of a particular frequency has the same energy. This means that a 100W source of photons of a specific frequency will emit more photons per second than a 40W source of photons at the same frequency.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566838",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Why is electric field inside a conductor non-zero even if there is point charge placed inside it? If I place a point charge $q$ inside a conductor, The electric field at any point inside it will be non zero ($Kq/x^{2}$). If we draw a Gaussian surface inside the conductor, the net enclosed charge will be $q$ that will p... | The free charges will reposition in such a way that the field vanishes, because in a conductor there is no other force acting on them. This also means that any point charge inside a closed surface will be compensated by conducting electrons.
All of this only holds at scale much larger than atomic . At atomic scale the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566908",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
What is “spectral turnover”? In a paper which deals with the spectra of radio frequency cosmic events, the word “spectral turnover” is used. What is “spectral turnover”?
| It just means, that when you look at the spectrum on a log-log plot, that it become flat or even reverses slope, in contrast to a steeper power law spectrum at higher and/or lower frequencies.
There are various physical reasons why a turnover might appear in the spectrum (e.g. a flattening in the underlying power-law d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Work done when lifting an object at constant speed A previous post (What Is Energy? Where did it come from?) defines work qualitatively as "a process in which energy is transformed from one form to another form". And mathematically, work is defined as:
$$\Delta KE=\int_{C} \vec{F}\cdot\mathrm d\vec{r}$$
But if you imag... | Assume you have two opposite forces of the same magnitude acting on a particle. The total work is zero, and there is no change in kinetic energy. However one of the forces made positive work on the particle and the other negative work. Whatever did positive work lost some form of energy, and the one that did negative w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567240",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 7,
"answer_id": 2
} |
Will cutting sand paper with scissors make the scissors sharper or duller? This is a little question that I have been wondering when I need to cut sand paper with scissors.
Sand paper can be used to sharpen knives etc. when applied parallel with the blade surface. Also it can be used to dull sharp edges when applied no... | The answer given by Duller is halfway correct.When the blade is very blunt , the point of contact is flattened or shapeless. When you cut sandpaper , it being abrasive itself it abrades the blunt edge at the cutting point , this making the scissors sharper than before. The finer the sandpaper the better the sharpening.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 3,
"answer_id": 2
} |
Confusion over spontaneous symmetry breaking Consider a complex scalar field with Lagrangian
$$\mathcal{L} = (\partial_{\mu} \bar{\phi})(\partial^{\mu} \phi) - V(\phi)$$
with potential
$$V(\phi) = \frac{1}{4}\lambda(\bar{\phi}\phi - \eta^2)^2$$
The model is invariant under global $U(1)$ phase transformations. The minim... | Even though this question has been successfully answered already, I just wanted to emphasize some points about spontaneous symmetry breaking.
When a symmetry is 'spontaneously broken', it is not true that it is no longer a symmetry of the theory, as is so commonly implied in textbooks. Indeed, the broken symmetry is st... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567436",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Common misunderstanding of Birkhoff Theorem I just found a paper "On a common misunderstanding of the Birkhoff theorem". This means that inside a spherically symmetric thin shell there is no gravitational force, BUT there is time dilation, and so the interior solution is NOT the Minkowski metric, right?
| In GR you use coordinate charts which cover some specified open region of spacetime. You are allowed to choose the region that you want to cover, and it may be all of spacetime or it may be some smaller region.
For a spherically symmetric thin shell, if the chosen region is strictly inside the shell then it is the Mink... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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... | Just came up today. Needed a comparator that would trip at 2.8V. Had a 3.3V supply. So, voltage divider of 3.32k/17.8k driving one input of comparator (current load is negligible), test voltage to other input. Just everyday EE.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567978",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 8,
"answer_id": 7
} |
Is magnetic field due to current carrying circular coil, zero everywhere except at its axis?
Consider a current ($I$) carrying circular coil of radius$ R$ of $N$ turns.Consider a rectangular loop $ABCD$,where length $AB=CD=\infty$
Performing the integral for axial points,
$$\int_ {-\infty}^{\infty}\vec{B}\cdot \vec{dx... | Not only must you assume that lengths AB and CD are infinite, but also BC and DA. So the field strength is zero all along DA, AB and BC for the rather unsubtle reason that these three sides are all an infinite distance from the current-carrying loop (whose field falls off as $r^{-3}$ and faster).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/568056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Do Maxwell's Equations depend upon an orientation of space? Even when we cast Maxwell's Equations in as coordinate-independent form as possible, $dF=0$ and $d \star F = J$, we still have to make use of the Hodge star $\star$ which is defined relative to an orientation. It doesn't look like the equations are preserved ... | It is only necessary that the space of solutions is preserved. (And, after all, elementary particle reactions do not preserve parity.) But the physical solutions to Maxwell's equations are unchanged if you choose a different orientation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/568170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Question on Feynman's Proof of Energy Conservation
Since this is two-dimensional motion, why would $m(dv/dt)$ not have some directionality in addition to being the rate of change of the magnitude of momentum? Is Feynman assuming that the directionality doesn't change in infinitesimal time?
| If $v$ is treated as the velocity instead of the speed of the object then $m(dv/dt)$ has direction and would be simply the rate of change of momentum, rather than the rate of change of the magnitude of the momentum.
