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 to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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30 views

Proof that oscillations in 1d potential well occur between certain points

In >>this<< situation, a particle with energy $E$ will oscillate between the positions $x_1$ and $x_2$ indicated on the diagram. This simple fact is taught in many introductory courses however I ...
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6answers
346 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. ...
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1answer
103 views

simple question on torques on an ellipsoid

I have an ellipsoid, and in the reference frame where the x-, y- and z-axis are aligned with its eigenvectors I compute the torque $\vec\tau$ acting on it. And I'm asking myself how can I quantify ...
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1answer
476 views

Hamiltonian Noether's theorem in classical mechanics [duplicate]

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 ...
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0answers
34 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
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0answers
14 views

What physical parameters are really being described when a rope manufacturer cites “elongation %”?

I have a precision pulley system sensitive to micron displacements. I am having issues because I need a cord with low tensioning force, but also low stretch. I am getting some weird hysteresis in the ...
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1answer
158 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 ...
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1answer
103 views

Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
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1answer
23 views

Motion in oscillating field: expanding in powers of $\xi$ [closed]

I'm reading an excerpt from Landau/Lifschitz's Mechanics book about motion in oscillating fields. Two equations for the motion of a particle with mass $m$ are set out: \begin{equation} m\ddot{x} = ...
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2answers
57 views

How 'rare' is no-slipping?

I have come across a lot of questions that say something like: A ball rolls down a hill without slipping... But I have done the maths and found that a ball would only 'not slip' if the friction ...
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1answer
38 views

Angular momentum and the Units

I'm just curious about why many physical identities build relationship with the same units as angular momentum like the action, Lagrangian$\cdot$time, Hamiltonian$\cdot$time, phase space area etc?
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1answer
78 views

Work and chemical energy “paradox”

This is a mistake I've seen many people make, a few physicists included, but I haven't ever seen a satisfactory explanation for what's going on. Apologies for the lengthy setup. Setup Suppose I ...
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1answer
36 views

What does a scale accelerating on an incline read?

I was watching an online video lecture about dynamics, and then I came across this brain teaser, and I've been thinking it over for a couple of hours but can't seem to find the solution. I hope ...
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1answer
73 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
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2answers
117 views

What is the difference between configuration space and phase space?

What is the difference between configuration space and phase space? In particular, I notices that Lagrangians are defined over configuration space and Hamiltonians over phase space. Liouville's ...
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0answers
27 views

Force acting on a wheel of a two-wheeled self balancing bot

Proceeding further with my work on a self-balancing bot as posted here: http://bit.ly/1FfI6LK I've gotten stuck at the following equation: n = Gear ratio $K_t$ = DC motor torque constant $i_l$ = DC ...
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1answer
59 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and ...
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1answer
55 views

Can someone explain what's the difference between all these terms in “Simple Words” with their “applications”? [closed]

I'm very confused between all these terms. Can someone explain what's the difference between Classical Mechanics, Relativistic Mechanics, Quantum Mechanics, Quantum Field Theory, ...
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1answer
74 views

Solving the Three-body problem numerically

I want to create a program in $Mathematica$ that solves numerically the Three-body problem by Euler-Lagrange's equations. I was searching some methods to sucessfully do it. So I found a way to solve ...
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1answer
106 views

How does one express a Lagrangian and Action in the language of forms?

In Lipschitzs Classical Mechanics a Lagrangian is defined as: $L(q,q',t)$ for some trajectory $q(t)$ of a particle And the action is defined as: $S:=\int^a_b L(q,q',t) dt$ How does one ...
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1answer
53 views

Hamilton-Jacobi problem

In analytical mechanics by Fasano and Marmi they consider the Hamilton-Jacobi equation for a conservative autonomous system in one dimension with the following Hamiltonian, \begin{equation} ...
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1answer
3k views

Determine the maximum height a pump can suck up water

I am working on a homework problem that presents the scenario of trying to raise water from a small reservoir of depth 8 m whose surface is 25 m below a pump that can maintain a pressure differential ...
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1answer
57 views

Jacobi energy function $h$ and the Hamilton $H$ and the Hamilton-Jacobi equation

My understanding of the Jacobi energy function $h$ as defined in Goldstein is that it is the total energy $T+V$ expressed as, \begin{equation} h(q,\dot q,t)=\sum \frac{\partial L}{\partial \dot q}\dot ...
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1answer
24 views

What can I say about a graph depicting orbit a particle has gone through? Acceleration VS friction

I have an orbit in which a particle is told to have gone through. There is a straight part, and a curved part. I am asked to mark the right statements, which are: a. Without any further data, there ...
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1answer
28 views

Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
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1answer
55 views

Proving independence of the lagrangian on position of a free particle using the euler-lagrange equation

I asked a similar question some time back but am trying to work this from another angle. In deriving the lagrangian of a free particle, we use the homogeneity of space to conclude that the lagrangian ...
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9answers
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How to explain independence of momentum and energy conservation in elementary terms?

