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Suppose two bodies B1 and B2 are in contact with each other in a static situation. A torque M1 is applied to the first body B2. The torque M1 is transmitted to the second body B1. Both bodies won't move because they hinder each others movement due to the inclined contact surfaces.
Now my first question is, what force ... |
I am trying to figure out how to estimate how far (in meters) that a solid fuel model rocket will land from its launching point. To do this, I have figured out I will need to estimate the maximum altitude that the rocket will reach, and the time of the flight from the maximum altitude all the way to the impact point. H... |
The question is quite long, this because many topics are touched, but I tried to make it the more self-contained I could: on the other side, many arguments are touched also to make it self-contained.
I really love to discuss, so please if you have some free time to read it, see it more like a relaxed discussion than a ... |
Please can someone give the proof of all restricted Lorentz transformation matrix can uniquely decomposed into product of pure rotation and pure boost? Or at least give some hint how to proceed to prove it?
|
I read a literature, which discusses the orbital operator.
$^2$ and $_$ are square of the orbital operator and the $z$-axis component of orbital operator respectively. $|l\rangle$ and $|m\rangle$ are the eigenvectors for the $^2$ and $_$ operators respectively. $_+$ is defined as $_+=_+_$.
The literature says that $$(^... |
In the context of Newtonian mechanics, is it possible to have an isolated system which does not lose/gain particles, but whose mass changes over time? I have been trying to think of such an example for a while, but have been unable to come up with one.
I understand that this phenomenon is common in special relativity, ... |
Does the physics community have a term for the time per travel distance, $dt/dx$? I.e. the reciprocal of the speed. Runners call this their pace.
|
I am doing some research in a condensed matter system, and found this Berry curvature / vector field configuration that is unusual. I cannot find another example of something similar, either from physics or math examples. To me it looks like a i=+2 that had another half turn added to one side.
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Could someone please tell me why there is both a positive and negative sign with the systematic error? I thought it could only be either positive or negative.
A student uses a digital ammeter to measure a current. The reading of the ammeter is found to fluctuate between 1.98A and 2.02A.
The manufacturer of the ammeter ... |
I have a question to this proof here: Adding a total time derivative term to the Lagrangian
I was asking myself why $$\frac{\partial \dot{F}}{\partial \dot{q}} = \frac{\partial F}{\partial q}.\tag{1}$$ So to add a bit of context: We consider the Lagrangian $\mathcal L^{*} = \mathcal L(q, \dot{q}, t) + \frac{dF}{dt},$ w... |
Given the following Young tableaux
for $SU(3)$, how can I deduce that it corresponds to the adjoint representation?
I was thinking that the dimension of this representation is 8, as in the case of the adjoint representation. Is this sufficient?
|
I am working with some field theory and I am at a point where I would like to change my sign convention from $(-,+,+,+)$ to $(+,-,-,-)$. I am worried at some point I will just equations with the wrong sign because I am used to it and just going by memory.
Is there any table with the differences in sign for the "standar... |
I'm looking at some dispersion relations for some complex systems and realised I actually don't have a clear understanding of what physics I can get from a dispersion relation from equations that produce complex relations between frequencies and wavevectors. For instance, if you take a diffusion equation
$$\dot u=\nabl... |
Currently I am reading Das' Finite Temperature Field Theory. After computing the first order correction to the potential with a cut-off (eq. 6.77) Das states that, "we add counterterms and renormalize our theory by demanding that the renormalized mass and the coupling constant of the theory up to one loop are given by"... |
Today, I learned that the kinetic energy of an object can be described by
$$KE=\gamma mc^2=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}mc^2.$$
I have been taught in school that the kinetic energy of an object is $$KE=\frac{1}{2}mv^2$$ for non-relativistic velocities.
