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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Why are there only 3 Additive Integrals of Motion?

1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19: "There are no other additive integrals of the motion. Thus every closed system has seven such ...
0
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0answers
10 views

Slowly Varying Functions for Adiabatic Invariants - The Same as Karamata's?

In section 49 (and 50) of Landau and Lifschitz's "Classical Mechanics", adiabatic invariants are discussed, which are related to functions which vary adiabatically or "slowly" with time. Admittedly ...
5
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1answer
38 views

Understanding potential energy

I am self-studying the classical mechanics using the book by Taylor, and I have a question about the potential energy. The book (pg 111) says: If all forces on an object are conservative, we can ...
1
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1answer
258 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
3
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1answer
38 views

Why is the Virial Theorem not a Special Case of the Ergodic Theorem? What is their Relationship?

The virial theorem involves the time-averages of the potential and kinetic energies if the motion of the system is bounded to a finite region of space. An ergodic theorem relates the time and space ...
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3answers
1k views

Complete vs General Integral of first order PDE

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics: ... we should recall the fact that every first-order partial differential equation has a solution depending ...
17
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3answers
346 views
+50

Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
0
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0answers
16 views

Springs and Cantilevers - how linear and repeatable are they under deformation?

I know you guys only deal with the ideal, but in practice how linear and repeatable is the response of a spring or cantilever when deformed under a test mass?
23
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4answers
995 views

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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1answer
64 views

Why does holding an object cost energy while no work is being done?

I was reading the discussion here: Why does holding something up cost energy while no work is being done? I feel as though the question is being avoided. Suppose instead of holding an object by hand ...
0
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1answer
55 views

Find the acceleration of the bead [on hold]

Two identical, uniform large rings, each of mass $\text{m}$ are connected through a bead of same mass, which can move freely. When bead is released, it starts sliding down. The large rings roll ...
0
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2answers
3k 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 ...
0
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2answers
28 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
10
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6answers
2k views

Light's inverse square law: Does it require a minimum distance from the source?

Does the inverse square law begin to take effect the moment light leaves its source? For example, does light's intensity decrease, i.e. does the area in which the photons might land increase, at a few ...
3
votes
2answers
69 views

Could 1 force cause a pure moment?

A friend of mine told me if there is only one force, it cannot cause only rotation. I wasn't convinced so I proposed a thought experiment, and now we are both confused. Suppose that we put a rod ( ...
-1
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0answers
23 views

Coupled spring mass-system [on hold]

Below is an old exam question I am trying to solve (it's not homework or an assignment, just an interest of mine). I have a few gaps in my attempted solution that I would like help with. Specifically: ...
8
votes
2answers
390 views

Why was the Stark effect discovered much later than the Zeeman effect?

This is strange. The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical ...
0
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4answers
39 views

How is it possible to exert a force on a static object?

Assuming mass doesn't change, force is defined as mass * acceleration. Acceleration is the change in velocity as time changes. How is it possible then to exert a force on an object that doesn't move? ...
23
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3answers
2k views

Why doesn't a fly fall off the wall?

Pretty simple question, but not an obvious answer at least not to me. I mean you can't just place a dead fly on the wall and expect it to stay there, he will fall off due to gravity. At first I ...
3
votes
1answer
62 views

Independent canonical coordinate variables?

In Goldstein's Classical Mechanics (2nd ed.) on section 9-1 page 382, there is a discussion about finding a canonical transformation $(q_i,p_i)\rightarrow (Q_j(q_i,p_i,t),P_j(q_i,p_i,t))$ from a given ...
0
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0answers
14 views

Stationary-state scattering process

In a stationary-state scattering process of an incoming plane wave, the outgoing spherical wave can be described by $\psi(\vec r) = e^{ikz} + f(\theta) \frac{e^{ikr}}{r}$. My question is, how is this ...
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1answer
291 views

Canonical transformation problem

(Apologies if HW questions are not allowed -- I couldn't really find a definite answer on this) Question Let $Q^1 = (q^1)^2, Q^2 = q^1+q^2, P_{\alpha} = P_{\alpha}\left(q,p \right), \alpha = 1,2$ ...
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1answer
34 views

Stable Sides of Polygon Objects

I have a physics question for you. Let us say a polygon shaped object is stable on a side when the center of mass "falls" inside the base. Is it possible in 2D to build an object that is unstable on ...
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0answers
32 views

physics thermofluid mechanics pressure force area [on hold]

As shown in the attached image, a tank has an inclined wall at an angle of $45^{\circ}$ to the horizontal. On this wall, there is a 1 m square door that is hinged at A and has a simple latch at B. The ...
0
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2answers
156 views

I dropped my tissue box on a glass table, the box didn't bounce back, table didn't move nor break, what happened?