I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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1answer
50 views

Maximum range of projectile from elevation, simply?

Let us say you have project a ball at velocity $u$ from a cliff hight $h$, and we want to find the maximum range of the ball. Ok so you could do this using equations of motion (for constant ...
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2answers
60 views

In which direction does mud fly off a moving bike's tire & why?

If a bike moves through a muddy area, mud gets on its tires. Then the mud flies off from the tires. Which forces are acting on it? In which direction does it fly off? On my physics test, I wrote ...
4
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3answers
268 views

Runge-Lenz vector and Keplerian Orbits

Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
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1answer
77 views

Lagrangian for free particle in special relativity

From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$. In special relativity we want Lorentz-invariant action thus we define free-particle ...
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0answers
15 views

How this tube rotates? [duplicate]

I recently seen a video where a tube is spin into space. When it starts to rotate, it keeps continuously to rotate along the axis of 180 degrees clockwise, then 180 counter-clockwise and so on. The ...
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0answers
33 views

name of this bouncing balls separator model

https://www.youtube.com/watch?v=SRGf0Mq2Zwg I want to read the physical and mathematical model of this "bouncing balls separator " in the above link . What is name of this experiment so I can search ...
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2answers
72 views

Relation between magnetic moment and angular momentum — classic theory

How do I prove the relation between the vectors of magnetic moment $\vec\mu$ and angular momentum $\vec L$, $$\vec\mu=\gamma\vec L$$ ? Many text books and lecture notes about the principles of ...
2
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3answers
309 views

Is there a quick way of finding the kinetic energy on spherical coordinates?

Assume a particle in 3D euclidean space. Its kinetic energy: $$ T = \frac{1}{2}m\left(\dot x^2 + \dot y^2 + \dot z^2\right) $$ I need to change to spherical coordinates and find its kinetic energy: ...
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4answers
125 views

Classical and quantum systems [closed]

What are the main differences between a quantum and classical system? How does one can distinguish them?
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2answers
73 views

do the planes of electron orbits make an angle?

if we think as the electrons around the atoms classically, then as the two electrons in the first shell (1s) go around the nucleus; do the planes of orbit make an angle with each other (as an average) ...
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1answer
51 views

Deriving lagrangian of a free particle - How do you arrive at Lagrangian independency conclusions

I guess this question has been asked before, but I'm looking at a slightly different aspect. I'm reading Landau's book on classical mechanics. In deriving the lagrangian for a free particle, I ...
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1answer
70 views

Equations of motion for a system of $n$ particles given the potetial [closed]

I am having difficulties on the following question: The equations of motion for a system of n particles are: $$m \ddot{x}_i = - \dfrac{\partial U(x_1,...,x_n)}{\partial x_i}$$ $$\ddot{x}_i = ...
2
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0answers
56 views

Decoupling of generalized coordinates in lagrangian

Say you have a lagrangian $L$ for a system of 2 degrees of freedom. The action, S is: $S[y,z] = \int_{t_1}^{t_2} L(t,y,y',z,z')\,dt \tag{1}$ If $y$ and $z$ are associated with two parts of the ...
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1answer
34 views

What stops the middle point of a power line from falling?

Say you have a system that is a uniformly weighted string with slack suspended from two points; i.e. a power line. There are three forces acting on any given point on this string: string tension ...
5
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2answers
290 views

How come a whistling kettle starts whistling only when water boils, and not long before - due to hot air escaping under pressure?

A whistling kettle will start to whistle when the water boils and turns into a jet of steam which then exits the small aperture in the spout. But why doesn't this happen much earlier - when the air ...
5
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1answer
220 views

Why do some impact craters have an elevation in the center?

Why do some impact craters have an elevation in the center? What processes lead to its formation?
1
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1answer
104 views

Coupled wheel and rod (analytical mechanics) [closed]

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
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1answer
85 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
3
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2answers
214 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
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1answer
62 views

Is there a speed limit for objects falling in gases or liquids? [duplicate]

Let $o$ be a spherical object with mass $m$ and surface $s$. Let $g$ be the gravitational acceleration and $h$ the height. Let the gas where we drop $o$ in have density $d$ and pressure $p$ at ...
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2answers
1k views

Countersteering a motorcycle

Everyone knows the story about countersteering. For those who don't I will explain it below and after the explanation i will ask my question. You can watch this short video as a beginning: ...
2
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1answer
86 views

Is it true that the self-force prevents a classical particle from falling into a Coulomb potential? What is the physical explanation of this result? [closed]

In 1943 CJ Eliezer published a paper claiming that the self-force prevents a zero angular momentum particle from ever reaching the center of an attractive Coulomb potential (and what's more that it ...