The reason for this imprecision probably stems from the two definitions of kinetic energy: it can be cal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/568296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why do electrons have fixed energy levels? I understand that electrons do not orbit the nucleus, instead they have a higher probability to be found at some specific regions.
But what makes they appear more frequently in the orbital regions? There are equations (like Schrödinger) that are able to describe this wave func... | Nobody knows the answer. All we know is that quantum mechanics is in perfect agreement with experiment. All you can do is to critically investigate any intuitive concepts that you may have that are incompatible with quantum mechanics.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/568554",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Conservation Laws and What Happens if they go Wrong? I read this excellent article on the Conservation Laws and also I was taught in Schools that Conservation Laws cannot be proven and only verified. I was wondering what would actually happen if a Conservation Law turned out to be false?
I know it would question our me... | My volume of Symon's Mechanics address' this question:
The conservation laws are in a sense not laws at all, but postulates which we insist must hold in any physical theory. If, for example, for moving charged particles, we find that the total energy, defined as (T + V) [kinetic plus potential], is not constant, we d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/568908",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
Work done on object being carried upwards If you carry a book in your hands, and you walk up stairs with a change in height of $h$, the net work on both you and the book would be $-M_{\mathrm{total}}gh$ since $W = - \Delta U$. This would be due to gravity.
However, when considering the book alone, the work done by the ... | Yes , you are . Net work done on an object is equal to change in kinetic energy and not in potential energy.
$\therefore$$W_g+W_n=0$ since the book is rest from your frame .I am assuming you hold the book still during your climb.
$W_g=-W_n$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/569042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Whats the center of gravity/mass of this figure? I've tried figuring this out, but I can't seem to find a way to find it, since I dont have any other information to calculate something. The only thing I could find out was that its possible to use symmetries to find out the center of mass/gravity.
My intuition tells me... | It can be shown by exclusion:
A and D are not possible, because they are to far of.
You can draw a ellipsoid around B, which contains the area left of B and is symmetric. Still, you are left with the two tails on the right.
only C is left, therefore its C.
Maybe one can use the fact, that this figure is "stackable" to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570373",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Do adjacent sarcomeres oppose each other during contraction? A sarcomere is the contractible portion of the muscle cell. And here is a figure of three sarcomeres in series before and after contraction:
I was taught that the thick fiber, myosin, pulls on the thin fiber, actin. I am confused as to how contraction can ha... | I think your two pictures show how the whole system can contract.
Maybe abstract it as a bunch of springs and balls in series.
s = spring
M = myosin (imagine it as a ball localized at the M line)
A = actin (imagine it as a ball localized at Z line)
Your first pic looks to me like
...MsAsMsAsM...
and the springs are all... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570469",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 2
} |
Different variations of covariant derivative product rule This is a follow-up question to the accepted answer to this question: Leibniz Rule for Covariant derivatives
The standard Leibniz rule for covariant derivatives is $$\nabla(T\otimes S)=\nabla T\otimes S+T\otimes\nabla S$$
so for $T\otimes\omega\otimes Y$ this wo... | In a chart $U_\alpha : M \rightarrow \mathbb{R}^n$, you have $\nabla_X = X^\mu \nabla_\mu$ so the result follows by patching on overlapping charts.
The last answer in the question cited gives all the details required to be honest.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Is there an equivalent of computation of physical processes in nature? I was watching a waterfall in the Austrian Alps. There were thousands of water droplets falling down, splattering on the stones below. I thought - how does nature find out so quickly where each droplet of water should go?
To find out what happens to... | Nobody knows, and perhaps nobody will ever know.
The only things that we can possibly know about the universe are the things that we can somehow observe, directly or indirectly. There's no way to gain information about how the universe operates other than observing its operation and thinking of rules that seem to expla... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570845",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 12,
"answer_id": 2
} |
Why do complex number seem to be so helpful in real-world problems? Complex numbers are often used in Physics especially in Electrical Circuits to analyze them as they are easy to move around like phasors. They make the processes easy but it seems kind of amusing to use something which has no other real world analogous... | Physics is replete with second-order differential equations, resulting e.g. from an action of the form $\int L(t,\,q,\,\dot{q})dt$ being stationary. If they are linear, or we approximate them as such close to an equilibrium, we get something like $\ddot{q}=Aq$ for some constant $A$, which is typically nonzero. A stable... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570908",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
What do I need to build special relativity? If I postulate the principle of relativity and the constancy of the speed of light for every inertial observer can I then prove all SR?
Or do I need some other postulate?
