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1answer
47 views

Why do molecules have $3N-5$ or $3N-6$ degrees of freedom?

In linear molecule, it has $3N-5$ degree of freedom in vibration mode and $3N-6$ in non-linear molecule. I can get idea about $5$ and $6$ which is related to translation and rotation but I cannot ...
1
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1answer
56 views

What is the degree of freedom of pure rolling motion?

A cylindrical body is pure rolling, what will be the degree of freedom for it? I am confused between 2 and 1 if slipping occurs than it has 2 but in pure rolling there's no slipping so what will it ...
3
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0answers
50 views

Integrals of motion for a free particle

I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion. In particular, I can't understand ...
0
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2answers
65 views

is curvilinear motion really a type of linear motion?

Let us consider any arbitrary curve except a straight line in the Cartesian coordinates. From the perspective of the particle tracing the curve the motion can only be linear. But from the point of ...
0
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1answer
86 views

Number of degrees of freedom in the Standard Model Lagrangian

Consider a Lagrangian $L$ which depends on a number of fields $F_1$, $\cdots$, $F_N$ and their (spacetime) derivatives. Each of those fields $F_n$ is valued in $\mathbb{R}^{k_n}$. Is the Standard ...
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1answer
70 views

Degrees of freedom of rolling coin

I gave a mental ability test yesterday in which this question was asked. A rolling coin on a flat surface has how many degrees of freedom? I read about degrees of freedom but I haven't had much ...
1
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1answer
88 views

How is no-conspiracy theory compatible with determinism? [closed]

Bell's theorem states that any physical theory that incorporates local realism and the no-conspiracy assumption cannot reproduce all the predictions of quantum mechanical theory. Hence, we cannot ...
0
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1answer
44 views

What causes the universe to manifest a given value upon measurement in super-deterministic theory? [closed]

Bell's inequalities show that we have to give up freedom or local realism. If we give up freedom, we have super-determinism, if we give up local realism, we have free-will. In super-deterministic ...
6
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2answers
213 views

Why are there only 3 Additive Integrals of Motion?

1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19: "There are no other additive integrals of the motion. Thus every closed system has seven such ...
1
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1answer
80 views

Unphysical degrees of freedom in the Yang Mills Lagrangian [duplicate]

Im taking my first course in QFT and has stumbled upon something that I do not understand. Given the Yang Mills lagrangian $$\mathcal{L} = -\frac{1}{4}F^{a}_{\mu \nu}F^{a\mu \nu}$$ with $F^{\mu \nu}...
6
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3answers
83 views

Degrees of freedom and temperature

I quote the following lines directly from the Wikipedia page titled "Heat capacity": "...rotational kinetic energy of gas molecules stores heat energy in a way that increases heat capacity, since ...
0
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1answer
36 views

Regarding $f$ degrees of freedom & $f\!-\!1$ constants & inclusion of these constants

In the classic & famous book "Electromagnetic fields & Interactions" by Richard Becker (Dover publishing), on page 55 (of volume 2) , author says: If the system possesses f degrees of ...
1
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3answers
180 views

Maxwell's equations - underdetermined - uniqueness

Maxwell's equations can be seen as two dynamical equations (the two curl equations), and two constraint equations (the two divergence equations). So we have 6 unknowns ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
0
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0answers
29 views

What does 'fully excited' actually mean?

In statistical mechanics you often hear the phrases such as 'when the degrees of freedom are fully excited then....'. An example would be the validity of the equipartition theorem. But what is the ...
0
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1answer
37 views

Two bodies connected to each other with with a string of lenth L is a rigid body? [duplicate]

Suppose we have two bodies A and B, they are connected to each other with an ideal string of length $L$. Then is this system a rigid body? This system has 5 degrees of freedom ( 6-1 constraint). But a ...
3
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1answer
44 views

About the holographic principle

I read at a book this quote "As the degrees of freedom of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-...
0
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1answer
81 views

What Magnitude(db) and Phase(deg) represent on Bode Diagram?

