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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Mechanical equilibrium : thermodynamics and classical mechanics

A similar question was asked here but mine is a bit different. In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid). In classical mechanics, equilibrium is ...
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Lagrangian $L' = L + \frac{df}{dt}$ gives the same equations of motion

It is well known that when a Lagrangian $L$ is incremented by the total time derivative of a function $f$ that does not depend on the time derivatives of the generalized coordinates, the same ...
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Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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Can the coefficient of friction be derived from fundamentals?

It is common to want to derive macroscopic laws from what we know microscopically - after all, given a (correct) microscopic description, everything larger should follow. Has it ever been done to ...
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Does the force of releasing the latch of a spring-latch contraption affects the force generated by the spring?

There is this contraption in my class, where a rod is attached to a latch and a spring. By pulling the latch back behind a piece of metal, the latch is secured, the rod if pulled back and the spring ...
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40 views

Determining the components of the force on a curved surface due to pressure

I have a cross section of a half-tube with a pressure gradient across it causing a force outwards. I am attempting to extract the vertical component (in relation to diagram) of the force on this ...
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41 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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1answer
15 views

Motion in a central field in Landau Mechanics

What does this mean when E=U_eff? I don't think this means the first term in E is zero. I don't understand the sentence ' This is a cubic equation for cos(theta)'
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$\mathbf{P}=M\mathbf{v}_{cm}$ for a continuous body?

While restudying some fundamental concepts with greater attention, I have reflected on the following deduction, which I find in my book of mechanics, of the identity of the temporal derivative ...
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Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
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Spring on a rotating disc [on hold]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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43 views

Total angular momentum of a continuous body

I find the definition of total angular momentum $\mathbf{L}$ of a system of $n$ material points with respect to a given point $Q$ as the sum of the momenta $\ell_i=\mathbf{r}_i\times\mathbf{p}_i$ ...
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How does the optimal-gear indicator work? [migrated]

Modern cars like BMW, Ford, Audi come with a system on the panel which tells the driver the next optimal gear to drive. How does it work ? What is the algorithm behind it? What data does it require ...
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22 views

Two blocks connected to a massive pulley [on hold]

As in the picture above, I'm trying to solve for the rotational acceleration of the pulley. We assume the string is massless and the surface is frictionless. I tried reasoning in the following ...
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2answers
48 views

Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
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97 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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22 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...
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58 views

How does electromagnetic radiation affect the velocity of a charged particle?

I've heard that the acceleration of a charged particle releases electromagnetic waves. So let's say there is a charged electron moving forwards in a region with a downwards magnetic field. If the ...
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70 views

Interesting approach to Kepler problem

I won't go into the explanation of this idea, because it is explained in this blog post. In this paper, which was featured on John Baez's blog, $\frac {dt}{d\lambda}$ is given as $\frac r V$, where ...
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46 views

How to relate internal energy to atomic motion?

I am trying to conceptualize how atomic motion leads to the thermodynamically-defined internal energy (denoted as $U$ below) through some broad mathematical relationships. I get that the internal ...
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26 views

Thermodynamics of a rubber band

I have a streched rubber band and I know that tension f is proportional to the temperature T when the length is constant. How can I proove that internal energy is only a function of temperature? I ...
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1answer
71 views

General construction of equations of motion for free particles

I've got a question regarding the different Symmetrie-Lie-Groups of Newtonian Mechanics and special realtivity. Is there a canonical way to obtain the equations of motion for a free particle only by ...
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1answer
43 views

Classical Hydrogen Atom

I was wondering about the Hamiltonian description of the classical hydrogen atom (two point particles interacting through a Coulumb potential). In particular, I want to know if the fact that ...
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1answer
68 views

Quantum mechanics and Classical limit(s)

I have tried to make sense of this and i am not sure i get it. What i gather from this page about the classical limit is: You need coherent states something like $\hbar \to 0$ is not really enaugh. ...
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Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
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1answer
28 views

Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
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Particle moving under force $F=-cx^3$ [closed]

A particle with mass $m$ moves under influence of a force $F=-cx^3$, with $c$ a constant. What is the potential energy function $V(x)$? And if it starts to move from rest from position $x=-a$, what ...
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120 views

Thermalization of coupled classical oscillators

I would like to understand if it is possible to perform an experiment, where a bunch of classical harmonic oscillators (e.g., LC circuits or mechanical pendula) coupled in a simple manner (e.g., one ...
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1answer
57 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid?