I have a box, it drops and thus by moving has Kinetic energy, It doesn't penetrate and impacts however the box doesn't rebound nor breaks the table. Its like when I slam my fist on a table but the ...
0
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1answer
322 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 ...
0
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1answer
45 views

Thermofluid mechanics inclined plane

As shown in the attacked image, a tank has an inclined wall at an angle of 450 to the horizontal. On this wall, there is a 1m square door that is hinged at A and has a simple latch at B. The distance ...
0
votes
1answer
54 views

Spring pendulum system [on hold]

Find the Lagrangian and the equations of motion for the system described by the figure using the Lagrange multipliers method. The mass $m$ can slide frictionless along the massless rigid rod of the ...
3
votes
2answers
37 views

Creasing of a material at the molecular level

What exactly happens when a material (particularly paper or even cloth or a metal) is folded to form a crease? Why is it that a creased material tends to retain form, while a lightly folded one, ...
0
votes
0answers
8 views

Is it possible to find the G forces of one of the axis rather than the total?

I am investigating the g-forces and acceleration experienced on roller coasters and have data for $x$, $y$ and $z$ acceleration every $0.2$ seconds of the ride as well as the total acceleration and ...
0
votes
0answers
25 views

Eddy current damping heat generation

Background According to this source (page 7): https://deepblue.lib.umich.edu/bitstream/handle/2027.42/109373/me450w10project16_report.pdf?sequence=1 the "braking" torque a magnetic field on a ...
-4
votes
1answer
39 views

Displacement of an object dropped from a cliff [closed]

An object is dropped from a cliff. How far does the object fall in the third second? Assume that $g = 10 \, \mathrm{m/s^2}$. A: 10 m B: 20 m C: 25 m D: 45 m
6
votes
2answers
926 views

Question about the apparent loophole in principle of least action

In Lagrangian formalism, given two points $(x_1,t_1)$ and $(x_2,t_2)$, we ask the question which paths $x(t)$ make the action $S=\displaystyle \int_{t_1}^{t_2}L\ \mathrm dt$ stationary and satisfy the ...
0
votes
1answer
26 views

How to solve for amplitude w.r.t time for a dad pushing his daughter on the swing with periodic force impulses? [closed]

A Dad is pushing his daughter on a swing. The homogeneous push lasts for α = 10% of the period and is centered around the phase φ = 0. The Fourier series expansion for this is, $$ ...
6
votes
2answers
1k views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
-3
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0answers
15 views

how to apply capstan law? [duplicate]

I am having trouble to apply Capstan Law. I don't know which side is supposed to be the large force and which the small. If you have a capstan that doesn't rotate, and you have a mass 1kg from one ...
2
votes
1answer
255 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 ...
0
votes
1answer
31 views

Common property of equal momentum of different masses [closed]

Two bodies of unlike masses are possessing the same momentum, now what phenomenon does these two bodies can perform likely. I'll use an example: assume a truck and a car of masses 5000 kg and 1000 ...
3
votes
1answer
118 views

Density of states and anisotropic distribution functions

We consider a $3D$ dynamical system. Its distribution function is given by the function ${ (\mathbf{x},\mathbf{v}) \mapsto f (\mathbf{x},\mathbf{v})}$, so that $$ \mathrm{d}^{3} \mathbf{x} \, ...
12
votes
5answers
2k views

Is there a proof from the first principle that the Lagrangian L = T - V?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are ...
3
votes
0answers
39 views

Dynamics of pairwise distances in the $n$-body problem

Consider the $n$-body problem where we are interested in describing the time evolution of $n$ masses interacting through a potential $U$. Let $D$ be the matrix containing all pairwise distances ...
0
votes
1answer
37 views

Coordinate Transformation in Classical Mechanics

The coordinates in one inertial frame are represented by $(x,t)$. Under coordinate transformation, the coordinates in another inertial frame can be represented by $f(x(t),t)$. It can be shown that the ...
5
votes
3answers
3k views

Why rubber is incompressible material?

Why rubber is incompressible material? I know its Poisson's ratio is nearing to 0.5. So I don't understand physically, what it means by 0.5 Poisson's ratio and incompressibility. When I tried ...
0
votes
0answers
29 views

Would it be possible to kill a flea or mosquito with a high probability using high pressure and low volume? [closed]

I was thinking about how to kill off some bugs in the house and it dawned on me that part of the ritual of spraying down insects is the spray itself - they don't seem to handle the pressure well, and ...
3
votes
2answers
155 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
3
votes
1answer
58 views

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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0answers
39 views

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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2answers
100 views

What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
0
votes
1answer
20 views

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 ...