For example: do I need to also postulate the structure of the Lorentz transformations or the Lorentz tran... | By more modern standards,
if you are looking for a proof
(and not just handwaving arguments),
you'll need to clearly state assumptions about the "space[time]"
and other mathematical structures that model the physics
that you are using as your starting point,
and formulate your postulates in precise terms
with those str... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/570980",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 1
} |
Optimizing engines to produce a certain torque and net force Say we have $n$ engines sitting on a rigid body. Each engine has position $R_i$ and points in a certain direction and generates a force in that direction, $F_i$. The magnitude of that force ($k_i$) follows this constraint: $0 \leq k_i \leq m_i$. In other word... | The problem is one of least squares (until the point where the magnitude is capped).
Consider the target force vector $\vec{F}$ and the target moment vector $\vec{T}$ as the right-hand side $\boldsymbol{b}$ of a linear system of equations, and the vector $\boldsymbol{x}$ of $n$ force magnitudes is the unknowns.
$$ \mat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571117",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does one divide by a vector when calculating pressure? Sir $P=F/A$
And since $F$ and $A$ both are vectors but $P$ is scalar. So doesn't it violates that "Division is NOT defined for vectors"?
| Pressure is actually $$P=\frac{F_\bot}{A}$$ where $F_\bot$ is the force component perpendicular to the surface in question, and $A$ is the area of the surface.
Therefore, there is no "division by a vector" here. Certainly, the area vector is used in various areas of physics; this is not one of those areas (pun always i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571209",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
What does the statement "A concave mirror always forms a real image of a virtual object" mean? My Physics teacher made the statement in a recent class.
"A concave mirror always forms a real image of a virtual object"
But, what did he mean by a virtual object? What does this statement exactly mean?
PS : I have just st... | A real image is formed when the rays converge in one point. That means, if an object emits light, and there is an optical system that makes those rays converge, then there is a real image where those rays converge.
On the other hand, a virtual image is formed if the rays do not converge, but their prolongations do. Thi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571351",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How to determine the result of 2D elastic collision
As shown by the image, a disk of radius $R_1$ mass $M_1$ and initial velocity $V_0$ collides with another still disk of radius $R_2$ mass $M_2$. Both disks has no rotation initially. The direction of $V_0$ is indicated by $\theta$. For three situations there are un... | I will post an answer myself, and we can discuss if it is correct.
First, I argue that this problem has a unique and deterministic answer:
*
*If you play pool, you will know that the balls after collision do not have random movement. Two identical hits will produce two identical results.
*This is also required by N... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why is $Q=p$, $P=-q$ a canonical transformation from the perspective of 2 variational principles satisfying boundary conditions? This is to ask a more general question: Landau-Lifshitz say that for the variational principles
$$\delta\int_{t_1}^{t_2}p\mathrm{d}q-H\mathrm{d}t =0$$$$ \delta\int_{t_1}^{t_2}P\mathrm{d}Q-H'\... | It is easy to check that OP's canonical transformation (CT) in the title has generator $F_1=Qq$.
OP's main question about boundary conditions (BCs) for CTs were asked before in great generality in this & this related Phys.SE posts. The latter post proved how pertinent BCs are satisfied for CTs of type 1.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/571828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Confusion on clock synchronization I am reading through Polonyi's Classical Field Theory notes. It begins with a discussion of special relativity, and near the bottom of page 3, it introduces a procedure for synchronizing clocks. I've reproduced the paragraph below.
Let us suppose that we can introduce a coordinate sy... | Yes, it takes an unknown amount of time to arrive, but the clock at $y$ already runs at the correct rate; you only need to set its zero point. So what you do is record the actual reading $t_2$ on the clock at $y$ when the light reflects off the mirror, and then whenever the value $(t_1-t_0)/2$ arrives at $y$, add $(t_1... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/572090",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
At higher temperatures, do metal wires have a greater chance of short circuiting? I’ve read that short circuiting means that a huge amount of current flows through the conductor in an extremely small period of time.
Also, resistance increases with temperature for conductors, right?
So if temperature increases, resistan... | In a tungsten filament light bulb, the temperature and resistance rise rapidly until the power being radiated away equals that being supplied. Normally this occurs at a temperature that is below the melting point of tungsten.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/572375",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
Why are the positive charged particles moving the the right direction?
The following is the description for this figure provided by my textbook:
The paths of different types of radiation in a magnetic field. Using the right-hand slap rule, we see that positively charged particles are forced to the right. [...]
Why a... | Well, the charges seem to come from the bottom of the page, going up: using the right-hand rule you place the velocity vector on the palm of your hand and close your hand towards the direction of the field, here directed upwards. And there it is, the force $\mathbf{F}\propto q(\mathbf{v}\times\mathbf{B})$ is directed a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/572583",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
} |
How do we determine the color of heated glass? If a glass of certain colour is heated, then how can we determine the corresponding colour that it will glow with?
For eg: I saw a question that asked "A blue glass when heated will glow with which colour?" and the answer was stated as "yellow" because "Blue glass appears ... | The spectral emissivity, $e_{\lambda}$, of a surface is the power it emits in a narrow band of wavelengths centred on $\lambda$, expressed as a fraction of the power emitted by a black body of the same area in the same band.