If we take the first, more precise equation and insert a non-r... |
Considering an electric and magnetic plane wave, $E(t)=E_p(\omega)e^{i\omega t}$ and $H(t)=H_p(\omega)e^{i\omega t}$, where $E_p(\omega)$ and $H_p(\omega)$ represent the frequency dependent peak amplitudes of the wave. The time-averaged Poynting vector is defined as $<S_x> = \frac{1}{2}\text{Re}\{E_p(\omega)H_p^*(\omeg... |
When the density/volume abruptly changes (isobar/isothermal) while providing a sufficient latent heat to the system, is this variation related to a high compression/expansion as it is illustrated to the continuity equation? Or it's related to the fact that molecules will have more degrees of freedom due to the extra en... |
I am currently trying to design a heat exchanger that transfers heat via a flowing steam working fluid over a pipe section carrying another flowing fluid.
Specifically, I have a fluid, (call it $fluid1$) that naturally convects at a constant temperature of $T=T_{sat}$ over a cylindrical pipe of length $L$, thermal cond... |
In the article "Identification of the velocity operator for an irreducible unitary representation of the Poincaré group", there is formula to implement a Lorentz transformation of the velocity as a unitary transformation.
https://aip.scitation.org/doi/10.1063/1.523342
It goes as follows: consider a Lorentz transformati... |
For the Bose-Hubbard model, we know that there are the Mott insulator phase with $\langle a_i \rangle = 0$ and the superfluid phase with $\langle a_i \rangle \neq 0$. However, when we are trying to solve the Bose-Hubbard model numerically, we often assume a fixed site number and a fixed total particle number. But if $\... |
I know the classic example for quasi static process with the banch of sand on a piston (neglecting the atmosphere pressure and friction). if we take 1 by 1 grain of sand, the process is quasi static.
My question is what happen if we are not neglecting the atmosphere pressure? I think the process of taking the grain of ... |
I have a metric:
$$g_{ab}=\text{diag}(-1,a(t)^2,r^2,r^2 \sin^2(\theta))$$ where $$a(t)^2=\frac{3}{B}\cosh^2(\sqrt{\frac{3}{B}}t)$$ where $B$ is constant.
Also a tangent vector given: $$k^\mu=(a(t)^{-1},a(t)^{-2},0,0).$$
The problem is that I need to show that this tangent vector is geodesic of this spacetime.
My way is... |
I came across this sentence in this paper.
Alternatively, we modulate the frequency of the microwave excitation
voltage at 971 Hz with a square wave and a bandwidth of 32MHz.
In my limited FM knowledge, this sounds like the carrier frequency is 971Hz, meaning the signal is modulated at 971 Hz. The bandwidth is the w... |
I am currently working on a web app (Pilot Logbook) that requires a user to automatically calculate the period of flight spent in the night.
Currently, I have
Departure Lat and Long and Departure Time in UTC
Arrival Lat and Long and Arrival Time in UTC
Sunset and Sunrise Times (Based on dates) for both Arrival and D... |
What is it about a capacitor which allows it to filter frequencies?
I understand the construction of a high-pass RC filter, and the mathematics behind it, but I'm struggling to find an explanation of the physics behind the phenomenon.
In my mind I can picture the broad spectrum signal hitting the capacitor, but I feel ... |
I have read some literature regarding FR argument and Wigner's friend.
In short about Wigner‘s Gedankenexperiment:
Wigner's friend is a thought experiment in theoretical quantum physics, first conceived by the physicist Eugene Wigner in 1961,[1] and developed into a thought experiment by David Deutsch in 1985.[2] The ... |
The Wikipedia article for complete set of commuting observables (CSCO) outlines a method for finding a CSCO. However, it does not suggest why such a set should exist. On one hand, I think it is very possible that it might not in general, as most systems are not integrable. But on the other hand, we normally talk of sym... |
How is Coulomb’s constant affected when it is not in a vacuum permittivity? And how do you determine the new value?
|
Consider a quantum system with Hamiltonian H and consider the measurement
of an observable $a_n$ associated with a different operator A.
Initially the system is an eigenstate $|\phi_n \rangle$ with eigenvalue $a_n$ and we begin to take measurements of the observable A.
