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 is velocity of outermost point on a rotating wheel double the velocity of centre of mass?

'In the answers to one of the questions based on rotation of a disc in my physics book the answer includes the statement 'As we know that the velocity of outermost point on a rotating disc is double ...
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383 views

Classical mechanics from Quantum mechanics

I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator $$K(x,x_0;t)=\langle x|e^{-i ...
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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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668 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: $$S=\...
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125 views

Why does taking a long step increase the chance of slipping?

Me and my friend were walking and it was raining. He didn't have any grip on the slippers so he took smaller steps to avoid slipping. We both were wondering why does taking a long step increase the ...
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Can we quantize Aristotelian physics?

Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an ...
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851 views

Why don't couple forces violate Newton's First Law?

If you have some random object at rest and you apply a couple to it, the net force acting on it is zero. However because a moment acts on it, it starts to rotate. So you had an object at rest, a net ...
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424 views

Why does moment equilibrium at one point of an object mean the moment is at equilibrium for the whole system?

In class my prof said that when showing a system is at equilibrium it suffices to show that the moment at one point is zero. Why? Why does showing the moment at a point is zero imply the moment of the ...
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712 views

Why is moment dependent on the distance from the point of rotation to the force?

The formula for moment is: $$M = Fd$$ Where F is the force applied on the object and d is the perpendicular distance from the point of rotation to the line of action of the force. Why? Intuitively, ...
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325 views

Equivalences and derivations in Newtonian/Classical Mechanics

In Newtonian mechanics there are several "laws" and axioms: Newton's Laws Conservation of: Mass, Energy, Momentum, Angular Momentum I know some are equivalent (e.g., conservation of momentum and ...
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Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
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156 views

Correct way to calculate torque produced by axle

For my electrical engineering course, we had to build a simple DC motor that can lift a coin. I have tested the motor, and here are the results: rotational speed (no load): 3630 RPM (380 rad/sec) ...
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355 views

Circular motion problem? [closed]

I am learning about circular motion and not quite sure how to approach this particular problem. Any help would be greatly appreciated! A particle moves along a circular path over a horizontal $x$-$...
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Lorentz force from velocity-dependent potential and Lagrangian

There is something i'm missing. I am at page 22-23 of Goldstein Classical Mechanics 3rd ed. Lorentz force can be derived from a potential $$U=q\phi-q\mathbf{A}\cdot\mathbf{v}$$ Where $\phi(t,x,y,z)$ ...
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Solve a problem of work and energy

A man pulling sled of his daughter by a massless rope, climbing a snowy hill whose slope is equal to 15 °. Considering that the mass of the sled is $4Kg$, the girl's $26Kg$ and $\mu _c = 0,25$, ...
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263 views

Can a particle with non-zero angular momentum pass through the center of a spherical potential?

Suppose you have a particle of mass $m$ moving in a potential $V(r) = -\frac{k}{r^2}$, with $r^2 = x^2+y^2+z^2$ and $k > 0$. Since the angular momentum $l$ is conserved, the particle will move in a ...
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155 views

Racing balls question

My question is related to simulation of racing ball demonstration. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=142 One ball goes on a straight path, while another one goes on a curved path. ...
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354 views

When motion begins, do objects go through an infinite number of position derivatives?

This might be a very vague and unclear question, but let me explain. When an object at rest moves, or moves from point $A$ to point $B$, we know the object must have had some velocity (1st derivative ...
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Two hanging masses connected by springs

I had this problem for a candidacy exam, but wasn't able to get the complete answer. Their spring constants and masses are not the same, find the equilibrium position and frequencies of the system. ...
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Why does friction cause a car to turn?

I've had a lot of difficulty conceptually understanding the physics of how a car turns on an unbanked curve, so I'm hoping you could help me out. When a car is moving in uniform circular motion, we ...
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371 views

Primary constraints for Hamiltonian field theories

I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures ...
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93 views

Vector Summation [closed]

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $ \sqrt{A^2 + B^2 +2ABcosθ} $. Any ...
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943 views

How do you derive Lagrange's equation of motion from a Routhian?

Given a Routhian $R(r,\dot{r},\phi,p_{\phi})$, how do you derive Lagrange's equation for $r$? Do you just solve the following for $r$? $$\frac{d}{dt}\frac{∂R}{∂\dot{\phi}}-\frac{∂R}{∂\phi}=0$$ And ...
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666 views

Virtual displacement and generalized coordinates

I have a doubt regarding the expression of a virtual displacement using generalized coordinates. I will state the definitions I'm taking and the problem. The system is composed by $n$ points with ...
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204 views

Friction From an Object On-Top of a Sliding Object

Consider a block $A$ lying on a flat and frictionless table, and a block $B$ lying on top of block $A$. A horizontal force $F$ is applied to block $A$. If there is no friction between blocks $A$ and $...
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projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of ...
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Relation between (super)integrability and closed orbits

Inspired by this recent question, I would like to understand from a more general and mathematical perspective why closed orbits are only found for the Kepler ($V(r) \sim 1/r$) or harmonic ($V(r) \sim ...
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787 views

Friction forces and sliding slabs

I have 2 questions, one generalizing the other. Question 1: Suppose we have 2 slabs resting horizontally on a table. Assume there is friction between the 2 slabs as well as between the bottom slab ...
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298 views

At what angle do billiard balls scatter if they collide off center?