The spectral absorptivity, $a_{\lambda}$, of a surface is the fraction of the incident radiant ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/572698",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Confusion in definition of emf The emf of a cell is defined as the work done per unit positive charge in taking it around the complete circuit of the cell (i.e. in the wire outside the cell and the electrolyte within the cell). But Kirchoff's Second Rule states that the work done in moving a charge around a closed loop... | The emf of the cell is the open circuit voltage at the terminals of the battery (i.e., voltage with no current delivered by the battery). But the cell has internal resistance, $r_b$. So if a wire of theoretically zero resistance were placed across the terminals of the battery the current $I$ that flows results in all t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573032",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Would a moving elementary particle follow the Heisenberg's Uncertainty Principle with respect to itself? An observer at rest or in motion different from the particle cannot determine its momentum and position to great accuracy at the same time. But what if the observer is on the particle itself or moving with the same ... | An electron feels its own field, which gives an infinity that has to be accounted for by renormalization. From this it is clear that the uncertainty relation does not apply to self interaction in QED.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573287",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Anti-gravity wheel? So I was just watching some YouTube videos on a spinning wheel that seemed to "defy" gravity. The creator made two videos on it, the first showing the wheel, and the second with an attempt to explain it. There are the names of the videos:
"Anti-Gravity Wheel?" by Veritasium
"Anti-Gravity Wheel Expl... | This doesn't violate Newton's second law.
Lifting the wheel over his head by holding it on the end of a long handle is hard because of torque (imagine lifting a broom holding it in the middle of the handle compared to just at the end of the handle). If he had been holding the wheel-handle arrangement at its center of m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573406",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Single Planck $h$ constants Planck developed his black body radiation theory assuming that atoms treated as simple harmonic oscillators can stay in states of very much defined energy. If normal frequency of such oscillator is $\nu$, then the energy levels are the multiples of $h \nu$ (that is $E_n = n h \nu$, forgettin... | There are three pillars of experiments that forced quantum mechanics at first as a phenomenological theory and then as a more formal theory of physics with principles and postulates and differential equations.
*
*atomic spectra
*black body radiation
*the photoelectric effect
Bohr's atom tied up the observations ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573524",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Motion of ball (air viscosity concerned) Suppose a ball of mass $m$ is thrown vertically upwards from the ground. I understand that the speed-time graph would be somewhat like a distorted parabola. But what about the velocity- time graph (considering air drag or viscosity)?
According to me it would attain a kind of ter... | Let, the viscous force drag,
$${F}={k}{v}$$ where ${k}$ is a constant and ${v}$ is the velocity at any instant. While moving up (upward acceleration is negative),
$${ma} = {mg} + {kv}$$
$${a}={g} + \frac{kv}{m}$$
While moving down (downward acceleration is positive),
$${ma}={mg}-{kv}$$
$${a}={g} - \frac{kv}{m}$$
From... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is curved space able to change an object's velocity (vector)? I don't really understand what is meant by curved space. Why does mass warp space? Why does curved space alter the velocity of a massive object? Normally to change an object's direction you have to apply some force to overcome inertia. So how does curved... | If you notice in GR, it always mentions space time is curved, it does not mention space is curved. When a heavy object curves space time, not only space component is affected, the time component is also affected. We all travel through time, even an absolute stationary object travels/ is moving in time domain. When a ob... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573709",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 6,
"answer_id": 4
} |
Can a single-slit experiment demonstrate the particle nature of light? Young's two-slit experiment is generally credited for demonstrating the wave nature of light. But what about a similar experiment with just one slit? My understanding is that this will create an interference pattern. Shouldn't that be enough to demo... | There is no experiment that sends light through one slit or multiple slits where a particle pattern, (one line on the screen) is the result. The particle nature is only revealed when individual photons are sent through the slit or slits, but even in single photon experiments the wave nature is still present. Evidence o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573765",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
If the photon is the force-carrier for the electromagnetic force, how does the electric charge of a black hole escape the event horizon? When people speak of the electric charge of a black hole, do we actually mean it affects things outside of the event-horizon or is it just a property it has?
| I'll answer the question in the body of your post and not in the original subject line (on force carriers) which is a different subject.
.
from our reference frame safely outside the black hole, all the objects that fall into it never make it through the event horizon: they appear to get stuck there in a vanishingly th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/573982",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Orbit around irregularly shaped asteroids I'm curious how would one calculate the shape of the orbit around irregular objects (let's call them asteroids).
How do you tackle this problem? How do you write down basic equations?
In classical mechanics we only mention very simplified problems and the force is always centra... | The gravitational potential of an object is
$$\varphi(\mathbf{r})=-G\int\frac{\rho(\mathbf{r}’)d^3\mathbf{r}’}{|\mathbf{r}-\mathbf{r}’|}$$
where $\rho$ is its mass density. (This is just summing $-Gdm/r$ for each bit of mass $dm$ in the object.)