We can approximate the probability of measuring a... |
Under Newtonian mechanics, an inertial reference frame is defined as one where Newton's second law applies, so if the Earth weren't rotating by this definition it would be one as things accelerate due to gravity. However, the frame of a falling object which is accelerating relative to Earth is also inertial. Is it the ... |
Why do we use lever arm? Torque is $\tau = \vec{r} \times \vec{F}$ or $\tau = rF\sin(\theta)$, but why when explaining what we mean do we choose to imagine a straight line to where the force would be perpendicular (essentially taking the "component" of $\vec{r}$, which is the distance straight from the rotation axis) i... |
Like the downpour creates a path between the high voltage wires and you or your car parked underneath them, would the current passes through you to the ground when you are walking close to electric poles or when you touch your parked car door?
|
Please, my question is at the end of this formulated problem.
In the case of the twin paradox, the travel can be made without never accelerating higher than $g$. So the one who remains on the earth will always be subject to $g$, while the traveler can be under $g$ only for some part of the trip for example:
First he l... |
We know that the magnetic force acting on two parallel wires carrying current in the same direction is attractive.
I am wondering: Say we have a thick wire carrying current, with initially the same charge density throughout the wire. If we view the thick wire as a bundle of many thinner wires, then these thinner wires ... |
I often do this while my remote battery gets low, I just hammer my TV remote two of three times. I have seen this to be work with other devices. But I never bother thinking about how this makes things working. So My question why this works? Is there any physics or it just happens because the part gets loose or somethin... |
The reflection at a dielectric interface was analysed in Griffiths introduction to electrodynamics using the following diagram.
I do not understand why the direction of $\vec E_r$ and $\vec B_r$ are as given. Why can't it be as drawn in a different colour?
I calculated with the new $\vec E_r$ and $\vec B_r$ and got a ... |
So I had a simple thought:
Venus is ~400C with 95% CO2, and Earth is ~15C with 0% CO2..
Assuming linearity, this equates to 1C for 1% atmospheric CO2.
Why is the relationship assumed to be so much more hyperbolic? There is no feedback loop where a little more CO2 unlocks more CO2 trapped in rocks - save for a little de... |
When an Electron Capture occurs a Neutron and a Neutrino are formed. Prior to this process due to the presence of the proton and electron an electric field must've existed however as soon as this process happens which is almost instantaneous i believe the electric field must vanish right? So what happens does this chan... |
Ignore the position i.e whether you are on one or other side of orbit. Does space quantization play any role.
|
how can i solve this
(*)The self inductance of the motor of an electric fan is 10 H. In order to impart maximum powr of 50 Hz, it should be connected to a capacitance of
what is the concept behind the formula
i know this is the formula for c
|
Quantum field theory uses a large amount of mathematics and I was wondering about some applications of cohomology theory in QFT, I understand it has applications in string theory but I was wondering about possible applications in more traditional QFT.
|
considering $L$ is always greater than $L_z$ i.e angle between angular momentum/magnetic moment and magnetic field/z direction cannot be zero. Means $B$ and magnetic moment cannot be in same direction. Then how is it possible in Paramagnetism that dipole completely aligns itself in the direction of field?
|
In his section on Helmholtz theorem Griffith uses primed coordinates in the integrals that define $U$ and $\mathbf{W}$. Now, I understand that primed coordinates are used for sources (charges and currents), but in this context, where Griffith is talking about general vector fields (not necessarily electric and magnetic... |
From a mathematical standpoint (CPT symmetry) it is most probable that antihydrogen has the same spectra (absorption and emission) as hydrogen. The CERN confirmed this hypothesis to a high accuracy for the 1S-2S ray: ALPHA CERN 1S-2S antihydrogen spectrum.