The angle defined by joining a line from the centers of the balls must be important. But do they follow this angle when viewed in the rest frame of one of the balls or in the CM frame? The spheres ...
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47 views

Decrease in Intensity [closed]

A beam of particles pass through a target made of thin foil of a very small thickness $\Delta x$ having $N$ particles per unit volume. Let the collision cross section be $\sigma$ . If the intensity of ...
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1answer
139 views

Landau Lifshitz energy for uniform rotation

Landau Lifshitz claim in their Mechanics book (39.11) that for a uniform rotation we have $ E = \frac{mv^2}{2} - \frac{m}{2} (\omega \times r)^2 + U,$ where the rotation is given by $v' = v + \omega ...
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481 views

Time it takes two oppositely charged particles to collide

I think this is supposed to be a simple problem but I am having a hang up converting it to a one-body problem. It's one-dimensional. +q and -q a distance d apart, held stationary then let go at t=0. ...
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504 views

Pendulum Hits a Mass and Spring

I think this problem’s solution is on the web but after a few days of searching, I can not find it. Can anyone give me a reference? Thanks in advance. A mass and spring are resting on a frictionless ...
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310 views

Uniform constant magnetic field and traditional attractive force

Why uniform constant magnetic fields can not exert net force on a piece of iron whatever strong it might get?
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158 views

How are fictitious forces related to my feeling?

This question arises when I am studying fictitious forces in an undergrad introduction to physics course. Suppose I am standing in an elevator with an acceleration $a$ directed upward. From the ...
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517 views

A thought experiment to understand (literal) bootstrapping

The common explanation of why you can't lift yourself off the ground by pulling your feet up with your hands, or in more cliched terms "pull yourself up by your own bootstraps", is that if you ...
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Why does a stationary force affect the conservation of momentum, but not the conservation of energy?

Let's say I have two positive charges approaching one another at the same speed with only their mutual forces acting on one another. Total momentum (= 0) and energy is conserved and the charges ...
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363 views

Axial shortening of a torsion rod loaded with pure torque

If you have a torsion rod and stress it with pure torsion you expect an axial shortening, too. If you have a lateral contraction property in your material (e.g. steel) I anyhow cannot calculate the ...
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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 ...
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449 views

Why is kinetic energy only “often $(1/2)mv^2$”?

I am reading the first few pages of Nakahara and refreshing my memory on physics I learned a while ago as a physics math undergrad. Nakahara defines a field $F$ to be conservative if it's the gradient ...
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186 views

Why isn't the product rule used in the definition of mechanical work?

Mechanical power is normally defined as $P = \mathrm{d}W/\mathrm{d}t$, and work is normally defined as $W = \vec F \cdot \vec x$. Today an undergrad pointed out a confusion he had from Griffiths' E&...
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354 views

Stable equilibrium given force

If a particle moves under the influence of a resistive force proportianal to velocity and a potential $U$, $$F(x,\dot x)=-b\dot x-\frac {\partial U}{\partial x}$$ Where b>0 and $U(x)=(x^2-a^2)^...
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Normal force of loop-the-loop at the side of the circle

In the loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has the mass of 230 kg and moves with the speed of 300 m/s. The loop-the-loop has a radius R=20 m. ...
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798 views

Deriving the Lorentz force from velocity dependent potential

We can achieve a simplified version of the Lorentz force by $$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$ where $\mathbf{A}$ is the magnetic vector potential and ...
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Why do we use operators in quantum mechanics?

In classical mechanics, physical quantities, such as, e.g. the coordinates of position, velocity, momentum, energy, etc, are real numbers, but in quantum mechanics they become operators. Why is this ...
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Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the physics?

Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the classical mechanics? I never saw (which is strange), but I think that it's possible.
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Extremizing a Hamilton-Jacobi Equation

How can one make sense of the idea of extremizing a Hamilton-Jacobi equation? In Schrödinger's paper "Quantisation as a Problem of Proper Values I" (Annalen der Physik (4), vol. 79, 1926, p. 1, ...
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Is there valid physics behind the bodybugg?

The bodybugg is a faddish gadget whose marketers claim it can measure your body's daily energy expenditure. Their sales literature says: As reported in the British Journal of Sports Medicine, 2008 ...
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240 views

Force on bolt holding up jet engine on plane

I am to solve the following: A jet engine of mass $m$ is fastened to the fuselage of a passenger jet by a bolt. During flight, the plane encounters turbulence, which suddenly imparts an upward ...
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258 views

Physics textbooks that distinguish between laws and definitions?

Often when I am learning physics I start to think about whether the laws I'm learning are mere definitions or experimentally determined, and usually the textbook does not make this clear. As Thomas ...