You may not be able to evaluate this integral analytically, but you can al... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574182",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What kind of matrix transformations are allowed in general relativity? In special relativity, one can transform a 4-vector as follows:
$$
x'=\Lambda x
$$
Of course in this case, $\Lambda$ cannot be an arbitrary $4\times 4$ matrix of $\mathbb{M}(4,\mathbb{C})$. For instance, it must invertible. I believe, technically, i... | GR is invariant under diffeomorphisms, i.e. (up to subtleties) any smooth change of coordinates
$$x^\mu \to x'^\mu = x'^\mu(x)$$
This can be non-linear and it definitely includes the Minkowski group as a subgroup.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574317",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Direction of frictional forces on front and back wheels Why are the directions of frictional forces on the front and rear wheels of a moving car in the opposite direction, when the only the front wheels are accelerated (or only the back wheels)?
When the car accelerates, the direction of the static friction exerted by ... | The simplest way to figure out what friction is doing is to see what happens when you turn friction off.
Assume a car on frictionless road.With no friction at all and the car stopped, pushing down on the accelerator makes the rear wheels spin clockwise. They spin on the frictionless surface, the front wheels do nothi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 0
} |
Why does the spring constant not depend on the mass of the object attached? It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the object. Then how is $k$ independent of the mass... | The unit of $k$ is $\frac N m=\frac{kgm}{{sec}^2}/m=\frac{kg}{{sec}^2}$, so $kx$ has the unit of a force, which is explicitly stated in Hooke's law, $F=ma=kx$. This means you can divide the mass out on both sides of the equation. So Hooke's law doesn't depend on the mass attached to a string.
For more information, see ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574540",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 2
} |
Why do electrons flow in the opposite direction to current? I'm 15 and just had a question about physics and electric fields.
I've read that electrons flow in the opposite direction to current. Isn't current the flow of negative charge and therefore the flow of electrons?
Or are they referring to conventional current?... | Looking from a layman perspective:
A flow/current is created only when there is a potential difference. By definition/convention a flow or current always flows from high potential to low potential. E.g. Water flows downwards, air flows from high pressure area to low pressure area and likewise.
In electrical world, this... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Is it possible to cool down air with warm water? Is there some condition in wich the water evaporation can cool down the air even if the water is hotter than the air?
| Certainly; an evaporative cooler(https://en.wikipedia.org/wiki/Evaporative_cooler), also called a water cooler or swamp cooler, cools air by the process of evaporating water. As liquid water evaporates, it becomes much cooler. So even if the liquid water is warmer than the air, the vapor could still be cooler than the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574798",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What will happen if we try to take a voltage reading by keeping it in current mode in a multimeter? There are different modes present in a multimeter. one is
the current mode and voltage mode for their respective measurements. what
will happen if one try to take a voltage reading by keeping it in current mode?
| An ammeter can be thought of as a galvanometer with a tiny shunt resistance in series (so as to not disturb the total current drawn from the source) and a voltmeter can be thought of as a galvanometer with a very high shunt resistance attached in parallel. Ammeters should thus be connected to a circuit in series in ord... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/574888",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is this a solution of Einstein's equations? Take infinite space. $\mathbb{R}^3$ Then cut a sphere (a 3-ball) out of it and discard it.
You now have $\mathbb{R}^3\backslash B_3$.
Now take each point on the surface of the hole and identify it with it's antipodal point on $S_2$. So it is like a self-wormhole.
You now have... | I think this space is a conical defect of order 2 at the center of $\mathbb{R}^3-\{0\}$. This means that any path traversing an angle $2\pi$ at some fixed radius has length $4\pi r$.
This is akin to 2d polar coordinates $ds^2 = 4r^2 d\theta^2 + dr^2$. Indeed the analogous construction is $\mathbb{R}^2$ with the disk $B... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575131",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 1
} |
Interpreting the Negative Sign in Simple Harmonic Motion What I Know:
$$ \vec F = -k \vec x $$
where the negative sign indicates the Force acts in the opposite direction to the displacement.
If we were to take the integral so...
$$\int_{x_i}^{x_f} Fdx = -\Delta U$$
What would the negative sign in this instance represen... | The -kx is the force exerted by the spring as it is stretched (or compressed) away from the equilibrium position. Your integral is the work done by the spring (which is negative when being stretched). To get the increase in energy being stored in the spring, you need the work done by an external force.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575237",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why does the Standard Model predict zero mass for all vector bosons? This video from 37:33 argues that the Standard Model predicts zero mass for all vector bosons as follows:
*
*Gauge bosons must have gauge invariance.
