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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Can the Lagrange Multipliers depend on the coordinates?

When dealing with Lagrange multipliers to solve systems with constraints we usually have two ways if the constraints are holonomic: Differentiate the constraint and add the appropiate term to the ...
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340 views

Curve object in liquid under pressure [duplicate]

I would like to know how red forces are compensate in this study. A black solid object is put in a liquid (helium or hydrogen for example). It's a curved solid. Solid don't move up or down, imagine it ...
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64 views

How to interpret the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$?

There is a small area element of size $da$ and normal vector $\hat n$. I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a ...
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568 views

How can you solve this “paradox”? Central potential

A mass of point performs an effectively 1-dimensional motion in the radial coordinate. If we use the conservation of angular momentum, the centrifugal potential should be added to the original one. ...
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455 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
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Classical Limit in Quantum Mechanics

Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will ...
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Internal kinetic energy and center of mass kinetic energy

For a given system, how can you tell which one is kinetic energy for center of mass and which one is internal kientic energy? K = Kcm + K int For example, "A 150 g trick baseball is thrown at 63 km/...
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248 views

A discrete approach to the catenary

I'm trying to work out a model for the system above, that is, $N$ particles of unitary mass subject to the constraints: $$1=\varphi _i(\mathbf r _1,\mathbf {r}_2,...,\mathbf r _n)=|\mathbf r_i-\mathbf ...
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152 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
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113 views

Classical mechanical problem

I have two planes, one characterized by equation $$\phi_1=f(x)-z=0$$ and another $$\phi_2=\alpha y-z=0$$ where $\alpha$ is arbitrary. In their line of intersection(we assume it exist and is continous) ...
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597 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= \...
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Explicit time dependence of the Lagrangian and Energy Conservation

Why is energy(or in more general terms,the Hamiltonian) not conserved when the Lagrangian has an explicit time dependence? I know that we can derive the identity: $\frac{\partial \mathcal{H}}{\...
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105 views

Classical mechanics problem for two boxes [closed]

![enter image description here][2] This question is truly annoying, and I have been stuck for an hour on part D, would greatly appreciate if anyone could shed a light on this problem. Why ans for ...
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58 views

Acceleration of 2 bodies tied with a string [closed]

Find the acceleration of the block of mass M shown in the figure . The co-efficient of friction between the 2 blocks is μ1 and that between the bigger block and ground is μ2. Could someone help ...
3
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68 views

Virial of a system

I had obtained $$\overline{E_{kin}} = -\frac{1}{2}\overline{\sum_j\mathbf{r}_j\cdot\mathbf{F}_j}$$ and was asked to show that if the forces are conservative then $$\overline{E_{kin}} = \frac{1}{2}\...
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142 views

Objects falling on Slopes [closed]

An object falls on a slope and then rebounces....and it is known it hits the slope again...how do I calculate it's second point of contact with the slope....how can a projectory equation be used in ...
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Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
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Conservation of angular momentum experiment

I've learned in that in this experiment: ...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum ...
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Block and inclined plane (INPhO Problem)

The figure shows two blocks on an inclined plane of mass 1kg each.The coefficient of static as well as kinetic friction is $0.6$ and angle of inclination is $30^\circ$ . Find the acceleration of the ...
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Does Hamilton Mechanics give a general phase-space conserving flux?

Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltonian theory like the flux of an ideal fluid, which doesn't change ...
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D'Alembert's Principle: Necesssity of virtual displacements

Why is the D'Alembert's Principle $$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$ stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary ...
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N-body forces in classical mechanics

For a system of two interacting particles 1, 2 we get from the conservation of momentum $$ \dot{\bf{p_1}} + \dot{\bf{p_2}} = 0$$ ...
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Direction of tension?

If you draw the free body diagram of the frame above, what direction would the tension force acting on the frame be - to the right or down? Because the rope it horizontal at some points but vertical ...
2
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1answer
202 views

Problem Of Lazy Fish [closed]

Fish achieve neutral buoyancy (so they don't have to swim constantly to stay in place) via a swim bladder. A swim bladder is a little internal sack that they can inflate/deflate with air, which ...
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70 views

Problem Of Pumping Rubber [closed]

One can work out by either lifting weights or using a tension band, which is like a big rubber band. If we model the rubber band as a big spring with spring constant $400 N/M$ how far in meters must I ...
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How to formally write down the Boltzmann equation?

Can someone write down the Boltzmann equation, not neglecting any of the variables of the involved functions and integrals? Specifically, how to concisely capture the "primed" variables in a sensible ...
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114 views

Can all systems be put in equilibrium?

