# Tagged Questions

Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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### How can I answer the critical questions of mechanics? [duplicate]

I have passed my 1st year of undergraduate study life somehow I could have managed. But recently I have decided to fill up the emptiness of knowledge over mechanics. Besides I have my studies of 2nd ...
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### How to find zero-point oscillations for this system?

Consider the following Hamiltonian which is absolutely relativistic literally: only sensitive to absolute pairwise relative phase space variables of objects for a system of $N$ objects moving in one ...
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### Rigid bodies - the wheel

As I've been taught lately in my mechanics course: the wheel has a unique property: at every moment of motion, the touching point between the wheel and the ground is not in movement and ...
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### Why does my door shut faster when the window is open?

I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if ...
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### Hamiltonian for forced systems

I am trying to learn Hamiltonian mechanics. While many textbooks treat closed systems, I have a hard time finding references for forced systems. For example, if I consider simple systems of masses ...
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### Symmetries for an inertial frame

According to Noether's theorem, a symmetry of space-time w.r.t. an observer, will yield a corresponding conservation law for a closed system w.r.t. that observer. Now if our space-time has 3 ...
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### Landau's argument for dependence of Lagrangian on magnitude of velocity

In chapter 1, of Landau-Lifshitz Mechanics' book, Landau through isotropy and homogeneity of space and homogeneity of time proves that the Lagrangian must depend of magnitude of velocity of the ...
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### How to check $\renewcommand{\vec}[1]{\mathbf{#1}} \vec{v'}\cdot\vec{V}$ and $\vec{v}'^2$ are time derivatives of some other functions?

From Landau, Lifshitz Mechanics p.127 $\renewcommand{\vec}[1]{\mathbf{#1}}L'=\frac{1}{2}m(\vec{v}'^2+\vec{v'}\cdot\vec{V}+\vec{V}^2)-U$ He states that "$\vec{V}^2(t)$ can be written as the total ...
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### Expansion of $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ [duplicate]

How can I find the expansion of the Lagragian (it it only dependent on $v^2$) $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ in powers of $\vec{\epsilon}$ ? (From L.Landau, E. Lifshitz, Mechanics , ...
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### Why doesn't Newton's Second Law include higher-order mass?

I suspect this has been asked here before, but I didn't find anything using Search. Why is Newton's second law only second-order in position? For instance, could there exist higher-order masses $m_i$ ...
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### Fixed lever arm spinning under gravity, why am I getting these results?

Suppose there is a lever arm of length $L$, a mass $m$, and it is fixed at one end. The lever is parallel to the ground. So the force acting on the center of mass of the lever would be $mg$. Now ...
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### Does an object on top of a lever arm have angular velocity at the moment when the lever is released?

Suppose there is a lever arm fixed at one end, and it is parallel to the ground. There is an object resting somewhere on top of the lever arm (the object is not attached to the lever). At the moment ...
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### Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt}$

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
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### How do I correctly choose signs for a falling particle?

An object falls from a height $h$ above water through air with negligible drag. In the water, the upward buoyancy exactly balances the downward gravitation force. The only remaining force on the ...
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### Looking for an intuitive understanding of normal force

I understand normal force to be the perpendicular force to a surface of contact. However, I have come across a problem which has caused me to rethink this. My initial understanding of force is ...
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### Classical point particles to classical fields

I often hear that in the continuum limit we can study large numbers of particles as fields. I always imagined that by removing all bounds on the number of particles (while keeping total energy, ...
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### Are the the elongation the same when one end of a spring is attached to the wall and

Consider there are 2 identical springs. One end of the first spring is attached to the wall and the other end is pulled by a force $\vec{F}$. It is depicted as shown in the first figure below. Both ...
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### Mechanics Landau Galilean Principle

I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is ...
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### How do you justify neglecting electron-electron interaction in the Drude model?

I'm sure there's some way to justify it. Maybe a screening effect?
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### Classical Mechanics & Coordinates [closed]

What is the meaning generalised coordinates in Classical Mechanics? How is Lagrangian formalism different from Hamiltonian formalism? How are they related to Hamilton's Principle? How are they ...
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### Deriving the law of moments

Recall the Law of Moments for a one dimensional rod: "When an object is in equilibrium the sum of the clockwise moments is equal to the sum of the anticlockwise moments." I understand that we ...
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### What if the kinetic energy of a particle was some other function $f(v)$?

This is a "what if this was how the universe worked" kind of question. I don't know if those belong in Physics StackExchange, and I apologize if they don't. Suppose we have two reference frames ...
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### Trouble with classical mechanics self-learning (How to avoid going down the Physics rabbit hole?) [duplicate]

I'm a retired police officer trying to learn classical mechanics on my own. I have gone through many links on the Internet including the classical mechanics quick reference textbooks from Physics ...
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### Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line?

I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am ...
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### Stationary action with maximized action [duplicate]

I would like to ask for an example (a lagrangian) both in classical and quantum level for which the action is maximaized (rather than minimized). What is special in these cases?
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### How to calculate the van der Waals force from the van der Walls equation?

Given the van der Waals equation $$\left(p+\frac{n^2a}{V^2}\right)\left(V-nb\right)=nRT$$ and the van der Waals constants $a$ and $b$, how can I find the van der Walls force between two atoms at ...
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### Friction on an object moving with momentum over a surface

I'm familiar with the equations for friction for a static object and an object moving at steady speed over a surface from high school physics. But we never learned how an object moving only due to ...
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### Emmy Noether's theorem in simpler terms

I'd like to understand Noether's theorem and its contents as to what it implies in a bit simpler terms. I am familiar with mathematics unto Calculus 1,2,3 and some linear algebra and group theory. I ...
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### Diffraction of sound

The sound waves, by the virtue of it being a wave, shows diffraction and interference. But in diffraction, I learnt that if the wave is allowed to enter through a small aperture, there is a central ...
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### prediction of a moving object

OK, this may be a hard question to answer and really all I am looking for is an equation as I don't even know what to call this. This is all for a game so bare with me please. In the game two ...
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### Transforming a lagrangian to hamiltonian and vice versa

I am not refering to Legendre transform, but to something more simple. In analytical mechanics, the Lagrangian can be described as $L=T-V$, and the Hamiltonian is if the Lagrangian doesn't explicitly ...
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### Why does centre of mass of ice-container system shift in absence of any net external force?

Consider a cube of ice in a flat based container(the base is very broad).The temperature of the system is at first fixed at a minus Celsius temperature, but then the system is left on a table with the ...
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### Symmetries of relativistic Lagrangian and Hamiltonian systems

In non-relativistic mechanics, the conserved quantities found using Noethers theorem in Lagrangian mechanics are the same as those quantities which are conserved under canonical commutation with the ...
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### Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...
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### Constraints of massive relativistic point particle in Hamiltonian mechanics

I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint: ...
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### Stable and Unstable Orbital Resonance

I was wondering if anyone can show me why some orbital resonances are unstable. For example in the asteroid belt there is a depleted distribution at 3:1 resonance with jupiter. What is the cause of ...
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### Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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### Three-mass, two springs copled oscillator NOT attached to walls

Int he three-mass coupled oscillator problem, we often see it stated that you have three masses, (they can be equal or not, but we'll assume they are equal here) connected by two springs and then ...
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### Work done by rolling vs skidding friction force

Two identical bicycles having equal weight riders are traveling along a level road adjacent to each other with the same non-zero velocity. Bike A, (the "skidder"), applies the rear brake strongly ...