# 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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### Degree of freedom - Lorentz transfomation reduces it? [duplicate]

I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count. See, for example, the ...
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### Counting degrees of freedom in theories with two-forms [duplicate]

I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
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### Is Bohr's model one-dimensional?

Purdue university in its article on Bohr's Model explains: At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular ...
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### Is the number of degrees of freedom always equals one?

If the number of degrees of freedom is the minimum number of independent variables necessary to describe the system, does this mean that this number is always equal to one? For example, if, as it ...
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### Equal average energies in translational and rotational degrees of freedom

In, An Introduction to Thermal Physics, Schroeder states It’s not obvious why a rotational degree of freedom should have exactly the same average energy as a translational degree of freedom. However, ...
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### How many degrees of freedom does a diatomic and triatomic molecule have at high temperatures?

I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is ...
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### Is the equation for degrees of freedom $f=3N-k$ valid for all cases?

Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of ...
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### How many independent equations do Maxwell's equations represent in arbitrary dimensions?

In an arbitrary number of spacetime dimensions $D$, Maxwell's equations are \begin{align*} \mathrm{d}F &= 0, \\ \mathrm{d}(\star F) &= -J. \end{align*} How many independent equations does this ...
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### Degrees of freedom in a molecule of $N$ atoms

I am trying to understand why the number of degrees of freedom in a molecule, $3N$, is the same as the number of degrees of freedom of $N$ independent particles. Why do the molecular constraints like ...
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### Regarding Degrees of Freedom and dynamics of polyatomic molecules [closed]

Justify how a molecule with N atoms have $3N-5$ vibrational degrees of freedom(Linear) and $3N-6$ vibrational degrees of freedom (Non-linear). Will this be valid for large number of N? Taking $H_2O$ ...
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### Doubt regarding kinetic theory of gases

My school teacher had told me that one of the assumptions of Kinetic Theory of Gases was that the molecules of a given gas were all identical and to be considered as very small elastic spheres. ...
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### Difference between Kopp-Neumann and Dulong-Petit law?

So this is basically a follow-up to this question: How many degrees of freedom does the water molecule have? I've done some further research and found that the main difference between Dulong-Petit and ...
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### Why expansion of real gases lead to cooling?

Paul Hewitt writes in his book Expansion of real gases lead to cooling as average translational kinetic energy per molecule decreases. The reason given is: During Expansion molecules collide with ...
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### How many degrees of freedom does the water molecule have? [duplicate]

This is mainly a question about molar heat capacity. I've read many different values for the degrees of freedom of water, for example f = 12 on (https://en.wikipedia.org/wiki/Molar_heat_capacity). But ...
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### Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?

Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$. Spin 1 ...
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### Fermionic and bosonic degrees of freedom of a vector superfield

I am currently studying supersymmetry with the SUSY primer of Stephen P. Martin (https://arxiv.org/abs/hep-ph/9709356) and there seem to be not equally many bosonic and fermionic degrees of freedom (...
1 vote
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### Why does a degree of freedom vanish from 3D to 2D in that tensor construction?

Let's assume an arbitrary tensor in 3D coordinates: $g_{ij}$ with $i, j$ in $[1,3]$. It shall be arbitrary, meaning not symmetric. It has 9 entries which equals 9 degrees of freedom (dof). Now, I ...
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### The equipartion theorem and degree of freedom in case of vibration

I have been taught in chemistry that, the energy of a vibrational freedom is $RT$ (ie, twice that of rotational/translational) The degree of freedom which I found in chemistry, for the vibrational ...
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### How can an object have more than 3 degrees of freedom?

In 1 of my robotics classes our professor told us that something can have up to 6 degrees of freedom:translation in the x axis , translation in the y axis,translation in the z axis,rotation around the ...
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### Does off-shell graviton in 3+1D still have two degree of freedom?

In general relativity, on-shell spin 2 graviton has 2 degree of freedom in 3+1D due to gauge symmetry, which is because of einstein equation, however, for off-shell graviton, does it still have 2 ...
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### Why is the heat capacity of water $9R$ and not $6R$?

From the equipartition theorem, the relationship between energy and temperature in a substance is $U=\frac{NRT}{2}$ for $N$ quadratic degrees of freedom associated with a particle of that substance. ...
1 vote
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### Elastic collisions and internal degrees of freedom

As I was considering elastic collisions today a question popped into my head. Do elastic collisions imply that there are no internal degrees of freedom in the colliding objects which couple ...
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### How many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity?

In $d$ dimensions, how many independent equations are contained in $R_{rsmn}=0$ in consideration of the Bianchi identity $\nabla_{[a}R_{bc]de}=0$? This discussion reveals the independent equations ...
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### Why do systems of $n$ coupled oscillators have $n$ normal modes?

Consider a linear system of $n$ differential equations with constant coefficients corresponding to a physical scenario where I have $n$ coupled oscillators (like $n$ masses attached by springs in ...
1 vote
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### How does a field $\phi(x,t)$ have infinite degrees of freedom and why are its inputs labels not variables?

Consider a classical Lagrangian $L(q, \dot{q})$, which by definition has a discrete number of degrees of freedom. Now suppose we have a quantum field (or any field) which we denote by $\phi(x,t)$. It ...
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### How to Conceptually Understand Long Wavelength Fluctuations?

I have been trying to conceptually understand long-wavelength fluctuations of degrees of freedom, and I have been reading this (RG) to do so. I understand was it means for a degree of freedom to ...
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### What do we mean by "Degrees of Freedom" when we Talk about the electromagentic field?

For point-like particles, the term "degree of freedom" seems rather clear: It's the number of independent coordinate functions $q_i(t)$ that we need to specify to completely describe the ...
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In the Newman-Penrose formalism one encodes the ten degrees of freedom of the Weyl tensor $C_{\alpha\beta\mu\nu}$ in the five complex scalar potentials $\Psi_0$, $\Psi_1$, $\Psi_2$, $\Psi_3$ and \$\...