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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Born-like measuring rule in classical experiments

this 2011 paper "Born's rule from measurements of classical signals by threshold detectors which are properly calibrated" by Khrennikov investigates the theoretical possibility of Born-like ...
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Different subscripts for $\nabla$ operators while deriving force on system of many particles

Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system: Total (external) force on ...
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How would an increase in temperature affect ooblek's (non newtonian fluid) viscosity?

Due to the fact that Ooblek (cornstarch and water), contains so much water and from what I understand it is non newtonian due to the particles suspended in it, would it therefore be correct to say ...
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59 views

Is the principle of indifference enough to derive the microcanonical ensemble?

The microcanonical ensemble is usual motivated solely by the principle of indifference. Textbooks usually say something along the lines of "If the only thing we know about a system is its total ...
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non constant acceleration problem [closed]

The acceleration of an arrow from a bow falls from $6000m/s^2$ to zero when it leaves the bow after travelling a distance $x=0.75m$. Assuming that this acceleration can be expressed by the linear ...
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49 views

What are the assumptions behind the Lagrangian derivation of energy?

What are the assumptions behind the Lagrangian derivation of energy? I understand that we're searching for a function $L$ that describes a set of physics so that solving the energy minimization ...
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36 views

Regarding $f$ degrees of freedom & $f\!-\!1$ constants & inclusion of these constants

In the classic & famous book "Electromagnetic fields & Interactions" by Richard Becker (Dover publishing), on page 55 (of volume 2) , author says: If the system possesses f degrees of ...
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1answer
23 views

Calculating the change in aceleration the earth feels when you push an object

I am learning newton's third law, and i got to this conclusion, i wanted to know if it's correct (within the boundaries of Newtonian mechanics) Say I'm pushing a cupboard with my body, and I apply a ...
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2answers
572 views

Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt} $

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
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640 views

Lagrangian and Hamiltonian EOM with dissipative force

I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...
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61 views

Physical motivation for Lagrangian formalism

This is more of a request for clarification of understanding and intuition rather than a question, but I hope people can help me with it. I have learned calculus of variations and have subsequently ...
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35 views

Is expectation value of the Hamiltonian always the energy? [duplicate]

There are time dependent & space dependent systems (magnetic fields) and time independent (particle in a box or harmonic oscillator). In the latter the expectation value is the 'average' energy ...
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The motion-independent definition of force

I think we must be able to accomodate a definition of a force on some particle which is independent of the motion of the particle, for all kinds of forces, to surely verify the statement like 'force ...
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55 views

Solenoidal forces

As far as I know a solenoidal vector field is such one that $$\vec\nabla\cdot \vec F=0.$$ However I saw a book on mechanics defining a solenoidal force as one for which the infinitesimal work ...
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2answers
77 views

Tension and friction. Cool question

I had an exercise like the image, where block A is pulled by a force F, there is that rope(tension) attached to the block B and the wall, and there is friction between A and B, and A and the ground, ...
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5answers
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Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
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4answers
351 views

What are the accelerations of blocks? [closed]

I've talked with 2 teachers about this situation: one teacher said he was completely sure that B have twice the acceleration of A, the other said he was completely sure they have same acceleration. ...
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Gradient effects in continuum mechanics

What I have learned is that inhomogenous materials (materials with different material properties over space and time) can be treated by the homogenization technique (https://en.wikipedia.org/wiki/...
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Mechanics around a rail tank wagon

Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it): ...
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2answers
40 views

“Sweet Spot” of Rod-Pendulum - Problem Clarification

I came across this problem in a book (shortened for brevity): Consider a rod of mass $m$ pivoted about one end, with the other end to rotate. Let the center of mass be a distance $a$ from the ...
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93 views

Higher than Lagrangian/action?

When you begin learning physics, you start with equations of motion applied to various physics systems. In classical mechanics course you learn, that exists Lagrangian/action of a system, which gives ...
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2answers
70 views

Projectile motion of a grenade [closed]

A small hand grenade is thrown with an initial speed V0 forming an angle ɵ with the horizontal ground. Assume that at its highest point the grenade explodes and is split into two identical ...
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1answer
49 views

The ratio of masses in an elastic collision [closed]

Two blocks of mass $M_1$ and $M_2$ moving along a 1-dimensional straight line with velocities $V_1$ and $V_2$, respectively, collide elastically. After the collision they move with respective ...
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0answers
40 views

Derivation of Bohr model equations (1) in his original paper

My question is rather straightforward. In his original paper ("On the Constitution of Atoms and Molecules") Bohr provides equations (1) for the frequency and major axis orbit: \begin{align} \omega &...
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1answer
25 views

Finding mass with an estimated gravitational force

As asteroids orbit the sun, they experience gravitational force exerted on them by the sun, and they in turn exert a very minute force back on the sun. Because of their small size, asteroids don't tug ...
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Do mechanical waves also carry momentum as well as energy? [closed]

I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special ...
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Why does higher acceleration minimize a car's fuel consumption?

