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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The tested scale of classical mechanics

I was reading this, but I was wondering actually how good an approximation is classical mechanics in very large chosen scales? Which makes me would like to ask a question here: to what scale, order ...
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Classical probability of harmonic oscillator

I am trying to derive the classical probability density function to find the harmonic oscillator at position $x$. I am confused between the random variables involved here $x, t$ and not able to ...
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22 views

First integrals for a particle in a central-force field

Consider an arbitrary dimension $n>3$. What are the independent first integrals for a particle? The Hamiltonian is $$ H = \frac{p^2}{2m} +V (|r|) . $$
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25 views

Will water vapour rise in vacuum?

If I put water vapour in vacuum, will it behave normally like a gas? Will it rise up in the vacuum?
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1answer
32 views

Intuition about Momentum Maps

I'm studying Classical Mechanics and there is one object that appeared recently on the book I'm not being able to get a physical intuition about it. The mathematical definition goes as follows: Let ...
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2answers
60 views

Is the universe a Turing machine?

Reading about Computable numbers I wondered if there is any physical experiment that returns non-computable numbers or if there is any physical theory that needs non-computable numbers. Because if ...
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1answer
69 views

Mathematics of the Virtual Displacement

So I'm pretty certain this question has been asked to death here, but I still can't find a good explanation of a very particular aspect of the virtual displacements in physics. Background For ...
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0answers
34 views

What is special about quantum entanglement? [duplicate]

Get two pieces of paper. In secret write the same number on both papers. Transfer one paper to the Moon. Look to the paper which is left at the Earth. Voila! We know what is on the Moon paper. The ...
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1answer
446 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
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1answer
27 views

Find the separation distance for a line of oil being squashed between two flat plates [on hold]

I was wondering if someone could give me some help on how to start this problem, I'm really struggling to get my head around it. A long line of oil is being squashed between two flat plates of length ...
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4answers
468 views

When/why does the principle of least action plus boundary conditions not uniquely specify a path?

A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, ...
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2answers
36 views

Where does the energy go when you stretch a rubber band?

There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same ...
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1answer
24 views

Efficiency of a gravity feed hose

If I am trying to fill a large cylindrical container with a gravity feed hose, would it be more efficient, time-wise, to drill a hole in the bottom of the container for a greater initial pressure ...
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5answers
99 views

How can we explain the difference in change of kinetic energy, due to different frames of reference?

Imagine a ball ($m= 1\,{\rm kg}$) moving at a velocity $2\,{\rm m}/{\rm s}$ towards a wall. When it hits the wall, it suddenly stops, thereby liberating all its ${\rm KE}$ as heat. Here, the initial ...
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0answers
73 views

Poisson brackets and magnetic field [on hold]

I'm a maths student trying to teach myself some physics so sorry if I'm missing something simple here. I think the main problem is lack of experience with the Levi-Cevita symbol. We have a particle ...
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3answers
66 views

What was the motivation behind the work formula?

Surely there must be a reason we decided to use this as a metric for mechanical energy.How was it developed and what made it more acceptable than other work formula candidates (Like force over time, ...
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1answer
79 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
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2answers
36 views

Is configuration space in any similar to vector spaces?

The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else. I have just learned about vector spaces and their properties and on the other hand have also ...
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What axial forces does the vertical load induce? [closed]

What axial forces does the vertical load P induce in the members of the system down in the figure? Neglect there weights of the members themselves and assume an ideal hinge at A and a perfectly ...
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1answer
51 views

Why is centre of mass taken as integral of x.dm and not m.dx?

Forgive me if I'm being naive, but, I don't understand why the X-coordinate of the Centre of mass is taken as an integral of x.dm and not m.dx. I understand the summation part, but how do we convert ...
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3answers
113 views
+50

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
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Hausdorff spaces and finite elements

Must the shape functions and the interpolation functions (which are the same in an isoparametric element) in a finite element model be elements of a Hausdorff space? If so, is this necessary to ...
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0answers
31 views

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
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47 views

why do things stick to surfaces when left for a really long time?

I tried to move a cardboard box off the top of a cabinet, which left it on for probably years, and it was insanely difficult to remove. I don't know why this happens, but it also seems that my feet ...
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1answer
27 views

How does height of a parachute affect air resistance compared to circumference or diameter?

I'm trying to find out how much a double in height (making it more ovular or oblong in shape) of the parachute affects air resistance compared to a double in circumference or diameter. Can someone ...
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0answers
38 views

Classical Statistical thermodynamics phase space and residue $h$

In classical statistical mechanics we have to divide the partition function by a factor of $1/h^n$. In almost every calculation of a real quantity this cancels out and is thought to be a remnant of ...
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3answers
169 views

Is there an intuitive explanation of the work formula?

Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
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25 views

Magnitude of acceleration uniform circular motion

A particle moves in a plane with uniform velocity $ r' = 4 m/s$. The angular velocity is constant and has magnitude $θ' = 2 rad/s$. When the particle is $3 m$ from the origin, find the magnitude of : ...
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44 views

Two Particles in a Harmonic Oscillator with repulsive short-range potential

Do bear with me, I am attempting to learn to write some simulations on the computer and learn some simple MD, so I defined sort of a toy problem. I have two particles confined in a Harmonic Potential ...
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1answer
49 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
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2answers
53 views

The pressure in a container of water is based on depth. So what happens if I remove the bottom of the container?

So I understand that if we have a system that involves a container of water the pressure will equal atmospheric pressure at the top and as we go further down the container the pressure will increase ...
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0answers
30 views

How is the Routhian of classical mechanics defined?

The Hamiltonian is a function on the cotangent bundle to a configuration manifold $H:T^*M\rightarrow \mathbb R$. The Lagrangian is a function on the tangent bundle to the configuration manifold ...
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2answers
51 views

How does friction act on a body, if only 2 regions on it are rough? [closed]

While tackling an Olympiad question, it came to my mind that friction need not act in the same direction at all points on a body. I thought of using integration to evaluate the net frictional force, ...
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1answer
45 views

Why do systems with a fixed gear-ratio still use gears?

From my understanding, there are two uses of a gearing system: to change the speed of output rotation (trading it with torque), and to change the axis of rotation. Now, in a car, for example, it is ...
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Why is sometimes more difficult to lift a baby?

I have a small cousin and she enjoys when I pick her up, which I can do pretty easily. Sometimes though she decides she wants to make my life difficult, and when she decides so, she tells me she is ...
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1answer
62 views

Why closed in the definition of a symplectic structure?

Why do we want the 2-form $\omega $ to be closed? What if it is not?
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1answer
78 views

Chaos and integrability in classical mechanics

An Liouville integrable system admits a set of action-angle variables and is by definition non-chaotic. Is the converse true however, are non-integrable systems automatically chaotic? Are there any ...
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1answer
23 views

Extension spring and permanent damage

Is there a way to calculate how far an extension spring can be extended before it suffers permanent damage? There are some online calculators, but how are they done? This calculator is the most ...
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53 views

How fast must a penny roll to remain upright?

I solved this question, however my professor's answer is different from mine. I modelled the penny as circular disc of radius $a$ so its moment of inertia is: $$I_s = \frac{ma^2}{2}$$ so $$I = ...
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1answer
35 views

Harmonic oscillator :Two masses are attached to one unfixed spring from both sides (vertically) [closed]

while ($t<0$) the system is still ($\Sigma$ F=0). Mass $m_2$ is held while $t<0$. Mass $m_1$ is located $h_0$ meters above the ground and the spring is currently stretched $L$ meters. The ...
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1answer
55 views

Why was the Stark effect discovered much later than the Zeeman effect?

This is strange. The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical ...
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3answers
99 views

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...
3
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1answer
26 views

What is the Optimal Separation Length for the Tines of a Tuning Fork?

I'm building tuning forks (for fun... why not?), and among one of the design decisions is how far apart should I place the tines (the two long prongs) from each other. I'm not entirely certain whether ...
2
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1answer
61 views

Every central-force field is integrable, right?

In 3d, there are four independent first integrals, namely, the three components of the angular momentum, and the total energy. So by the Liouville theorem, it is integrable, right?
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Why is the Hamilton-Jacobi equation important? [closed]

Someone may say it is related to the Schrodinger equation. Okay, let us forget about quantum mechanics. So, if we confine ourself to classical mechanics, why is the Hamilton-Jacobi equation important ...
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1answer
44 views

Limits of integration [closed]

In the following video can someone explain why did he take the limits of integration to be from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ ? ...
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0answers
53 views

Mechanics question I don't understand solution

A simple top consists of a heavy circular disc of mass m and radius a mounted at the center of a thin rod of mass $\frac{m}{2}$ and length a. If the top is set spinning at given rate S, and with the ...
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spin-orbit coupling for a rigid body

Consider the motion of a coffee cup in the gravitation field of earth. The force acting on the cup apparently depends on the orientation of the cup. Therefore, the internal rotation (with respect to ...
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29 views

Is there a Lagrangian that can lead to the Rayleigh-Jeans law?

Is there a way to derive the Rayleigh-Jean's law using classical statistical mechanics only? On the internet there is a common way to arrive at the equation by using concepts in electrodynamics. This ...
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Winch bridle force calculation for performer flying

Hi this is my first post o this site so please forgive me if I have got anything wrong in the process. I am trying to do some calculations on the forces some performer flying winches are seeing. ...