I'm in a first year statics course. We have spent the whole semester solving for forces and moments so that the system is in equilibrium. When we are given a system, we immediately begin solving for ...
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220 views

Non-uniqueness of solutions in Newtonian mechanics

In The Variational Principles of Mechanics by Lanczos, in section 1 of Chapter 1, Lanczos states that for a complicated situation, the Newtonian approach fails to give a unique answer to the problem, ...
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1answer
605 views

The virial theorem and a delta function potential

So the virial theorem tells us that: $2\langle T\rangle = \langle \textbf{r}\cdot\nabla V\rangle$. Now I was wondering what would happen if V has te form: $V(\textbf{r}-\textbf{r}') = V_0\delta^{(D)...
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3answers
157 views

How much energy does it take to simply run forward?

I'm interested in tracking as much data about my runs as I can in an effort to get faster, and while I can easily estimate energy expenditure during an uphill run due to the change in elevation, I can'...
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82 views

Why rendezvous attempt failed on Gemini 4? [closed]

It is said in Wikipedia, that On the first orbit, McDivitt attempted to rendezvous with the spent Titan second stage. This was unsuccessful for a number of reasons: NASA engineers had not ...
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793 views

What would happen if an unstoppable force hits an immovable object? [closed]

I realize that the question a rather large paradox, but I do wonder if such a thing were true what would happen, assuming that neither of these "objects" can be destroyed by each other?
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Why is velocity of outermost point on a rotating wheel double the velocity of centre of mass?

'In the answers to one of the questions based on rotation of a disc in my physics book the answer includes the statement 'As we know that the velocity of outermost point on a rotating disc is double ...
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1answer
385 views

Classical mechanics from Quantum mechanics

I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator $$K(x,x_0;t)=\langle x|e^{-i ...
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Does topology have any role in classical physics?

I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common? Is there any intuitive ...
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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: $$S=\...
2
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1answer
125 views

Why does taking a long step increase the chance of slipping?

Me and my friend were walking and it was raining. He didn't have any grip on the slippers so he took smaller steps to avoid slipping. We both were wondering why does taking a long step increase the ...
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Can we quantize Aristotelian physics?

Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an ...
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1answer
857 views

Why don't couple forces violate Newton's First Law?

If you have some random object at rest and you apply a couple to it, the net force acting on it is zero. However because a moment acts on it, it starts to rotate. So you had an object at rest, a net ...
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1answer
426 views

Why does moment equilibrium at one point of an object mean the moment is at equilibrium for the whole system?

In class my prof said that when showing a system is at equilibrium it suffices to show that the moment at one point is zero. Why? Why does showing the moment at a point is zero imply the moment of the ...
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723 views

Why is moment dependent on the distance from the point of rotation to the force?

The formula for moment is: $$M = Fd$$ Where F is the force applied on the object and d is the perpendicular distance from the point of rotation to the line of action of the force. Why? Intuitively, ...
3
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1answer
330 views

Equivalences and derivations in Newtonian/Classical Mechanics

In Newtonian mechanics there are several "laws" and axioms: Newton's Laws Conservation of: Mass, Energy, Momentum, Angular Momentum I know some are equivalent (e.g., conservation of momentum and ...
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Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
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Correct way to calculate torque produced by axle

For my electrical engineering course, we had to build a simple DC motor that can lift a coin. I have tested the motor, and here are the results: rotational speed (no load): 3630 RPM (380 rad/sec) ...
2
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1answer
360 views

Circular motion problem? [closed]

I am learning about circular motion and not quite sure how to approach this particular problem. Any help would be greatly appreciated! A particle moves along a circular path over a horizontal $x$-$...
2
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1answer
1k views

Lorentz force from velocity-dependent potential and Lagrangian

There is something i'm missing. I am at page 22-23 of Goldstein Classical Mechanics 3rd ed. Lorentz force can be derived from a potential $$U=q\phi-q\mathbf{A}\cdot\mathbf{v}$$ Where $\phi(t,x,y,z)$ ...
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Solve a problem of work and energy

A man pulling sled of his daughter by a massless rope, climbing a snowy hill whose slope is equal to 15 °. Considering that the mass of the sled is $4Kg$, the girl's $26Kg$ and $\mu _c = 0,25$, ...
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Can a particle with non-zero angular momentum pass through the center of a spherical potential?

Suppose you have a particle of mass $m$ moving in a potential $V(r) = -\frac{k}{r^2}$, with $r^2 = x^2+y^2+z^2$ and $k > 0$. Since the angular momentum $l$ is conserved, the particle will move in a ...
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Racing balls question

My question is related to simulation of racing ball demonstration. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=142 One ball goes on a straight path, while another one goes on a curved path. ...
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When motion begins, do objects go through an infinite number of position derivatives?

This might be a very vague and unclear question, but let me explain. When an object at rest moves, or moves from point $A$ to point $B$, we know the object must have had some velocity (1st derivative ...