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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Advantages of Lagrangian Mechanics over Newtonian Mechanics [closed]

Here, I'm going to pose a very serious list of doubts I have on Lagrangian Mechanics. Can we learn Lagrangian Mechanics without studying Newtonian Mechanics? Does Lagrangian help in solving problems ...
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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 ...
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1answer
52 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 ...
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1answer
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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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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 ...
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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?
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1answer
100 views

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

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
63 views

Find the acceleration of the bead [closed]

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 ...
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2answers
32 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 ...
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4answers
51 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? ...
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2answers
81 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 ( ...
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6answers
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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 ...
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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
89 views

Spring pendulum system [closed]

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 ...
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 ...
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2answers
44 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, ...
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1answer
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26 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 ...
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0answers
9 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
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1answer
30 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, $$ ...
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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 ...
6
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2answers
938 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 ...
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1answer
36 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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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 ...
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0answers
40 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
109 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 ...
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1answer
21 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 ...
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2answers
83 views

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 ...
0
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1answer
35 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
22 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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1answer
43 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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0answers
57 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 ...
2
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0answers
34 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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44 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 ...
5
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3answers
80 views

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 ...
3
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1answer
55 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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2answers
68 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, ...
3
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4answers
341 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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0answers
20 views

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 ...
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2answers
38 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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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 ...
0
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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 ...
0
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2answers
63 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 ...
0
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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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2answers
92 views

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 ...
4
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2answers
92 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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0answers
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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76 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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28 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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26 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 ...