All Questions
10,535 questions
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Centripetal Force A Level Physics. Can someone explain the answer to me please? [closed]
At Z why is the tension component greater than the weight? and why is it the opposite at X? I know the Centripetal force acts towards the centre, and i understand why they are added and subtracted at ...
0
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0
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26
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Why can't infinitesimal canonical transformations be used to represent infinitesimal boosts?
Consider the following differential form:
\begin{equation}
\textbf{d}F=Q\textbf{d}P+p\textbf{d}q+(K-H)\textbf{d}t
\end{equation}
The generating function for the canonical transformation is given ...
- 79
1
vote
1
answer
28
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From material derivatives to partial derivatives in the wave equation
Consider the Cauchy momentum equation:
$$\rho \frac{d^2 \mathbf{u}}{d t^2} = \nabla \cdot \boldsymbol{\sigma} + \rho \mathbf{f}$$
where $\rho(\mathbf{x},t)$ is the density, $\mathbf{u}(\mathbf{x},t)$ ...
- 225
2
votes
1
answer
431
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Can the gravitational force of a black hole "lock" a particle in an unstable equilibrium?
In classical mechanics, it is possible to have points of stable, unstable, and neutral equilibrium depending on the gradient of the potential field. Near a black hole, the gravitational potential ...
- 31
-1
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2
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36
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Why must the total time derivative only be a linear function of velocity? [duplicate]
I'm hung up on page 7 of Landau & Lifshitz Course on Mechanics. They claim,
$$L(v'^2) = L(v^2)+\frac{\partial L}{\partial v^2}2\textbf v\cdot \epsilon \tag{p.7}$$
The second term on the right of ...
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votes
1
answer
53
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How to show that angular velocity in 3D space is indeed a vector by using Feynman' method?
After reading this chapter of Feynman Lectures oh Physics: https://www.feynmanlectures.caltech.edu/I_20.html, inspired by Feynman's method in showing that torque is a vector, I decided to show that ...
- 421
1
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0
answers
32
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How much does classical mechanics depend on the choice of symplectic form?
TlDr; a different choice of symplectic structure on a phase-space $\mathcal{M}$ affects the Hamiltonian mechanics insofar as it could affect what the canonical coordinates are, but is this the only ...
- 230
2
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1
answer
56
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Why does the application of a magnetic field lead to non-thermodynamic equilibrium effects
There is a two-dimensional container filled with $N$ gas atoms, each with an electric charge $q$ and mass $m$. A magnetic field is gradually applied to this system in the direction perpendicular to ...
- 79
1
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1
answer
16
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Can the concept of angular velocity be uniquely defined for a deforming rigid body in non-uniform motion?
In rigid body mechanics, angular velocity is well-defined when the body maintains its rigidity. However, consider the case of a body that is deforming due to external forces while simultaneously ...
- 31
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2
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36
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What happens if a ball collides with a wall that provides a perfect rebound and the wall disappears after half the contact time?
I would like to pose a question that currently sparks my curiosity, and I would appreciate your help in answering it.
Imagine a ball colliding with a wall that provides a perfect rebound for the ball. ...
- 11
4
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2
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345
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Is there a classical Lagrangian system with essentially no cyclic coordinates?
Here is what I mean:
In Lagrangian mechanics, we have the equation
$$
\frac{\mathrm{d}}{\mathrm d t} \frac{\partial L}{\partial \dot q_i} = \frac{\partial L}{\partial q_i},\quad i = 1,2, \cdots, n.
$$
...
- 121
1
vote
1
answer
44
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Why do we include both local and temporal acceleration in fluid mechanics but only consider temporal acceleration in solid-body mechanics?
I am a beginner in physics, and I was studying fluid mechanics, specifically Newton's second law, when I was surprised to find that the expression for acceleration was composed of both local and ...
- 11
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1
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59
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Why are independent variables treated differently in kinetic energy calculations across problems?
In two different problems involving Lagrangian mechanics, I am confused about how independent variables are treated in the kinetic energy calculations. Specifically, in one case, an independent ...
- 101
3
votes
1
answer
118
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Covariant derivative acting on Dirac delta function
Pardon my naive computational question. In my calculations, I encounter the following expression:
\begin{equation} \label{eq1}
\frac{\delta}{\delta g^{\gamma \epsilon}(z)} \left( g_{\mu \alpha}(x) \...
- 85
1
vote
1
answer
49
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Exchange interactions between Spins in Ising model
I have studied Ising model and in general interactions inside the Hamiltonian of the form $ \sum_{ijk}k_{ijk}S_{i}S_{j}S_{k}$ (where k is the coupling constant) are disregarded.