Within this hypothesis, how can we state that a far (in a neigh... |
The hamiltonian for a free falling body is $$H = \dfrac{p^2}{2m} + mgy$$ and since we are using cartesian coordinates that do not depend on time and the potential only depends on the position, we know that $H=E$. For this hamiltonian, using the Hamilton's equations and initial conditions $y(0)=0$ and $p(0)=0$, we get t... |
Frictional force($f$) is calculated as the product of coefficient of friction and the normal forces. $$f=\mu N$$
If suppose an external force $F_{ext}$ is applied on a block (at rest) at an angle $\theta$ with the horizontal, then would $N = mg$ (weight of block) or $N =mg+F_{ext}sin\theta$ (I want to know the effect o... |
I have a follow-up on this post. The way I understand it, if one generally has a velocity-dependent potential $U(q, \dot q, t)$, then we can derive/define a generalized force $$Q_k = \frac{d}{dt}\frac{\partial U}{\partial \dot q_k} - \frac{\partial U}{\partial q_k}.$$
Now, this has a practical application when it comes... |
I was going through a worked special relativity example and found the following transformation equation, which I have not come across before. I tried but cannot derive it. Can anybody help?
$$ct'=\frac{1}{\beta (-x'+\frac{x}{\gamma})}$$
I think it comes from substituting $t$ from the $x$ to $x'$ transformation but I c... |
If both system is possible, how do we launch satellites so as to make orbital plane perpendicular or // to equatorial plane of earth?
|
By equating $F_{\rm gravitation}$ to $F_{\rm centripetal}$, the formula for the velocity of an object traveling along a certain orbital becomes $\sqrt{\frac{GM}{r}}$. The formula for angular momentum can be written as $L=mvr$. In elliptical motion, for example, when earth travels further away from the sun, the radius i... |
Regarding equation 3.16 on page 39 of Peskin and Schroeder, we are in the middle of talking about the $SU(2)$ group and its representations. It is said that we can write the generators of the algebra as an antisymmetric tensor:
$$J^{ij}=-i(x^i\nabla^j-x^j\nabla^i),\qquad i,j=1,2,3,$$
and that "the generalisation to fou... |
A particle of weight $W$ Newtons is supported on a smooth inclined plane by two forces each equal in
magnitude to half the weight, one acting horizontally and the other acting parallel to the plane.
We are asked to draw a diagram and here is the one provided by the answer:
First of all, why is the horizontal force (... |
I observed this phenomenon: When i strike a plastic bucket with a wooden stick, it produces a normal "plastic like" sound. But when the bucket is full of water, it produces an altogether different metallic sound. What could be the reason of this?
|
In YDSE, $D=1m$, $d=1mm $ and $\lambda=0.5mm$. Find the distance between the central maximum and the first maximum.
My attempt:
The distance between the central maximum and the first maximum is the definition of fringe width, hence:
$$\beta=\frac{\lambda D}{d}=0.5$$
Given solution:
Let the angular position of first m... |
Ignoring air resistace, I have that the height of our canon is $8.2$m and the height of the target is $6.34$m. And that our initial veocity $v_0=18$m/s. I have to determine a way to find the angle required to hit this target.
My work:
We have our initial position $(0, 8.2)$ and target is at $(x,6.4)$
The component of t... |
There has to be a reason behind why we add fractional errors when the involved quantities are being multiplied or divided, or why, when converting units, do we have to divide the uncertainty with the number that divides the value.
|
When two positive charges are kept close, they get repelled in the direction of a line joining both the charges. Why is it so?
Also, why is the repulsion in a straight path?
In both the cases, the potential energy of the charge which gets repelled decreases. What makes it repel in a straight line such that the line p... |
It makes sense that UV rays can fuse two base pairs of DNA since it's probably the right size (between 400 and 10 nm).
I imagine it happens when the bottom of the UVC wave touches one DNA base, at the same that the pick of the wave touches the other base (I guess the distance between both bases probably is the same as ... |
The motion of a particle of mass $m$ is given by $x = 0$ for $t < 0$, $x(t) = A \sin 4pi t$ for $0 < t <(1/4) s$ ($A > 0$), and $x = 0$ for $t >(1/4) s$.
