# Questions tagged [degrees-of-freedom]

This tag is for questions relating to the Degree of Freedom (DOF) of a mechanical system. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering.

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### Why can't a particle rotate about its axis? [duplicate]

When treating an atom as a point partcle, it is usually assumed that it cannot rotate about its axis. Is it that anything considered as a point particle cannot rotate about its own axis? If so, why is ...
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### What is 'degrees of freedom' when using Fourier series to express a periodic waveform?

We can express any desired periodic waveform using Fourier series. In the book I am studying from it's said: 'We see that with Fourier series, we can produce any desired periodic waveform and extract ...
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### Degrees of freedom for a bead on a parabolic wire?

How many degrees of freedom does a bead on a parabolic wire have? I think it must be two degrees of freedom since the bead is constrained to move on the wire (up, down motion and left/right motion). ...
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### How do you find the degrees of freedom of a rigid body moving parallel to a fixed plane surface? [closed]

Find the degrees of freedom of a rigid body moving parallel to a fixed plane surface. I know the definition of degrees of freedom which meant we need minimum number of coordinate to specify something....
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### A problem on Degrees of Freedom

Degrees of freedom of a massless rod, moving freely in space with a speck which is constrained to move on it? It seems massless rod is ideal I am very confused how to regulate degrees of freedom. ...
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### Does emergence or the second law create more degrees of freedom total? [closed]

Here's my layman thought process: By emergence and the second law, new "modes" or points in configuration space become "unlocked" with macroscopic systems. One is a brain, which ...
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### How to count degrees of freedom in a symmetric $N \times N$ matrix?

I am reading Wayne Hu's short lecture on cosmology mathematical infrastructure (https://arxiv.org/abs/astro-ph/0402060), and have several questions. Some background for us lazy people that don't want ...
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### Why particles can have different number of degree of freedom in a 3D + 1T dimension?

Air molecule has $6$ degrees of freedoms: it can move up & down, left & right, front & back, rotate along $x$-axis, $y$-axis, $z$-axis. But I heard about graviton, a hypothetical particle ...
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### How do we know from representation theory that a massless spin-1 particle has only two polarizations?

In chapter 8.2.3 of Schwartz' textbook "Quantum Field Theory and the Standard Model", the author states the following, Finally, we expect from representation theory that there should only be two ...
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### Generalized coordinates of two unequal masses attached to a mass-less rigid rod

Consider a system of two particles of masses $m_1$ and $m_2$ moving in a plane. Let the respective position vectors be $\mathbf{r_1}$ and $\mathbf{r_2}$. The particles are attached at the end of a ...
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### Is three dimensional supergravity dynamical?

So it is well known that standard $D = 3$ Einstein gravity is non-dynamical in the sense that the graviton has no on-shell degrees of freedom (d.o.f $= D(D-3)/2$ and the theory is topological). ...
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### Gauge invariance and the degrees of freedom [duplicate]

I am currently starting to learn some QFT. And I am very confused by the fact that the freedom to choose a gauge for a theory controls the physical degrees of freedom. Please correct me if i am wrong ...
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### What is the origin of the irreducible error $\propto e^{-N}$?

In this (timestamped) lecture, the professor says that any measurement includes an irreducible error that scales as $e^{-N}$ where $N$ is the number of degrees of freedom in the measurement apparatus ...
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### Effective degrees of freedom of relativistic gases: Intuition for fermion factor 7/8?

When calculating the number density of a gas of identical massless particles you get the following integral $$I_{n,\,\pm} \equiv \int_0^{\infty} \frac{u^2}{e^u\pm1} \,\text{d}u$$ with (+) for ...
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### Reviewing an old argument about the number of DOFs of EM field

For free electromagnetic fields, it is possible to choose a gauge such that the scalar potential $\phi(t,{\bf x})=0$ and the vector potential ${\bf A}(t,{\bf x})$ satisfies the Coulomb gauge condition ...
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### How do I calculate the bosonic/fermionic degrees of freedom from the helicity content?

After constructing a physical state and discovering the particle content, how can one find the fermionic and bosonic degrees of freedom? Eg. Constructing the physical states of an $\mathcal{N} = 2$ ...
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### Degrees of freedom of large molecules

I know how to calculate degrees of freedom for small molecules, but how do I calculate degrees of freedom for larger molecules? For example, Benzene.
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### graph relativistic degrees of freedom

I'm trying to graph the relativistic degrees of freedom, which should look like the figure And I am trying to guide me with this Phys.SE answer: Number $g(T)$ of relativistic degrees of freedom as a ...
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### Number of independent components of the electromagnetic field

I'm taking a course on electrodynamics and I'm confused when we start talking about potentials. The electromagnetic field seems to have 6 independent components to me. It's described by six dynamical ...
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### Spin of the particle and degrees of freedom

Wigner showed that irreducible representations of the Poincare group can be listed, depending of the mass being zero or larger then zero, as $2J+1$ dimensional representations where $J$ is half-...