*For a vector field $A$ define a transformation $\alpha(t,x,y,z)$ which acts on $A$ such that $A\r... | The massive intermediate vector boson theory is not renormalizable. Also it is not gauge invariant. The Standard Model therefore starts out with massless gauge bosons and later adds the mass using the Higgs mechanism. Gerard 't Hooft then succeeded in renormalizing the theory, for which he obtained the Nobel prize.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575637",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Closed form solution of the normal density of a superfluid for the Bogoliubov spectrum I've been trying to solve the following definite integral
$$
\int_0^\infty dx\, x^4\, \frac{e^{\sqrt{x^4+2 x^2}/Tp}}{\left(e^{\sqrt{x^4+2 x^2}/Tp}-1\right)^2}\, ,\quad Tp = \frac{T}{Un}
$$
This is the density of the normal part of a ... | Since the integral depends only one parameter $Tp$, a good approach is to evaluate it numerically, since all you need is the dependence on this parameter. One could also try to evaluate analytically limiting cases: $Tp \ll 1$ and $Tp \gg 1$.
It is possible that by a clever substitution this integral can be reduced to o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/575873",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Can a photon increase its frequency by bouncing against a mirror moving toward it? As discussed in preceding questions, photons can lower their frequency after a reflection happens and radiation pressure sets the mirror in motion.
I wonder if the opposite can happen, i.e. increasing a photon frequency by transfering mo... | Conserning the first question, yes. The reasoning is the same, as in that post. Write the conservation of energy and momentum:
$$
\begin{align}
k + m v &= k^{'} + mv^{'} \\
k + \frac{1}{2} m v^2 &= k^{'} + \frac{1}{2} m v^{'2}
\end{align}
$$
Where unprimed indices denote the initial momentum of the photon and velocity ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576017",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Use of a geometric series sum in derivation of Bose-Einstein distribution In the following Wiki derivation of the Bose-Einstein distribution, a geometric sum is used to make the following step
$$
\sum_{n=0}^\infty\left (\exp \left (\frac{\mu -\epsilon}{k_B T}\right)\right)^n = \frac{1}{1-\exp\left(\frac{\mu -\epsilon}... | The chemical potential of a Boson gas is always negative or (at worst) zero. (See here for why.)
Since the system is considered to be non-interacting (ideal), the Hamiltonian is just the kinetic energy. The lowest energy is thus the $\epsilon_0=0$ state. This means that in general $\epsilon\geq0$, and so $$\exp{\left(\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why should the particles meet at a common point? I saw a question in my physics book asking for the time when all the three particles (each at the corner of an equilateral triangle and each having constant velocity v along the sides of the triangle) meet at a common point.
I can't find the reason why these particles s... | The question says that the particles always point towards each other. This is a very famous question in India for Jee's preparation for kinematics. Here is the question:
Three particles A, B, and C are situated at the vertices of an equilateral triangle ABC with sides d at t = 0. Each of the particles moving with cons... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 1
} |
Can rockets fly without burning any fuel with the help of gases under extreme pressure only? Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of rockets?
If it is done to create a greater reaction force on the rocket then why can't we get the same lift with just adjusting the speed of... | "Cold gas" thrusters (i.e. pressurized gas released through a nozzle without combustion) are used for attitude control on some rockets (notably on the Falcon 9 first-stage, for attitude control in the recovery phase), but they have a much lower specific impulse than hydrogen-oxygen combustion. Their advantage is their ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
"answer_count": 12,
"answer_id": 5
} |
Particle Hole Symmetry of BdG Hamiltonians It is straight-forward to verify that any Hermitian BdG Hamiltonian of the form
$$
\mathcal{H} = (c_1^\dagger, c_1, c_2^\dagger, c_2,...)
\begin{pmatrix}
H_{11} & H_{12} & \cdots \\
H_{21} & H_{22} & \cdots \\
\vdots & \vdots & \ddots
\end{pmatrix}
\begin{pmatrix}
c_1 \\ c_1... | Your first statement is a little ambiguous, let me rephrase it.
Any Hermitian Hamiltonian of the form
$$
\mathcal{H} = (c_1^\dagger, c_1, c_2^\dagger, c_2,...)
\begin{pmatrix}
H_{11} & H_{12} & \cdots \\
H_{21} & H_{22} & \cdots \\
\vdots & \vdots & \ddots
\end{pmatrix}
\begin{pmatrix}
c_1 \\ c_1^\dagger\\ c_2 \\ c_2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576749",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Acceleration transformation in special relativity I am having a hard time understanding the transformation of acceleration when it is not parallel to the instantaneous displacement of the particle, in particular the its dimension.
Suppose a particle is in projectile motion. Acceleration is downward because of gravity b... | Vertical motion of the projectile means that energy is lost or gained by the projectile.
Horizontal motion of the projectile means that the the projectile moves relative to the aforementioned energy. The projectile receives a horizontal impulse when it absorbs some energy that has some horizontal momentum.