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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114 views

Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
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31 views

Rain falling into a cart on an incline [closed]

I have a practise question in which a cart on and incline of angle $\alpha$ and starts initially at velocity $v_ 0$. Just as the cart moves off it starts raining vertically and the mass of the rain ...
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42 views

How does one find the phonon frequencies for a 1D anharmonic interaction potential?

Suppose there is a one-dimensional crystal with an anharmonic interaction potential between particles (e.g. $U = ax^2+bx^3$ where $x = d-a$ with $d$ as the distance between two particles and $a$ as ...
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Good reference on angular motion especially on linear and angular velocity? [duplicate]

I am currently using a book called "Classical Mechanics" by Goldstein, which is a very good text and has amazing introdution to Lagrangian mechanics. Unfortunately not too much is said about angular ...
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Why does the period/frequency of a fan slow down significantly when I taped a piece of rubber band to it?

All of this was done with a standing fan set horizontally on a table. During an experiment, I had to tape a piece of rubber band to one of the standing fan's blade and measured the period of the fan. ...
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60 views

Bicycle gyroscopes [migrated]

I've been having this idea for some time but never worked it out properly, mainly because I lack the required engineering knowledge. I wondered if it would be possible to convert the energy you ...
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16 views

Calculate bicycle efficiency power transmission?

How can I calculate the efficiency of power transmission from a person to a bicycle with standard flat pedals? How can I calculate the efficiency of power transmission from a person to a bicycle with ...
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1answer
36 views

Which of the Physics textbooks would you recommend I read this quarter (Analytical Mechanics)? [duplicate]

My Analytical Mechanics class this quarter has one required textbook: "Classical Dynamics of Particles and Systems" by Thornton & Marion and three recommended readings: "Mechanics" by Landau ...
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1answer
51 views

Determine the equation of motion [closed]

The problem is the following. A ring of mass $m=1$ is moving along a circle of radius $R$ without friction. It's tied to a spring (coefficient $k$) of natural length $0$. The other end of the spring ...
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1answer
44 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
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2answers
122 views

Momentum is a cotangent vector?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...
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1answer
53 views

Definition of kinetic energy without the second Law of Newton

As I see it, the definition of kinetic energy $$T= {1\over2} m u^2 \text { where $u<<c$}$$ comes by using the definition of work $$W= {\int F\cdot\ dx }$$ and we use for the meaning of ...
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2answers
62 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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242 views

Fluid flow: Force acting on the fluid and the Navier-Stokes equation

Consider a one dimensional fluid flow in a rectangular tube. Typical streams are the poiseuille streams. Consider the case in wich we apply a force on the fluid. The Navier-Stokes equation (for ...
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2answers
68 views

What is the significance of angular frequency $\omega$ with regards to wave functions?

What is the physical significance of $\omega$ in a function like $$ f(x) = Asin(kx + \omega t) $$ The only place that I am familiar with angular frequency is when dealing with circular motion, but ...
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1answer
103 views

What is the physical interpretation of the Poisson bracket [duplicate]

Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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30 views

Ratio between power of chaotic and regular airflow

Turbulent field is created as a result of an impact of an airjet on an edge (the flow velocity is high enough). The field of velocities have a regular and a chaotic component. What I need is to ...
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Does the second law of thermodynamics take into consideration of attractive interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...