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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41 views

Massive Spin-1 Lagrangian: Removal of Spin-0 degree of freedom

I am currently reading Schwartz on QFT and the Standard Model and arrived now at Chapter 8.2.2, where he derives a Lagrangian for a massive Spin-1 field. The final Lagrangian looks like this: $$ \...
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What effect Heisenberg uncertainity principle can have on the degree of freedom of a molecule?

Though I don't know much of the details of the above mentioned principle, I came to know that it allows measurement of spin of electrons in only clockwise and anticlockwise manner of the same axis. So ...
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Why do we not consider rotation as a Degree of Freedom in Monoatomic Gases?

I completely understand that the average energy of each degree of freedom in a thermodynamic system is (1/2)kT and that we do not consider the spin about an axis of symmetry in a polyatomic molecule ...
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Independent coordinates of a rigid body

This is a quote from Classical mechanics by Goldstein: "To fix a point in a rigid body, it is not necessary to specify its distances to all other points in the body ; we need only state the ...
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Why are constant volume and constant pressure heat capacities basically the same for solids? Are degrees of freedom involved?

I knowv that $C_V=\frac{\frac{f}{2} Nk_B}{m}$ and $C_P=\frac{(\frac{f}{2} +1)Nk_B}{m}$. Since for solids their values are very close to each other, I would assume $\frac{f}{2} +1$ is very close to $\...
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What is the proof of law of equipartition of energy?

In thermodynamics, law of equipartition of energy states that if we have any gas sample then the total kinetic energy will be distributed among the different degrees of freedom of the gas sample. Each ...
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117 views

What is the proof of $C_{V} = \frac{fR}{2}$?

I came across this formula in thermodynamics. Please give me a rigorous proof to this formula. My teacher did not even give any proof neither do any of my books. The formula is : $C_{V}=\frac{fR}{2}$ ...
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24 views

Why do you have to ponder the number of degrees of freedom of a specie by its temperature?

When calculating the number of degrees of freedom that contribute to the energy of the universe, one uses the following expression: $$ g(T) = \sum_B g_B\left(\frac{T_B}{T}\right)^4 + \frac{7}{8}\sum_F ...
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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 ...
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28 views

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 ...
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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 ...
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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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How many degrees of freedom of $n$ spin 1/2 particles (discard spatial degrees of freedom)?

I think the state of the system can be expanded by basis $\{|000...0\rangle,|100...0\rangle,...|111...1\rangle\}$. So we can be completely certain of this state if we know the coefficient of these $2^{...
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All possible choices for two independent thermodynamic variables for a one-component, one-phase system

I am confused about the independent variables in thermodynamics. I know that for a one-component, one-phase system, there are only two independent intensive variables that can be chosen and which ...
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Double Spring Damper Mass System Transfer function

I am attempting to find the resonance frequency of a double mass spring system as shown in the image. I need to find the resonance frequency so that I can input it into my sin wave generator in MATLAB ...
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Rotational equation for variable mass in Matlab/Simulink ignores relative angular velocity of the mass flow?

I am building a simulation using the Matlab/Simulink software. The software block I am using called 'Custom Variable Mass 6DOF (Euler Angles)'. This link provides the documentation of the simulation ...
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Completeness of Maxwell's equations

If we consider Maxwell's equations in the form: $\nabla\cdot\overrightarrow{E}=\frac{\rho}{\epsilon_0}$$\nabla\cdot\overrightarrow{B}=0$$\nabla\times\overrightarrow{E}=-\frac{\partial\overrightarrow{B}...
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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 ...
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32 views

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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Why isn't energy conservation equation sufficient to determine the motion?

The star of large mass $M$ is orbited by planets of masses $m_1$ and $m_2$. The energy conservation equation for this system is$$\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}-MG\left(\frac{m_1}{...
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Confusion with degrees of freedom [closed]

I am facing a lot of confusion regarding the degrees of freedom of various molecules. I want to know some facts with certainty. I will talk about what I have read, please correct me if I am wrong. I ...
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209 views

Understanding dependent/independent variables in physics

How does one determine the independent and dependent variables? What do the terms mean? Can they be derived from a formula? For example I saw in a textbook $F = k\Delta l$, Hooke's Law, that $F$ is ...
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271 views

Number degrees of freedom for Sphere on a inclined plane

How many generalized coordinates are required to describe the dynamics of a solid sphere is rolling without slipping on an inclined plane? What I think is that there two translational degrees of ...
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How does gauge symmetry constrain the dynamics of a field's physical degrees of freedom?

My rough understanding of gauge theory is that some of a field's degrees of freedom (d.o.f.) may turn out to be "non-physical" due to local symmetries. But does gauge symmetry constrain the ...
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112 views

What is the theoretical justification for the Law of Equipartition of Energy?

What is the theoretical justification for the Law of Equipartition of Energy? Why are equal energies distributed in each degree of freedom even though sometimes they are completely different (like ...
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457 views

How many Degrees of Freedom do Linear Triatomic Gas Molecules Have and Why?

I read this in one of my textbooks that stated Linear Triatomic Gas Molecules like CO2, HCN, CS2 in which all the atoms are linear, the total number of degrees of freedom are Nf = NT + NR + NV where ...
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1answer
57 views

What are the physical degrees of freedom in Yang-Mills theories?

I am pretty familiar with the Lagrangian formulation of quantum electrodynamics and perturbation theory techniques; however, I am hoping to move into QCD and other Yang-Mills Theories. As I do, I am ...
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82 views

Number of degrees of freedom if independent coordinates are functions of time

If there are $n$ independent coordinates for a system of particles, but all of them are functions of time, is it correct to say that the degree of freedom is 1? If we know the instant of time we're ...
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151 views

Degrees of freedom of a rolling sphere [closed]

How many degrees of freedom does a sphere rolling on a smooth (frictionless) plane has?
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377 views

Degree of freedom of a Sphere

We all have learnt that a single atom posses 3 translational degree of freedom and no other. But it happen to be a sphere too. Is it correct to say that a sphere has 3 rotational degree of freedom? ...
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86 views

How to make derivative of antisymmetric tensor?

When I read the Conformal Field Theory of Di Francesco et al, I found I will get two different answers from the same expression. To get the (2.131) $$ \dfrac{\delta x^{\mu}}{\delta\omega_{\rho\nu}}=\...
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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 ...
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119 views

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 $3N-6$ ...
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2answers
272 views

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 ...
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53 views

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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86 views

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 ...
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1answer
74 views

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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100 views

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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Degrees of freedom in a Kahlerian NLSM

Lagrangian for $d=1$ $\mathcal{N}=4$ SUSY model on a $n$-complex dimensional Kahlerian target space is given as (see p.213, eqn. (10.251) in the Mirror Symmetry book (pdf)) $$\begin{equation} L= ...
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64 views

Does the ideal gas law apply to gases which consist of more than one atom?

In the derivation of the ideal gas law, one sets for the average kinetical energy $f = 3$ degrees of freedom. This refers to the transition in x,y,z axes. This is true for gases, which consist of only ...
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Counting supersymmetries in $d=4$ vs in $d=1+1$

Having studied supersymmetry in $d=4$, my understanding is that we count supersymmetries by the number of pair of complex supercharges $$ Q_\alpha^I = \begin{pmatrix} Q_1^I \\ Q_2^I \end{pmatrix}~,~ \...
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7answers
249 views

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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1answer
104 views

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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156 views

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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1answer
236 views

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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2answers
166 views

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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