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; ...

learn more… | top users | synonyms (1)

0
votes
2answers
2k views

Potential energy from opposing magnets repelling each other with a gap of 1 mm

I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the ...
4
votes
1answer
105 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 ...
2
votes
2answers
71 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 ...
0
votes
0answers
25 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 ...
0
votes
0answers
21 views

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 ...
4
votes
1answer
121 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
0
votes
0answers
71 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 ...
4
votes
1answer
73 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 ...
2
votes
0answers
51 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 ...
3
votes
5answers
319 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
0
votes
0answers
32 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 ...
1
vote
2answers
561 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
-1
votes
2answers
872 views

Find generating function $F_1$ for canonical trasformation

I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation. For example, considering the transformation $$q=Q^{1/2}e^{-P}$$ $$p=Q^{1/2}e^P$$ ...
12
votes
2answers
548 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
4
votes
2answers
250 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 ...
0
votes
1answer
40 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?
1
vote
1answer
51 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 ...
3
votes
0answers
129 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 ...
23
votes
16answers
4k views

Can a car get better mileage driving over hills?

Two towns are at the same elevation and are connected by two roads of the same length. One road is flat, the other road goes up and down some hills. Will an automobile always get the best mileage ...
2
votes
1answer
75 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. ...
0
votes
0answers
26 views

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 ...
2
votes
0answers
41 views

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 ...
2
votes
3answers
97 views

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 ...
2
votes
1answer
65 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 ...
1
vote
1answer
4k views

Floating Objects and Weight

The Situation: A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string. The Question: The ball is attached to the beaker, thus ...
0
votes
1answer
67 views

Normal force, work and conservativity

I have searched very much on line, both in this site and elsewhere, but found no proof of whether the normal force is conservative or is not, in general. Clearly, if the force is orthogonal to the ...
0
votes
0answers
48 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 ...
1
vote
0answers
35 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 ...
3
votes
1answer
41 views

Limits for the linear wave equation

In acoustics and continuum mechanics the following wave equation (for Speed of Sound $c$) for the pressure field $p$ is well-known: $\partial_t \partial_t p = c^2 \Delta p$. This wave equation can be ...
2
votes
0answers
42 views

How did Lord Rayleigh find the volume fraction of argon to air?

In order to isolate for pure nitrogen, Lord Rayleigh and his colleagues took some air and removed oxygen, carbon dioxide, and water vapour, leaving behind what he believed to be pure nitrogen. In ...
1
vote
0answers
10 views

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 ...
2
votes
2answers
53 views

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. ...
0
votes
1answer
39 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 ...
-1
votes
1answer
57 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 ...
1
vote
1answer
51 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 ...
2
votes
1answer
154 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
1
vote
1answer
59 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 ...
2
votes
2answers
62 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
0
votes
2answers
69 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 ...
1
vote
2answers
160 views

Is it possible to write explicitly the exact solution for forced damped harmonic oscillator?

Preamble Consider a damped harmonic oscillator, with his well know differential equation \begin{equation*} m \ddot{x} + c \dot{x} + kx=0 \end{equation*} and let's find the solution that satisfies ...
0
votes
2answers
74 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 ...
8
votes
1answer
120 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 ...
0
votes
0answers
34 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 ...
1
vote
2answers
171 views

Can we describe the classical laws of physics in a frame-of-reference-independent way?

First of all, I am not a physicist, so I cannot guarantee things I say will make sense. I will try my best, though. In classical mechanics we have the notion of inertial frame of reference. If my ...
3
votes
4answers
431 views

Is this solveable? Simultaneous elastic collision of 4 objects in XY plane

I'm writing a computer program/game and can't figure something out; I want to be able to calculate the resulting velocities of 4 particles (hexagons, specifically) after they simultaneously ...
1
vote
1answer
75 views

Relative kinematics and laws of Newton

I am an engineering student and currently taking a class on kinematics and dynamics. I study at a German university so it may be that I don't translate everything correctly. In the first module of ...
0
votes
2answers
101 views

Maximum Extension of a Spring [closed]

In the given figure: m= 5kg, F = 30N, K = 700N/m In the figure shown above. the surfaces are friction-less. The blocks are initially at rest and the spring is initially in its natural length. What ...
3
votes
1answer
425 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
0
votes
2answers
75 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
5
votes
2answers
452 views

Heisenberg picture of QM as a result of Hamilton formalism

Consider the formula for the total time-derivative of a physical value in Poisson's formalism: $$\tag{1} \frac{dA}{dt} = -\{H, A\}_{P.B.} + \frac{\partial A}{\partial t}, $$ where $\{A, B\}_{P.B.}$ is ...