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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Notation of $\nabla_{ij}V_{ij}$ Referring to a Potential

There's a brief section in Goldstein's Classical Mechanics book in chapter 1 that derives some useful basic mechanics things. In talking about the total internal energy of the system, there's a ...
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712 views

What is Maupertuis' principle good for?

The strength of Hamilton's principle is obvious to me and I see the advantage. Now, for conservative systems we also have Maupertuis' principle that says: $$ \delta \int p dq =0$$ and I am not sure ...
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626 views

Variable Tension in the string [closed]

A body of mass $m$ is hanging with a string having linear mass density $\lambda$. What is the tension at point $A$ as shown in the figure. I am aware of the scenarios in which string is ...
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95 views

Consistency of equation with special relativity?

The following is the equation which, I want to know, if it is valid in relativistic domain. Consider two equal charges moving in same direction with velocity $v$ and charge $q$ at a separation of ...
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302 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
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389 views

Can the laws of classical mechanics be derived from quantum mechanics? [duplicate]

Can classical mechanics be derived from quantum mechanics as the same way thermodynamics derived from statistical mechanics?
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242 views

Is there any quantum analogs of three body problem?

IS there any quantum analogy where a three state (or three body) system shows chaotic dynamics as three body problem in classical mechanics?
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1k views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
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473 views

General Solution of Mechanics Problem

I had a homework problem that Given velocity, $v^2(t)=\frac{K}{x(t)}$, where $x(t)$ is distance, find $v$ as a function of $t$. Of course if we assume a positive root, it is easy but what if ...
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What happens, if a rocket is filled with a vacuum instead of high pressured air?

Suppose you put wheels under a compressed air tank so that it can move horizontally to the right and to the left. Suppose there is a nozzle on the right hand side of the tank (in the picture on the ...
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2answers
265 views

Classically efficient universal quantum computation (P=BQP) with magic and bound states

$\text P$ vs $\text {BQP}$ is an open question. That is, "can systems which require a polynomial number of qubits in the size of an input be described with only a polynomial number of bits?" If the ...
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3answers
470 views

A few questions about the concept of work

From Wikipedia: The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: $$W = Fd.$$ If I lift some object from a ground, ...
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572 views

Heisenberg picture of QM as a result of Hamilton formalism

Consider the formula for the total time-derivative of a physical value in Poisson's formalism: $$\tag{1} \frac{dA}{dt} = -\{H, A\}_{P.B.} + \frac{\partial A}{\partial t}, $$ where $\{A, B\}_{P.B.}$ is ...
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53 views

Helping/explanatory notes for Landau&Lifschitz Physics Course [duplicate]

I've recently restored my interest on theoretical physics (I have a master degree in Electrical Engineering) and began my study with first volume of the Physics Course by Landau and Lifshitz. This is ...
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1answer
668 views

D'Alembert's principle

Actually I have some troubles to understand what this principle is all about, so I want to use the simple pendulum in order to get the idea. Since I have read a few passages that dealt with this ...
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2answers
3k views

How to transform mechanical work into electrical energy without using piezoelectricity?

can someone help me with the following issue. I need a method for transforming mechanical work into electrical energy without using piezoelectricity. I have such kind of mechanical forces (like on the ...
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1answer
204 views

Do we need infinite energy to make 2 similar charges touch only in theory?

By Coulomb's law, say if we have 2 point particles each having a charge of +1C then by the formula, F = k/(d)^2 if we need to make the distance between them zero, clearly y the formula, we need to ...
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968 views

How do I calculate electric fields due to currents of magnetic dipoles?

Short version of my question: Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the ...
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1answer
323 views

Derivation of differential scattering cross section - off-center target

This is a followup question to this pretty good answer regarding deriving the Boltzmann equation. What if the center of the target particle is actually not the same with the scattering center (or may ...
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1k views

What is the amplitude of the limit cycle of the van der Pol oscillator?

In the second edition of Classical dynamics of particles and systems by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where ...
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1answer
357 views

What are the determining factors for the velocity of orbiting bodies?

Please bear with me, as I'm not in the field of physics, this question may seem a bit simple. The scenario is the following; A specific stable orbit radius of a small body, say a satellite, to ...
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1answer
352 views

Constrained motion in a parabolic tube [closed]

A smooth parabolic tube is placed with vertex downwards in a vertical plane. A particle slides down the tube from rest under the influence of gravity. Prove that in any position, the reaction of ...
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1answer
134 views

If transported back to the 18th century could you solve the Longitude Problem without an accurate clock?

Seeing an interesting BBC article today at http://www.bbc.co.uk/news/science-environment-23514521 about the Longitude Problem, I wondered if it could have been solved, in a way practical at the time ...
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1answer
261 views

Centrifugal force on tilted object

The centrifugal force acting on a revolving particle with negligible size is $\frac{mv^2}{r}$. What if the size is not negligible? Say we are talking about a large homogeneous circular disc, so its ...
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1answer
402 views

Can soldiers marching at the right frequency realistically cause a bridge to break?

In my physics class it was suggested that ancient armies had a rough understanding of the idea of a resonant frequency and so they "broke step" when crossing bridges so as to avoid a very high $Q$. I ...
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174 views

Is the traditional free-body diagram invalid in situations in which equal forces produce unequal powers?