I generally try to optimize my car's fuel consumption when driving, using my car's real-time MPG gauge and average-trip MPG indicator. Until recently, I believed the slower the acceleration, the ...
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41 views

Build Hamiltonian function

Suppose we have three-point system Points A and B are connected with rod of fixed length $r_0$. Point C rotates around rod, vector R begins at rod's centre of mass. There is a potential of general ...
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96 views

Simple real life applications of Euler-Lagrange equations of motion

If you read some introductory mechanics text like David Morin's Introduction to Classical Mechanics about Euler Lagrange Equations you get a large amount of simple examples like the "moving plane" (...
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29 views

Interpretation of contourplot pendulum

I've made this plot of a function that evaluates the size of the angle on the x-axis, and the velocity of the angle for the pendulum on the y-axis. I'm having a hard time interpreting the meaning of ...
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29 views

Reversibility principle for classical mechanic

I'm studying this colloquium about quantum fluctuation relations for nonlinear thermodynamic, but I'm having a problem. Reading about the principle of micro-reversibility of the dynamic of a system i ...
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2answers
51 views

Is the wave equation a periodic wave equation?

I have seen that in the derivation of wave equation, they always use the periodic property of waves in the derivation. But what about non-periodic waves? Do they have some different wave equation? Is ...
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2answers
70 views

What information am I losing out when I assume that the displacement in S.H.M. is small?

While making calculations for simple harmonic motion, we take the force as $F=F(x)$. Then we use Taylor's expansion and calculate as follows: $$\begin{align} F(x) &=F(0+x) \\ & = F(0)+xF'(0)+...
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0answers
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A Canonical Transformation that deletes one canonical coordinate?

I am self studying some classical mechanics, and came across a problem in Goldstein that has me stumped. It is problem 1 in chapter 10. It basically says "Given some conservative system show that a ...
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1answer
90 views

Why does the magnitude of linear momentum of a particle in circular motion change with radius? [duplicate]

My problem is with linear momentum of a particle in circular motion. If we imagine a particle moving around a circle, if there are no torques acting, then we can say its angular momentum is conserved, ...
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1answer
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Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and no torque is acting?

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to ...
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0answers
35 views

Relative angular momentum?

Let there be a point $P$. A point $C$ is located at a radius vector $r$ from $P$. $C$ is the centre of mass of a rigid body. The rigid body is rotating with an angular velocity $\omega$ about an axis $...
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1answer
26 views

Does stretching a spring with a relatively high spring constant value require more force because of its inertia?

Other than the fact that a spring has a relatively high spring constant (say 1000 N/m) and therefore requires more force per meter to stretch (not bend or twist).
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1answer
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Ring Ascending a Step

Consider a thin circular ring of mass $m$, radius $r$ rolling without slipping with velocity $v$ towards a step of height $h$ $(<r)$. Assume no rebound and no slipping at the time of contact. What ...
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1answer
32 views

How does the viscosity of a non Newtonian fluid (ooblek) affect its resistance to electricity?

I know the conductivity of water is based on whatever is dissolved into the solution, hence pure water does not conduct electricity. However, these ions in solution must also be free to move around. ...
5
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4answers
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Why is it easier for the ocean to push someone over by exerting force on their front side than by exerting force on their left or right side?

If I put two clones of normal weight on a beach in the ocean, with one standing perpendicular to the waves, and the other standing parallel to them, the one standing perpendicular to the waves will be ...
1
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1answer
52 views

Magnetic field of rotating capacitor [duplicate]

Does the rotating charged capacitor (both plates) produce magnetic field? and what about rotating both plates in opposite directions?
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1answer
77 views

Multiplying Lagrangian by a constant

Does a Lagrangian of a system multiplied by an arbitrary constant still work? If if I apply the Euler-Lagrange equations, do they still guarantee that the action is extremal? I arrived to the ...
0
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1answer
73 views

Is the acceleration due to a fictitious force independent of mass in general?

Intuitively (at least to me) it seems that the answer should be "yes", since a fictitious force arises due to being in a non-inertial frame; the frame is accelerating, but the objects within this ...
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7answers
755 views

Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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2answers
1k 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?
2
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1answer
428 views

Euler-Lagrange Equation with logarithmic potential

A particle moving towards the origin has initial conditions $x(t=0) = 1$ and $\dot{x}(t=0)=0$. If the Lagrangian is $$L:=\frac{m}{2}\dot{x}^2 -\frac{m}{2}\ln|x|$$ This should satisfy Euler ...
2
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1answer
548 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
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3answers
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An example of non-Hamiltonian systems [closed]

I am preparing for the exam. And I need to know the answer to one question which I can't understand. "Give an example of non-Hamiltonian systems: in case of infinite number of particles; for a finite ...
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Angular momentum consevation and central force

A circular orbit of radius $a$ passing through the centre of a central force is given by the equation $r=2a\cos\theta$. Then using the orbit equation one can show that the force varies as $\vec F(|\...