Which of the following statements is true?
(a) The force at t=(1/8)s on the particle is –16Amπ^2.
(b) The particle is acted upon by on impulse of magnitude 4Amπ^2 at ... |
ok, the original text is \
But Gauss's Law tell us that dE, the change in E through the thin slab, is just $\rho/ \epsilon_0 dx $, Hence $\quad\rho dx $ in Eq.33 can be replaced by $\quad\epsilon_0 dE\quad$ and the intergral becomes
\begin{equation*}
F = \epsilon_0\int_{E_1}^{{E_2}}E dE = 2(E_2^2-E_!^2)/\epsilon_0 \... |
I have been asked to find the most probable position of electron in infinitesimal space $dV$ orbiting a Hydrogen atom. I know that probability $P$ of finding the electron in a volume $dV$ is given by
$$
P = |\psi(\vec r,t)|^2 dV
$$
where $\psi(\vec r,t) = A e^{-r/a_0}e^{-iE_1t/\bar{h}}$.
The time dependence is irrelev... |
According to McQuarrie, we can write the definition of a Hermitian operator as an operator that satisfies $$\int_{-\infty}^{+\infty}f^*\hat{A}fdx=\int_{-\infty}^{+\infty}f\hat{A^*}f^*dx$$ and the average value of the observable corresponding to $\hat{A}$ is given by $$\langle a\rangle=\int_{-\infty}^{+\infty}\Psi^*\hat... |
A collapsed state should act like a particle and a non-collapsed like a wave. Is this statement true? So if you had a single slit and detectors behind it off to the sides... The collapsed state should form a bar through the slit and the non-collapsed should spread out like a wave. So then the detectors to the side shou... |
We are stating that energy neither be created nor be destroyed. Then where does it come from?
|
Before $t=0$: object is not moving
At $t=0$: I push object with sufficient force to overcome static friction
After $t=0$: Object accelerates. Resultant force is greater than $0$. Dynamic friction is less than the push. So why does the object stop accelerating after say $t=2$ (either starts to decelerates or reaches con... |
For a driven damped oscillator, my book only shows the solution for the driving force being a term of cos(t). However, in Fourier Series, the force may have terms of sin(t). How do I convert the cosine solution for the position x(t) into a solution for sines? If needed, the book is "Classical Mechanics" by John R. Tayl... |
Let's assume we have two observers one is on Earth and the other one is inside a spaceship with relativistic speed.
Would the time inside the ship slow down while also the spaceship is getting shorter for an observer on Earth?
Most of the examples I saw online are referring to the relation of time dilation for one obse... |
The following image is from Greiner's book, Field Quantisation, where he carried out the derivative in question. The only way I could make sense of it, was that the derivative acts only on the last integral of element $dt_n$ because the latter is essentially the only variable and all others depend on it (?); it gives t... |
Here is a Mythbusters clip showing that you actually can blow your own sail.
They install a sail on a swamp boat and reverse the direction of the fan. There are other examples that the ideas works, like, notably, thrust reversers on jet airplanes.
https://www.youtube.com/watch?v=uKXMTzMQWjo
This initially strikes most... |
In Weinberg's Gravitation and Cosmology, the author mentions that an infinitesimal Lorentz transformation (in the four-vector representation of the Lorentz group) has the form $$\Lambda^{\alpha}_{\phantom{\alpha}\beta}=\delta^{\alpha}_{\phantom{\alpha}\beta}+\omega^{\alpha}_{\phantom{\alpha}\beta}.\tag{$\dagger$}$$ It ... |
I found this question, which seemed very easy to me at first, but when I revisited the problem I started to have some doubts about my approach, so I would appreciate any form of discussion or approval for my idea.
The problem is:
An infinite wire with radius R is rotating with the angular velocity $\omega$ on the x-y-... |
I am trying to understand BCOV's paper: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes.