This question is in response to question B1 in the problems/solutions located at http://aapt.org/physicsteam/2013/upload/E3-1-7-solutions.pdf. In question B1, there is a wind-powered vehicle that can ...
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318 views

Can classical systems exhibit “strong coupling”?

Does the concept of strong coupling mean anything in a classical setting? If strong coupling means just an inability to apply perturbative methods to the Hamiltonian, then obviously yes, we can ...
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716 views

Uniqueness of the number of degrees of freedom

As per my knowledge, degrees of freedom of any physical system are the number of independent quantities(coordinates) which need to be specified in order to specify the state of a system uniquely. ...
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1answer
715 views

What is the friction between cylinder and wall (ground)?

A hollow cylinder (radius $R$) is rolling against the wall at angular speed $\omega$. The coefficient of friction between the cylinder and the wall(ground) is $\mu$. After how many rotations the ...
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247 views

A column falls, how will it break?

I'm not expecting a definitive answer. But I would like someone to explain which are the main forces that interact in this situation: An ideal cylindrical column that is at first vertical is pushed ...
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2answers
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Why does dry spaghetti break into three pieces as opposed to only two?

You can try it with your own uncooked spaghetti if you want; it almost always breaks into three when you snap it. I am asking for a good physical theory on why this is along with evidence to back it ...
2
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1answer
760 views

Canonical transformation generated by hamiltonian?

Someone told me that, in a hamiltonian system, the hamilonian function is the generating function of the canonical transformation given by time translation. However, this statement doesn't make any ...
4
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1answer
331 views

Saturation of the Cauchy-Schwarz Inequality

Going to as little details as possible, here is a statement from Wald's text on QFT in curved spacetimes(I am not quoting the book) He considers two vector spaces ${\cal S}$ and ${\cal H}$. Note ...
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267 views

Reason for different type of energy transfer for two kinds of collisions

According to my physics book, if an electron were accelerated with 15 MeV of (kinetic?) energy and collided into a 100g thermally insulated copper block (not sure if the fact it is thermally insulated ...
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2answers
406 views

Coincidence, purposeful definition, or something else in formulas for energy

In the small amount of physics that I have learned thus far, there seems to be a (possibly superficial pattern) that I have been wondering about. The formula for the kinetic energy of a moving ...
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1answer
880 views

Resisting force depends on velocity? [duplicate]

Why does resisting force depend on velocity? I think there is no relation between resisting force and velocity of object. Please speak about it logically.
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1answer
5k views

What force does bathroom scale measure?

When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) ...
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267 views

Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$ \mathbf{F} = -\nabla V $$ Suppose a rigid body is placed inside this ...
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1k views

effect of atmospheric pressure on reading of a weighing scale

Let us consider a completely sealed weighing scale such that the air pressure above and below the pan of the scale are equal and is equal to 1 atm. pressure. The scale initially reads zero. Now if ...
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2answers
446 views

The “stationary potential energy” condition for static equilibrium in mechanical systems

I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the ...
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4answers
754 views

Are Lagrangians and Hamiltonians used by Engineers?

Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges ...
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90 views

What is the optimal diameter for the exhaust hole in a pressurized vessel to deliver highest acceleration ?

Imagine you have a sealed cylindrical vessel with a given radius with a compressed gas inside. Let's give some numbers, 5 cm radius and 100 atm pressure. You poke a hole in the vessel and the gas will ...
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0answers
59 views

The mighty man and the bridge [duplicate]

Let us say we have a mighty man crossing a bridge, carrying 4 bags of concrete, each of which weighs 50 pounds. Let us say, for the sake of the argument, that the mighty man himself weighs 300 ...
3
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1answer
216 views

How practical is fracture mechanics?

I have been reading fracture mechanics recently and have encountered many beautifully elegant theories. However, one thing keeps bothering me: How practical is fracture mechanics in the real world? ...
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4answers
4k views

How to find out whether a transformation is a canonical transformation?

We had a couple of examples where we were supposed to calculate the Canonical Transformation (CT), but we never actually talked about a condition that decides whether a transformation is a canonical ...
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1answer
276 views

Two components of angular momentum conserved $\Rightarrow $ All three components are conserved?

I was wondering whether it is correct to say that if two components of the angular momentum are conserved, then all three Cartesian coordinates of the angular momentum are conserved? I would regard ...
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3answers
466 views

Interpreting Aristotle's law of motion $\vec F = R\vec v$

The Aristotle's law of motion, which is incorrect, states that The velocity of an object $\vec v$ is directly proportional to the force $\vec F$ acting on it or $\vec F \propto \vec v$ ...
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1answer
133 views

Duhamel formula for propagators

Let $\dot{z} = A(t)z + b(t)$ with $ z(t) \in \mathbb{R}^n$ and $A(t)$ be a linear map from $\mathbb{R}^n \rightarrow \mathbb{R}^n$. A propagator is also a linear map $P(t,s):$ $\mathbb{R}^n ...
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1answer
203 views

Definition of Kinetic energy

In class we had that $ T= \frac{1}{2}T_{ij}v_iv_j$ where we used the Einstein summation convention. Hitherto we only discussed examples where the kinetic energy was dependent of the square of one ...
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730 views

Mechanical similarity in Landau

I've read this very short paragraph from Landau & Lifshitz's Mechanics (Chap.2, Par.10) (that you can find here) about Mechanical similarity. I was looking for some more detailed explanations of ...