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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Is there a speed limit for objects falling in gases or liquids? [duplicate]

Let $o$ be a spherical object with mass $m$ and surface $s$. Let $g$ be the gravitational acceleration and $h$ the height. Let the gas where we drop $o$ in have density $d$ and pressure $p$ at ...
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364 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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1k views

Countersteering a motorcycle

Everyone knows the story about countersteering. For those who don't I will explain it below and after the explanation i will ask my question. You can watch this short video as a beginning: ...
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125 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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77 views

Is it true that the self-force prevents a classical particle from falling into a Coulomb potential? What is the physical explanation of this result? [closed]

In 1943 CJ Eliezer published a paper claiming that the self-force prevents a zero angular momentum particle from ever reaching the center of an attractive Coulomb potential (and what's more that it ...
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175 views

Is there a rotational equivalent to newtons laws?

Newtons three laws of motion appears to apply only for linear motion: An object remains at rest or moves in a straight line at uniform velocity unless a force is applied. Force is mass times ...
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24 views

Ratio of oscillation amplitudes of a box on a gasket to floor

So the problem is that I have a box and I put it on a gasket to preserve it from vertical oscillations. The gasket is compressed by the box by a quantity of $h$. The floor is oscillating at frequency ...
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140 views

Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
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67 views

Can you determine acceleration from positions and velocities only?

I just began reading the Landau and Lifshitz book on classical mechanics. It states on the first page of Chapter 1 that: Mathematically, this means that, if all the coordinates $q$ and velocities ...
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42 views

Cart speed and wheel rotation

Say you have a horse drawn cart. Does the outside of the wheel spin at the same velocity that the cart moves forward? The reason I ask is because I am working on a problem where a piece of mud ...
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32 views

Hamiltonian flow?

I was wondering what the Hamiltonian flow actually is? Here is my idea, I just wanted to know if I am correct about this. So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and ...
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216 views

Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
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58 views

Mechanical equilibrium : thermodynamics and classical mechanics

A similar question was asked here but mine is a bit different. In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid). In classical mechanics, equilibrium is ...
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188 views

Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?

I am trying to figure out how much force $F$ is needed to push a syringe plunger. The plunger needs to overcome the friction force $F_1$ and (a much smaller) inertia force $F_2=ma$, giving the total ...
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147 views

Can the coefficient of friction be derived from fundamentals?

It is common to want to derive macroscopic laws from what we know microscopically - after all, given a (correct) microscopic description, everything larger should follow. Has it ever been done to ...
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75 views

Lagrangian $L' = L + \frac{df}{dt}$ gives the same equations of motion

It is well known that when a Lagrangian $L$ is incremented by the total time derivative of a function $f$ that does not depend on the time derivatives of the generalized coordinates, the same ...
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45 views

Determining the components of the force on a curved surface due to pressure

I have a cross section of a half-tube with a pressure gradient across it causing a force outwards. I am attempting to extract the vertical component (in relation to diagram) of the force on this ...
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3answers
111 views

What is a “Reversed Effective Force”?

I have some confusion about the "Reversed effective force" as it appears in the derivation of D'Alembert's principle. In Goldstein d'Alembert's principle is given as: $(F-\dot{p}) \cdot \delta r = ...
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132 views

Momentum is a cotangent vector?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...
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Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
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679 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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1answer
29 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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Does the force of releasing the latch of a spring-latch contraption affects the force generated by the spring?

There is this contraption in my class, where a rod is attached to a latch and a spring. By pulling the latch back behind a piece of metal, the latch is secured, the rod if pulled back and the spring ...
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52 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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94 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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Motion in a central field in Landau Mechanics

What does this mean when E=U_eff? I don't think this means the first term in E is zero. I don't understand the sentence ' This is a cubic equation for cos(theta)'
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$\mathbf{P}=M\mathbf{v}_{cm}$ for a continuous body?

While restudying some fundamental concepts with greater attention, I have reflected on the following deduction, which I find in my book of mechanics, of the identity of the temporal derivative ...
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How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
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Drag on a spinning ball in fluid

I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I ...
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33 views

Spring on a rotating disc [closed]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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2answers
578 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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44 views

Total angular momentum of a continuous body

I find the definition of total angular momentum $\mathbf{L}$ of a system of $n$ material points with respect to a given point $Q$ as the sum of the momenta $\ell_i=\mathbf{r}_i\times\mathbf{p}_i$ ...
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54 views

Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
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28 views

How does the optimal-gear indicator work? [migrated]

Modern cars like BMW, Ford, Audi come with a system on the panel which tells the driver the next optimal gear to drive. How does it work ? What is the algorithm behind it? What data does it require ...
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90 views

Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
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17answers
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Why does one experience a short pull in the wrong direction when a vehicle stops?

When you're in a train and it slows down, you experience the push forward from the deceleration which is no surprise since the force one experiences results from good old $F=m a$. However, the moment ...
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Looking for an intuitive understanding of normal force

I understand normal force to be the perpendicular force to a surface of contact. However, I have come across a problem which has caused me to rethink this. My initial understanding of force is ...
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2answers
2k 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 ...
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104 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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69 views

How does electromagnetic radiation affect the velocity of a charged particle?

I've heard that the acceleration of a charged particle releases electromagnetic waves. So let's say there is a charged electron moving forwards in a region with a downwards magnetic field. If the ...
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25 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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21 views

Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...
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121 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
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71 views

Interesting approach to Kepler problem

I won't go into the explanation of this idea, because it is explained in this blog post. In this paper, which was featured on John Baez's blog, $\frac {dt}{d\lambda}$ is given as $\frac r V$, where ...
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73 views

General construction of equations of motion for free particles

I've got a question regarding the different Symmetrie-Lie-Groups of Newtonian Mechanics and special realtivity. Is there a canonical way to obtain the equations of motion for a free particle only by ...
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How to relate internal energy to atomic motion?

I am trying to conceptualize how atomic motion leads to the thermodynamically-defined internal energy (denoted as $U$ below) through some broad mathematical relationships. I get that the internal ...
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Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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Thermodynamics of a rubber band

I have a streched rubber band and I know that tension f is proportional to the temperature T when the length is constant. How can I proove that internal energy is only a function of temperature? I ...