In this paper, it was shown that the higher genus string amplitude for B-model could be computed by the path integral of its string field theory, which is Kodaira-Spencer theory introduced in the ... |
I am stuck in a thermodynamic problem. Say there is a gas of internal energy $u$ in a unit volume. Suppose the internal energy per unit volume, $u$, is only a function of temperature $T$, i.e. $u=u(T)$. Given the equation of state
$$p = \frac{1}{7}u(T),$$ where $p$ is the pressure of the gas, what is the functional for... |
I attempted to ask this question previously here: How does the whole universe agree on the laws of physics? [duplicate]
but I didn't make myself clear, and it ended in confusion. I will try again.
If we take two particles of the same type, say two electrons, we find that they behave the same way. They interact with ot... |
I just don't understand how to get to the normal force from the P.E. given; specially, when its circular motion. I'm stuck on this one question. Thanks in advance for helping me out!
|
Given a trace function, say the von Neumann entropy $S(\rho) = - \mathrm{tr}(\rho \log \rho)$, can it be express as a matrix $M$ where $S(\rho) = \mathrm{tr}(M^\dagger\rho)$ is given by the Hilbert-Schmidt inner product?
|
Imagine there is an object placed on bed of a moving truck, I understood from a previous answer that the direction of frictional force acting on object will be same as direction of moving truck.
I haven't quite understood this because I study in High school and I don't know about Inertial frames or something, so can yo... |
What I understood is that By the math, the Riemann tensor is obtained by parallel-transporting a vector along a closed curve in the considered space, then apply Stoke's theorem.
Now if physics is considered then the space becomes spacetime, and hence it is based on a CTC.
But how could determinism, supported by Einstei... |
For generic black holes one demonstrates that the event horizon is just a coordinate singularity by changing coordinates to a system where the metric is well defined. For example we have Kruskal-type coordinates $U_\pm\sim e^{\pm \kappa u_\pm}$ with $\kappa$ the surface gravity. In terms of these coordinates one usuall... |
When reading "Modern techniques of Surface Science" by D.P. Woodruff, it is stated that:
"The main methods used to achieve this in situ cleaning are (...)cleavage."
This is in the context of requirements for studies of properties of ideal surfaces, as an extra step before requiring UHV (Ultra-high vacuum).
It is also m... |
It is said that things like the rest mass and internal energy are measured the same by any inertial observers regardless of their relative speeds, however, I cannot get my head around the following problem:
Assume that a point laser diode moves at a speed very close to that of light. Two similar photons with the same f... |
I'm starting to study the special theory of relativity, so the concepts and the 'methods' to solve problems are still not very clear in my mind. The question is basically:
A person is running towards a tunnel (which has length $L$) with velocity $v$, at the moment she's about to enter, a photon is emitted on the other... |
For every example I've seen this was an assumption I have made. However with this example, I am unsure. Either the electric field is constant through the e1 dielectric meaning e2 and e3 must be equal, or a dielectric can have a changing electric field.
When we solve a simple single material parallel plate capacitor, ... |
Consider the electric quadruple moment operators as follows:
$Q_{20} = \frac{e}{2}(x^2+y^2-2z^2) $
$Q_{2 \pm1} = \frac{e\sqrt{6}}{2}z(x\pm iy) $
$Q_{2 \pm2} = - \frac{e\sqrt{6}}{4}(x\pm iy)^2 $
I know that the Electric quadrupole transitions are as follows:
$$\Delta l = 0, \pm 2$$
$$\Delta m_l = 0, \pm1, \pm 2$$
I was... |
According to Stephen-Boltzmann law Wikipedia article,
the total energy radiated per unit surface area of a black body across
all wavelengths per unit time
is:
$$j=\sigma T^4$$
So the total energy radiated accounting for the whole surface area is $E_{total}=\sigma T^4 A$.
I also know that the quantity:
$$\frac{2h\nu^3... |
I will prefix this question by noting that my understanding of relativity is little more then that of a first year physics course, as well as Youtube videos and documentaries. However, I am a mathematician specialising in numerical PDEs and believe I have a preliminary understanding of the mathematics behind relativity... |
Working through David Tong's sheet here https://www.damtp.cam.ac.uk/user/tong/qft/oh1.pdf and can't follow how to get the Levi-Cevita symbol out the front? Its equation 15.