What Magnitude(db) and Phase(deg) represent on Bode Diagram? I am working on 2 DOF System and I want to understand some basic things. Below (on the picture) you can see the system, the transfer ...
1
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2answers
160 views

Degrees of freedom of quantum scalar field

In Srednicki P33, we tried to generalize the time evolution equation in Heisenberg picture: $$ e^{+iHt/\hbar}\varphi(\mathbf x, 0)e^{-iHt/\hbar}=\varphi(\mathbf x, t) $$ into relativistic form: $$ e^{-...
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0answers
15 views

Microscopy - Depth of Field Shrinks with Magnification

From empirical results I was able to gather that the DOF of a microscope I was working with had been reduced, when I swapped the tube lens to a one with greater magnification (but the same objective ...
0
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0answers
27 views

How can I get the Resonant Frequencies (Bode plot)? (Response of 2-DOF System)

I want to study the response of the system. I want to find the resonant frequency of the sprung mass (m1) and the resonant frequency of the unsprung mass (m2). Because I am not sure if I have ...
0
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0answers
33 views

Why changes in the degrees of freedom implies changes in the internal energy?

In Thermodynamics we describe equilibrium states of macroscopic systems. For those equilibrium states we make a description giving one macroscopic coordinate for each measured degree of freedom (like ...
0
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1answer
40 views

Question about the concept of particle's degrees of freedom

For all I know, an one-dimensional free particle has 1 degree of freedom and 3 degrees of freedom in the 3-D world. And in thermal physics, one-dimensional simple harmonic oscillator has 2 degrees of ...
6
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1answer
112 views

Are path integrals integrals with countable or uncountable infinite dimensions?

Path integrals are integrals with infinite dimensions. But I recently became confused about if the number of dimensions are discrete/countable or continuous/uncountable. I always thought it should be ...
0
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0answers
53 views

Splitting different aspects of a system in Quantum Mechanics with tensor products

My understanding from Classical Mechanics is that the degrees of freedom of a system are the generalized coordinates which we use to describe the system. In that case the number of degrees of freedom ...
0
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0answers
38 views

Number of components of a One-Form Superfield

A Supersymmetric Yang Mills theory has 8 bosonic and 8 fermionic components. Since SUSY YM Theory is described via the Vector Superfield, $$V=C(x)+i\theta\chi(x)-i\bar{\theta}\bar{\chi}(x) \dots.$$ ...
1
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1answer
73 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has $\frac{n+n^2}...
0
votes
1answer
28 views

Indistinguishability versus Lack of energy for degrees of freedom of a symmetrical atom

Consider the degrees of freedom (thermodynamic) for an Argon atom. It has 3 translational degrees of freedom. Everyone seems to agree that at normal temperatures it has no rotational degrees of ...
3
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1answer
98 views

On the c-theorem

I have been reading a few papers on CFT and AdS/CFT regarding the c-theorem and I have a few questions regarding c-theorems: a) Why is it that the c-theorem is usually considered for only unitary ...
0
votes
1answer
50 views

Counting number of degrees of freedom in constrained system

Following Counting degrees of freedom in presence of constraints, we know that there would be N-2M-S dofs if we have M 1st-class constraints and S 2nd-class constraints in N-dim phase space. I don't ...
2
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1answer
61 views

Kinetic theory of physics [closed]

$$E = (3/2) kT$$ For average kinetic energy of a molecule gas.The constant $k$ does not depend on the type of molecule. Can this result be true for both hydrogen and chlorine?
1
vote
1answer
28 views

Degrees of freedom for custom made finger

I'm designing a 3D printable prosthetic hand. Each finger has 3 joints. The first 2 joints let the finger only move in the vertical (y) direction. The final joint is like a ball and socket joint (...
0
votes
0answers
45 views

General relativity degrees of freedom — simplified version?

I'm afraid my question may be too general, but I would like to ask how I could find out the degrees of freedom in a given tensor. I have had this question since I started studying GR. At first, I ...
3
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1answer
158 views

Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
1
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1answer
54 views

Why do $\psi_a$ and $\bar{\psi}_{\dot{\alpha}}$ represent two different degrees of freedom?