This is a mu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/576816",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Plugging a global phase into an operator Cheers to everyone. I' ve got a serious doubt about the following: consider the annihilation operator $\hat a$. For practical reasons, I sometimes find useful redefining it in the following way : $\hat a' =\hat a e^{i \phi}$, with $\phi \in \mathbb R$. If I add a new global phas... | $$\mathcal H = \alpha \hat a + \alpha^* \hat a^\dagger\\
=\alpha e^{-i\phi}~\hat a' + (\alpha e^{-i\phi})^* \hat {a'}~^\dagger\\
\equiv \alpha' \hat a' + (\alpha ')^* \hat {a'}~^\dagger.$$
Names, by themselves, cannot affect physical relevance. Arbitrary complex number coefficients present differently in the unprimed ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577054",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is volume an extensive property but molar volume an intensive one? If we take volume of a system, then it's often defined as volume of container and is an extensive property but it's often said that molar volume is an intensive property. How exactly does dividing the volume by number of moles turn an extensive pro... | The number of moles is proportional to the number of atoms/molecules in the system.
Suppose you bring another identical copy of the system, and consider the two copies as a whole.
The number of atoms/molecules will double, so will the number of moles.
For usual solids and liquids, the volume will double (assuming exter... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577302",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
On the meaning of $dU = \delta w$ for adiabatic processes For an adiabatic transformation between state A and B $\delta q = 0$ and consequently from the first law of thermodynamics $dU = \delta w$, since $U$ is a state function its variation should be the same whether the process is reversible or irreversible.
The poss... | You are assuming that you can take either a reversible or irreversible adiabatic path and end up in the same final state. On the irreversible you will generate entropy and since the path is adiabatic you cannot pass that entropy to the surroundings as heat, so the final state of the irreversible path will have a higher... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577374",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
How to derive Euler-Lagrange equation for isochronous curve of Leibniz in terms of $t$, $x(t)$, $\dot{x}(t)$?
According to this source, "An isochronous curve of Leibniz is a curve such that if a particle comes down along it by the pull of gravity, the vertical component of the speed is constant, when the gravitational... | according to your source :
$$\dot{y}^2=2\,g\,x$$
thus:
$$T=\frac 12 m\,(\dot{x}^2+2\,g\,x)$$
$$U=g\,x$$
with E.L: you obtain
$$\ddot{x}=0$$
$\Rightarrow$
$$x(t)=v_0\,t$$
$$\dot{y}=\sqrt{2\,g\,v_0\,t}~,y(t)=\frac 23\,{t}^{\frac 32}\sqrt {2}\sqrt {g}\sqrt {{v_0}}$$
so you get the same result that given in your source
$$y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577458",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Why does gravity act at the centre? Why does gravity act at the centre of earth and how does that happen?
| Every single particle in Earth exerts gravitational attraction to an object in your example, and, all these effects add up/cancel, and the net of these is pointing towards the center.
Actually, at the center, all these effects cancel out, and you feel weightless.
Correct. If you split the earth up into spherical shell... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Peaks in Co-60 gamma spectrum The following plot shows data collected from a Co-60 coincidence experiment. The detectors used were NaI(T) scintillation detectors.
One detector was gated around the 1.33 MeV peak and the second detector collected the data shown below. I have been trying to figure out what the two peaks a... | You have already identified the peak at about 195 keV as backscatter peak.
Apparently, you have used a NaI(Tl) detector. Photoelectric absorption by iodine of NaI results in a characteristic x-ray with 28 keV. If this x-ray exits the detector crystal, it results in a secondary peak 28 keV below the corresponding photop... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577859",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is the centripetal force when instead of a mass point we have a physical rotating body? I was wondering what is the centripetal force of a body rotating in a circular motion. I know that the centripetal force of a point mass is $mv^2/r$. I only have done an introductory physics class so I can not find the answer.
|
I was wondering what is the centripetal force of a body rotating in a
circular motion.
It does not only apply to point masses. You can apply it to the center of mass of a rotating body.
Refer to the figure below of a figure skating pair. The woman skater is moving in a circular path around the male skater. The center... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/577965",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Do electrons experience wind resistance? Electrons have a mass, as a particle with mass, they experience most effects of objects with a mass. So do they experience any sort of wind resistance? Or is that simply explained by their cross section interaction probability with a given particle?
| If one imagines a macroscopic object moving through air, one can very well approximate air resistance as the action of a continuous fluid. At low speeds, this situation can be described by viscous friction, which is a force proportional to the speed of the object, and with direction opposite to its direction of motion ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578078",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 6,
"answer_id": 0
} |
Why do electric field lines curve at the edges of a uniform electric field? I see a lot of images, including one in my textbook, like this one, where at the ends of a uniform field, field lines curve.
However, I know that field lines are perpendicular to the surface. The only case I see them curving is when drawing fi... | This is one of those questions where you just have to see it. Here is fieldline drawing of two charges. Red is a positive charge and blue is negative.
Now for 6 charges:
and finally for 40 charges:
Here is the Mathematica code for anyone interested
range = 1.4;
nCharges = 20;
xSeparation = .5;
e[r_, r0_] := (r - r0)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578146",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 4,
"answer_id": 3
} |
Can we Predict the Trajectory of a hypersonic missile? I read in a newspaper that we can't predict the trajectory of a hypersonic missile and that this property renders the missile undetectable.