I was looking at trying to use an identity with the Kronecker Deltas in the energy momentum tensor but I am really stuck. Below is the conserved c... |
I'm given these following.
Mass of the car $= 1800 \text{ kg}$
Friction coefficient $= 0.6$
Velocity $= 8.3 \text{ m}/\text{s}$
I need to find the stopping distance and deceleration using this and I have no idea how.
|
https://www.youtube.com/watch?v=yWO-cvGETRQ
Is it true that if you could see and track every atom there is, you could see the entire history of the universe?
I thought that when matter is changed through chemical or physical phenomena, some information would be permanently lost at a certain point, but the video seems t... |
Would magnets work in outer space, but very far from any planet or star, outside their magnetic fields? And electro-magnets?
Would they still repel each other? If so, would it be with much less force or almost the same force?
|
As Griffiths says:
Suppose we have a piece of polarized material - that is, an object containing a lot of microscopic dipoles lined up. The dipole moment per unit volume P is given. What is the electric potential produced by this object (not the field that may have caused the polarization, but the field the polarizati... |
Hi I am going through Fetter's Quantum Theory of Many-Particle Systems Dover Edition.
In ch. 31 he computed the relation between $\bar{G}(\mathbf{k},\omega)$, ${\bar{G}}^{R}(\mathbf{k},\omega)$ and $\bar{G}^{A}(\mathbf{k},\omega)$ where each of them are the real-time Fourier transformation of the corresponding real-tim... |
Please help me understand (geometrically) how is the parallel transport of a vector performed (along the surface of a sphere along a given path). Consider the parallel transport of a vector from the north pole N of a sphere to an arbitrary point P on the equator along a curve NP.
How do I draw parallel transport of thi... |
The geodesic deviation equation can be written in the following form
$$
\nabla_U^2 \xi = R (U, \xi) U
\tag{1}
$$
where $R$ is the Ricci tensor. It can also be written component-wise using the Riemann tensor
$$
(\nabla_U^2 \xi)^\alpha = R^\alpha_{\;\, \beta \mu \nu} \: U^\beta U^\mu \xi^\nu
\tag{2}
$$
I'm interested in ... |
The potential energy of a dipole moment $\vec{p}$ in a uniform electric field $\vec{E}$ can be expressed as the negative dot product of the two vectors, with $U = 0$ defined at $90$ degrees.
$$U=-\vec{p}\cdot\vec{E}.$$
The negative derivative of a potential energy function with respect to angle yields the torque, $\vec... |
Now I understand the concept of friction.
But I just wanted to clear a confusion. As we keep increasing applied force, static friction acts till its maximum limit. After that the body comes in motion and kinetic friction starts acting which is less than static friction.
At the limiting point, will there be a sudden bre... |
I was just thinking about a situation in which a big truck is moving in high speed say ( $80 \ miles/hr$). There is a swing attached with the ceiling of the truck container which can move freely in the direction of truck motion.
How does the motion of truck affect the swing in which a person wants to play it? What is t... |
I have been learning about tension and was doing some reading on trying to explain these forces at the intermolecular level and later also trying to see how it fits in view of Newton's third law- I did come to certain conclusions but I am not sure if I am understanding them correctly.
As much as I have understood, I ga... |
Imagine a system of particles with the internal force on $i^{th}$ particle due to $j^{th}$ particle being given as $f_{ij}$
From the derivation of law of conservation of momentum and law conservation of angular momentum, I know that
Momentum would be conserved only if internal forces obey third law
$f_{ij} = - f_{ji}$... |
Since when we slap something, some of the kinetic energy turns into thermal energy, is it possible to slap a human so quick and hard, that it gets cooked? And how many slaps at the least possible time be needed to cook a human ?
|
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