# 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 massless particles have less number of possible polarisations than massive ones? [duplicate]

It is stated that according to quantum field theory the value $0$ for the projection of the spin of the photon would be impossible because the photon has null mass, thus photon has two polarizations ...
1answer
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### Electromagnetic waves how many polarizations for numberwaves?

I'm reading about stationary waves in a cube with side of length $L$. The electric field is described from a vector $E$ where each component is of the type $sin(\frac{\pi}{L}n_{j}x_{j})$ and the ...
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### Comparing heat capacity at different temperatures of $\rm CO_2$ at steam at different temperatures

How does the heat capacity of steam compare to that of $\rm CO_2$ at high temperatures and low temperatures where vibrations and rotations are “frozen out”? My thinking was that at higher temperatures ...
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### Degrees of Freedom of water and $\rm CO_2$ at high temperatures

How do I calculate the degrees of freedom for $\rm CO_2$ and water at high temperatures? I'm confused because I know $\rm CO_2$ is linear while H2O is nonlinear, and am wondering how this would affect ...
1answer
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### How many degrees of freedom would water have at $\rm 500K$?

At this temperature, and lower, the rotational degrees of freedom would already be in action, then at this higher temperature id think vibration degrees of freedom are no longer frozen out. So this ...
2answers
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### How many numbers are required to describe attitude or orientation in $n$-dimensions?

In general, the attitude or orientation of a rigid object is described by three numbers. For an aircraft, these might be the pitch, roll, and yaw with respect to the direction of motion. For a ...
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### Are gravitons possible in 2+1 spacetime dimensions?

Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal ...
1answer
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### Properly accounting for indistinguishability of (homonuclear) diatomic molecules in “internal” partition function

I have always liked Schroeder's take on the partition function being a product of translational and internal degrees of freedom: $$Z_1 = Z_{\text {trans}} Z_{\text{int}}$$ where $Z_{\text{int}}$ can ...
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### How to determine the degrees of freedom and generalised coordinates in this satellite exercise?

(image below) We have a satellite on an elliptical orbit. m1=m2=m in this case. The problem is only 2 dimensional in the x-y-plane. One should determine the degrees of freedom and choose suitable ...
1answer
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### Understanding vibrational mode of a molecule and its contribution to average energy

I'm facing difficulty understanding how vibrational energy modes contribute to a molecule's average energy (or heat capacity). What I know is : For a polyatomic non-linear molecule, there are $3N-6$ ...
2answers
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### How to determine the number of generalized coordinates in the following example?

Question: In this exercise one needs to determine the generalised coordinates. We have a pendulum in a magnetic field $B$. The pendulum rotates around its axis with an angular velocity $ω$ on the ...
2answers
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### How to determine the number of constraints in this problem set?

I don't understand how to determine the number of constraints in this given problem set in classical mechanics (picture attached down below). Now lets take a look at this problem for example where a ...
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### What is the internal energy of water vapor? OR How many degrees of freedom does $\rm H_2O$ have?

Here are the "knowns" that I'm working with. Internal Energy for a monatomic gas is $$U = (3/2)nRT$$ For a diatomic gas its $$U = (5/2)nRT$$ All of my textbooks and online sources indicate ...
1answer
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### How many degrees of freedom are there in the universal physical constants?

If you were to change one universal physical constant (say, electron charge) then the universe would behave differently in observable ways. For one thing, this would change the fine structure constant,...
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### Why do some gases have fewer degrees of freedom at same temperature?

I am trying to understand the degres of freedom for gases. Air has 5 degrees of freedom at room temperature but why does Argon, $Ar$ have 3 degrees of freedom while $O_2$ has 5 at the same temperature ...
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### What does this graph represent?

I dont understand the second graph below. If I understand the first one right, it represents the potential energy between two atoms. So if we bring them closer together or separate them past the ...
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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 ...
1answer
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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 ...
1answer
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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). ...
1answer
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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....
2answers
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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 ...