What I don't ...
- 79
0
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1
answer
47
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Non-periodic motion in systems of 2 DOF
I was learning the vibrations of systems of 2 DOF.
One of the most simple examples is the following system:
Since it is a system of 2 DOF, it has 2 natural frequencies $\omega_{n1}$ and $\omega_{n2}$;...
- 904
-6
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0
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69
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How to create a physics theory? [closed]
I am interested on creating a new physics theory, so I want to know how to do it in the correct way. I also want to learn more physics, because I want to know how the world works.
1
vote
0
answers
40
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Mass Conservation in Kinetic Theory
In chapter 9 (The Boltzmann Equation) of Schwabl's 2006 text 'Statistical Mechanics', the author has the following statement of conservation of mass,
$$ \frac{\partial n}{\partial t} + \nabla \mathrm{...
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0
answers
29
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Energy conservation as a time translation symmetry [duplicate]
Noether's theorem says that a time translation symmetry gives rise to conservation of energy. However, my classical mechanics professor said in class that it was time reversal symmetry that gives rise ...
-1
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0
answers
63
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Four gradient relation
I'm doing an exercise in QFT and I have to calculate the energy-momentum tensor for the Klein-Gordon Lagrangian and by doing it I got the following term:
$$ \frac{\partial \ \partial^{\nu}\phi}{\...
- 141
2
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5
answers
234
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In special relativity, can a transfer of energy increase only the mass of a point particle and not its speed?
According to the mass-energy equivalence, if we have a point particle without internal degrees of freedom, then the energy content of this particle includes contributions from the mass as well as the ...
- 3,451
3
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2
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401
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Why Lagrangian mechanics cannot find the state of a system at any instant during the entire course of time? But Hamiltonian mechanics does
During the introductory class on Hamiltonian mechanics after we had learnt the Lagrangian formalism, our professor said
"We cannot use Lagrangian mechanics to find the state of a system at any ...
2
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1
answer
83
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Does a pop pop boat work with vacuum above the water?
(Given that there is an internal oxygen source then, of course.)
In other words:
Does the fluid pressure due to the boat's pipe(s) being underwater add to the water being pressed into the tube(s) in ...
- 226
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0
answers
25
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Virial theorem for liquids and solids?
It might be a stupid question, but I was wondering whether or not the virial theorem, or a generalized one, can be used for liquids or solids. I know one of the key thing is having a central force ...
0
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0
answers
29
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Does the trajectory of a body in a central-force field leave the force undetermined if I don't specify the number of bodies interacting?
Suppose I have a body orbiting in a (unstable, as shown by the effective potential of the system) circular orbit around another one in accordance to a inverse law of the form $$-kmm_1\frac{1}{r^4}$$
...
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2
votes
3
answers
84
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Deriving differential equation for the path of a particle in potential $U(r)$ using Maupertuis’ principle
I came across this Maupertuis' principle in Landau and Lifshitz, which, in it's final form looks like $$\delta\int\sqrt{2m(E-U)}dl=0.\tag{44.10}$$
They used this equation to show that path of a free ...
- 109
0
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3
answers
241
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Pivoting rod analyzed about a rotating axis
When solving a classic rotational dynamics problem — a uniform rod of length $L$ and mass $m$, pivoted at one end by frictionless pin and released from rest in the horizontal position rotates under ...
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4
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1
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148
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Is the Classical limit of Quantum theory the Newtonian Mechanics?
Recently I started to study Quantum Dissipative models like Caldeira-Leggett model and it occurs to me that this model provides a Quantum to Classical transition, but the Classical resultant system ...
- 3,387
3
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2
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340
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Understanding the definition of the covariant derivative
I'm currently working my way through the book "Mathematical Methods for Physics - An Introduction to Group Theory, Topology and Geometry" and I think I have a very fundamental ...
- 61
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1
answer
41
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Connection between gravitational potential function and Gaussian distribution function in 3 dimensions
I was reading Kai Lai Chung's book Green, Brown, and Probability. Consider the Gaussian distribution function in 3 dimensions:-
Now, this is a function of y, mean is x, and variance is t, which is ...
- 181
-2
votes
1
answer
59
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Need help in understanding Tangential Acceleration [closed]
I am studying Circular motion and I am confused about tangential acceleration and tangential velocity. I am studying uniform circular motion and it says the tangential acceleration is $0$ in uniform ...
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0
answers
47
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Identical particles and the fundamental group of classical configuration space
I have read through Leinaas and Myrheim's paper. I will first present my understanding, then ask my questions.
My Understanding
We consider some classical configuration space$^1$ $X$. Let $h$ be a ...