I am taking a course in QFT and I've been introduced to the concept of left-handed (undotted) and right-handed spinors (dotted). I know that left-handed spinors are associated with the irreducible ...
1
vote
1answer
47 views

Why does a system whose equations of movement are $\lambda^2U^{\alpha} + \partial_{\mu}F^{\mu \alpha} = 0$ have three degrees of freedom?

I'm trying to understand the solution of a problem where I have to study a field ($U^\mu$) which Lagrangian is: $$\mathscr{L} = - \frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \frac{1}{2} \lambda^2 U_{\mu} U^...
0
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1answer
48 views

Prove that $n$ degrees of freedom leads to $n$ normal modes

I have probably missed that during my studies. I intuitively know (but then I might be wrong in some detail, that's why I am asking), that $n$ degrees of freedom in oscillating system leads to $n$ ...
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0answers
56 views

Find the Kinematic degrees of freedom of the following contraption

In the above mechanism it is required to find the generalized coordinates to write equation of motion of the MDOF system. I just want to ask how do we actually approach such a problem? How to identify ...
-1
votes
1answer
48 views

At what temperature does the vibrational degree of freedom becomes significant for an ideal diatomic molecule?

For ideal diatomic molecules such as $\text{H}_2$, $\text{N}_2$ and $\text{O}_2$, at what temperature does the vibrational degree of freedom significantly contributes to the calculations such as that ...
1
vote
1answer
66 views

State counting in the d = 1+2, $\cal{N} = 2$ vector multiplet

The question is from Box 8.2, page 282 of the book "Gauge Gravity Duality" by Ammon and Erdmenger. The link to the specific page from Google Books is here. According to the authors, a $\mathcal{N} = ...
2
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1answer
85 views

Matching bosonic and fermionic degrees of freedom in Wess-Zumino Lagrangian

In Wess-Zumino model, supersymmetric Lagrangian in addition to the ordinary complex scalar field $\phi$ contains auxiliary field $F$ (also complex scalar) to match the degrees of freedom of the Weyl (...
0
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0answers
32 views

How many degrees of freedom to diagonalize the metric?

In A. Zee's Einstein Gravity in a Nutshell, he starts with the following expansion of the metric at some point $P$ of a Riemannian manifold, with coordinates $x^\mu$ that have the origin at $P$: $$ ...
0
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2answers
140 views

What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
0
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4answers
519 views

For a diatomic molecule, what is the specific heat per mole at constant pressure/volume?

At high temperatures, the specific heat at constant volume $\text{C}_{v}$ has three degrees of freedom from rotation, two from translation, and two from vibration. That means $\text{C}_{v}=\frac{7}{...
2
votes
1answer
3k views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
1
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2answers
163 views

The “potential energy” degree of freedom?

I'm reading Schroeder's "An Introduction to Thermal Physics" and he mentions the vibrational degrees of freedom of a diatomic molecule: A diatomic molecule can also vibrate, as if the two atoms ...
0
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1answer
102 views

Rotational/spin degrees of freedom for a monoatomic gas in free space [duplicate]

How many degrees of freedom does a monoatomic gas have? According to my Thermal Physics textbook, there are $3N$ degrees of freedom for $N$ particles because the particle is free to move in the $x$, ...
0
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0answers
138 views

What is the degrees of freedom of metric tensor?

As $g_{\mu\nu}$ can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions. But, why we call these 10 functions as the degrees of freedom of the metric while they are the ...
3
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1answer
177 views

Do photons have six degrees of freedom?

Calculations involving pressure and volume relationships of photon gas during the cosmologic expansion of the universe posit an adiabatic cooling process with a heat capacity ration of 4/3. This ratio ...
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0answers
71 views

Finding the configuration space and degrees of freedom of spherical pendulum

Suppose we have a spherical pendulum tethered to the origin in $\mathbb{R}^3$ where the length of the rod is a time varying function $l(t)$. What is the configuration space of this system, and how ...
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3answers
2k views

Why do we say linear molecules only have 2 rotational degrees of freedom? Why does the third 'frozen' one not count?

It is possible to excite rotations around the axes perpendicular to the bond of a linear molecule. However, rotation around the axis along the bond of the molecule would require huge energies, due to ...