However, what I could not understand is why can't we predict it's trajectory? What factors do we have to look at for predicti... | Of course the missile's trajectory is predictable if you know everything about its thrust, position, and momentum at all times since its launch. The problem is that someone who launches a hypersonic missile generally does not inform the opposing missile defense systems, "Hey, I launched a missile at this time and place... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Does doubling density (keeping average gas molecule speed the same), increase temperature recorded on a thermometer? At the end of the day what the thermometer is measuring as temperature is energy of the air molecules (which could come in the form of kinetic energy). Now, imagine the following scenario :
*
*Take a b... | Assuming an ideal gas, if you are keeping the average speed of the molecules the same then you are holding the temperature of the gas constant. Assuming the container keeps the same volume, by the ideal gas law it must be that the pressure of the gas increases as you add more molecules.
Yes there are more molecules hit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578584",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 6,
"answer_id": 1
} |
Can we represent 4D graphically? Actually I know that axes are always perpendicular but after three axes we cannot draw any other axis that is perpendicular to all the other three axes.
can any one say how can we draw another axes which is mutually perpendicular
| Truth is if you want 4 dimensions that are orthogonal, they do not even need to be spatial. For example you can use color to add an extra dimension. Or another example, you can use time. There are many dimensions that we can see. You can even make extra spatial dimensions using local dimensions techniques. For example ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Is there anything such as gravitational field-lines in GR similar to the electric/magnetic field lines in electromagnetism? I sometimes mistake space-time curvature for gravitational field lines. Do geodesics in some ways represent $g$-field lines? Why is not it traditional to show $g$-field lines around a massive obje... | Probably not just as you ask, but there are interesting ideas for visulazations in
Visualizing spacetime curvature via frame-drag vortexes and tidal tendexes. II. Stationary black holes by David A. Nichols, Robert Owen, Fan Zhang, Aaron Zimmerman, Jeandrew Brink, Yanbei Chen, Jeffrey D. Kaplan, Geoffrey Lovelace, Keith... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578862",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Will a plastic feel less heavy when I put it in a bucket of water and carry it? If I'm carrying a bucket of water in one hand and a piece of plastic in the other, and then I decide to keep the plastic in the bucket of water (it floats). Will it feel less heavy in the second case?
I think it will feel the same because i... | As Bob D says, it will weigh the same unless some of the water spills out.
But it's likely to feel somewhat heavier because you do better with weights balanced in both hands than all the weight in one hand. And if you carry one bucket with both hands that will be awkward, unless it's an unusually small bucket.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/578995",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 7,
"answer_id": 4
} |
Deriving ideal gas law from Boyle and Charles My textbook states
Notice that since $PV = \text{constant}$ and $\frac{V}{T} = \text{constant}$ for a given
quantity of gas, then $\frac{PV}{T}$ should also be a constant.
I tried to prove this, but no success:
$$PV = a$$
$$\frac{V}{T} = b$$
$$\frac{PV^2}{T} = ab$$
$$PT... | You can't derive it like that because the proportionality relations hold only when the third parameter is kept constant.
However, you can derive the ideal gas law by noting that for high temperature, we get a limit as shown below:
$$ \lim_{ p \to 0 } p \overline{V} = f(T)$$
So, the limit of the product as pressure dr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579140",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 1
} |
Are there multiple Rydberg constants? I'm sorry if this is a trivial question, I'm trying to understand the Rydberg formula and unsure if there are different values for the Rydberg constant?
According to Wikipedia's articles about Hydrogen spectral series, Rydberg formula and Rydberg constant, there are two different R... | http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html
quote from here one for the sources of the wiki article
"The reason for the variation of R is that for hydrogen the mass of the orbiting electron is not negligible compared to the proton at the high accuracy at which spectral measurement is done. So the reduced mass ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579262",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Radiative transfer equation for a three-level system I am trying to derive the radiative transfer equation for a three-level system, which is supposed to be given by:
$\frac{dI(\omega,x)}{dx}+N [\alpha\rho_{11}-\beta( \rho_{22}+\rho_{33})]I(\omega,x)=\beta(\rho_{22}+\rho_{33})$,
where $I(\omega,x)$ is the specific inte... | The derivation is easy but a bit long, so I'm going to link a clear resource and just say the steps.
Step 1: Write the total Hamiltonian of the system
Step 2: perform rotating wave approximation and co-rotating frame to remove time dependence of problem. Your hamiltonian looks something like this now:
Step 3: Calculat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
How much energy is transferred to a human hit by lightning? Wikipedia tells me that a bolt of lightning releases roughly 1 GJ of energy, but I'm guessing that's along the entire length of the bolt and that most of it is dissipated as heat and light to the surrounding atmosphere.
Don't know much about the physics behind... | Energy transferred by current is defined as :
$$ E = I Q R $$
Where $I$ is current strength in amperes, $Q$ - transmitted charge and $R$ conductor resistance in $\text[ohms]$.
Typical lightning bolt current is about $30~000 ~\text{[A]}$, and transmits $15 ~\text{[C]}$ charge. If lightning passes through internal body ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/579852",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.