- 3,295
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2
answers
46
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How does larger change in KE lead to Oberth effect (or is it something else)?
(I know, there are similar questions here already, but not identical, and I haven't found a satisfying answer on any of them yet. If you do find one, let me know)
In short, I still don't get how the ...
- 113
4
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0
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108
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Is there an equivalent of Newton's laws for fields?
When discussing classical fields (I mean simple stuff like ordinary strings or water waves), could one construct some kind of Newton's law of motions for fields?
The first law is unusual in this ...
- 5,851
1
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1
answer
47
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Invariance under certain transformation in quantum mechanics and classical mechanics
I'm an undergraduate student in physics and have learned quantum mechanics (Griffiths) and classical mechanics (Marion). My question is bearing on the invariance under specific transformation.
In ...
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2
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1
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180
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Hamiltonian under the transformation induced by its own flow
Suppose we have a Hamiltonian $H(q,p)$ that leads to the flow:
$$
\begin{cases}
q=q(Q,P,t) \\[2mm]
p=p(Q,P,t)
\end{cases}
$$
where $P=p(0)$ and $Q=q(0)$ are the initial conditions.
I noticed that ...
- 114
3
votes
1
answer
67
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"Deriving" the covariant derivative
Suppose we are working in scalar QED with Lagrangian
$$\mathscr{L} = (D_\mu \phi)(D^\mu \phi)^* - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}.$$
I now want to find the form of the covariant derivative $D_\mu$ ...
- 283
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1
answer
53
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Derivative for the Maxwell field [closed]
I'm struggling with the following expression, which occurs in the derivation of the Maxwell Lagrangian in field theory.
$$\frac{\partial(\partial_{\mu}A^{\sigma})}{\partial(\partial^{\nu}A_{\lambda})}...
0
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1
answer
80
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The definition of the Lie Derivative
I am aware that an answer to an almost identical question already exist, however, I found the already existing answer not helpful (at least to my current question).
Carroll defines, in his book, the ...
2
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0
answers
101
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New equations of motion generated by symmetry transformations in Noether's theorem
Let us consider a mechanical system with coordinates $q^k$ ($k = 1, 2, \dots, N$) and a Lagrangian $L(q, \dot{q}, t)$. We introduce infinitesimal transformations of time and trajectories
\begin{...
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0
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14
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Is energy on the string part (when the wave moves) constant?
I have trouble understanding why the energy is constant in a part of the string. In my calculations, when I integrated the energy density over some interval, I obtained:
$$ \int_{0}^{a} u(x,t) \, dx ...
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3
answers
68
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What are "interaction particles" that cause gyroscope precession?
To move or rotate any object, we need some force, this force can interact with object in different ways, contact force(electromagnetic force between atoms), magnetic force etc. All these forces have ...
- 730
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1
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70
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Why are Weyl's Equations composed of only first-order derivatives?
I'm studying the Weyl's Equations from Section 1.5 of Perkins' Introduction to High Energy Physics.
The author says this:
Dirac set out to formulate a wave equation symmetric in space and time, ...
- 1,637
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0
answers
50
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Noether's theorem: action invariance vs lagrangian invariance
While trying to better understand Noether's theorem, I kept coming across three different formulations of it that seem to be distinct from each other. I'll be focusing on classical field theory in ...
- 269
2
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0
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117
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When does the Magnus Expansion converge for integrating angular velocity?
Because three-dimensional rotations about different axes do not commute, the angular velocity vector is not equal to the derivative of the angular displacement vector with respect to time. Instead ...
- 2,999
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1
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62
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Equivalent Russian / Soviet books for HC Verma "Concepts of Physics"
Yeah.. it is in the question. HC Verma "Concepts of Physics" is one of the most popular physics books in India. I didn't like that book much and I am looking for a Russian alternative to ...
2
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1
answer
61
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Tension in a ring rotating about its diameter [closed]
We have all seen the classic question to find the tension in a ring rotating about its own axis.
What about finding the variation of tension (with angle $\theta$) in a ring rotating about its ...
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4
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4k
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Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant, but rate of change of velocity is constant?
Like speed is only the magnitude, so ...
1
vote
1
answer
64
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Non-holonomic generalised forces of constraint
I am currently studying Analytical Mechanics having among one of the many references the book “Classical Mecanics” by Goldstein. And it is with respect to this that I have a doubt. My goal at the ...
- 11
1
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1
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27
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Method for minimising mass and maximising surface area of a parachute
I am participating in an Egg drop challenge, I want to design a parachute so that its impact force is less than $20 \, \text{N}$ to ensure the egg's survival. To do so I would need to balance mass and ...
- 11