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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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 ...
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Is the wave equation a periodic wave equation?

I have seen that in the derivation of wave equation, they always use the periodic property of waves in the derivation. But what about non-periodic waves? Do they have some different wave equation? Is ...
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A Canonical Transformation that deletes one canonical coordinate?

I am self studying some classical mechanics, and came across a problem in Goldstein that has me stumped. It is problem 1 in chapter 10. It basically says "Given some conservative system show that a ...
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70 views

What information am I losing out when I assume that the displacement in S.H.M. is small?

While making calculations for simple harmonic motion, we take the force as $F=F(x)$. Then we use Taylor's expansion and calculate as follows: $$\begin{align} F(x) &=F(0+x) \\ & = ...
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36 views

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and no torque is acting?

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to ...
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71 views

Why does the magnitude of linear momentum of a particle in circular motion change with radius? [duplicate]

My problem is with linear momentum of a particle in circular motion. If we imagine a particle moving around a circle, if there are no torques acting, then we can say its angular momentum is conserved, ...
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35 views

Relative angular momentum?

Let there be a point $P$. A point $C$ is located at a radius vector $r$ from $P$. $C$ is the centre of mass of a rigid body. The rigid body is rotating with an angular velocity $\omega$ about an axis ...
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26 views

Does stretching a spring with a relatively high spring constant value require more force because of its inertia?

Other than the fact that a spring has a relatively high spring constant (say 1000 N/m) and therefore requires more force per meter to stretch (not bend or twist).
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20 views

Ring Ascending a Step

Consider a thin circular ring of mass $m$, radius $r$ rolling without slipping with velocity $v$ towards a step of height $h$ $(<r)$. Assume no rebound and no slipping at the time of contact. What ...
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1answer
32 views

How does the viscosity of a non Newtonian fluid (ooblek) affect its resistance to electricity?

I know the conductivity of water is based on whatever is dissolved into the solution, hence pure water does not conduct electricity. However, these ions in solution must also be free to move around. ...
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1answer
50 views

Magnetic field of rotating capacitor [duplicate]

Does the rotating charged capacitor (both plates) produce magnetic field? and what about rotating both plates in opposite directions?
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61 views

Which makes for a better equivalent capacitor? In series or in parrallel?

I understand how capacitors in series and in parallel work. However, I am wondering if it makes a difference, in terms of making a better capacitor that can store more charge, would you connect them ...
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71 views

Is the acceleration due to a fictitious force independent of mass in general?

Intuitively (at least to me) it seems that the answer should be "yes", since a fictitious force arises due to being in a non-inertial frame; the frame is accelerating, but the objects within this ...
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1answer
42 views

Angular momentum consevation and central force

A circular orbit of radius $a$ passing through the centre of a central force is given by the equation $r=2a\cos\theta$. Then using the orbit equation one can show that the force varies as $\vec ...
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1answer
35 views

Acceleration of moving reference frame

I want to simulate the readings of an accelerometer that is arbitrarily moved through 3D space. In an inertial reference frame $W$, the motion of the accelerometer is described by it's linear ...
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2answers
30 views

Current loop and direction ambiguity of the magnetic moment

Consider a circular loop in the XY-plane which carries a current $I$. Then it behaves as a magnetic dipole with moment $\textbf{m}=I\int d\textbf{S}$ where $\int d\textbf{S}$ is the area of the loop ...
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Euler-Lagrange problem of single mass double pendulum in plane [closed]

Problem: "A rod with a length of $l$, mass $m$, is attached by a thread of length $l/2$ according to figure. The rod may perform small, planar swings. Determine its eigen-frequencies." Figure: ...
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1answer
56 views

Massless ladder against a frictionless wall [closed]

I am confused by a review problem for my physics course. I keep getting a different answer from the solution (which was given to us) and not sure what I am missing. A massless ladder has a length of ...
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1answer
52 views

Deriving Hamilton's equations from KdV Hamiltonian

Let $f=f(q,p)$, $g=g(q,p)$ and Possion bracket $$\{f,g\}=\frac{\partial f}{\partial q}\frac{\partial g}{\partial p}-\frac{\partial f}{\partial p}\frac{\partial g}{\partial q}. \tag{1}$$ Then ...
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41 views

relationship between torque and potential energy for electromagnetism

It is well known that the energy of a magnetic dipole in a magnetic field is taken as $U = - \bf{m}.\bf{B}$. The dipole also experiences a torque $\bf{\tau = m \times B}$. In classical mechanics the ...
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35 views

How to calculate the forces that create precessing motion of a spinning top?

I'm trying to create a a spinning top simulation, and I have a problem with simulating the precession. I read the Wiki article about precession, which have the formula for angular velocity of ...
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35 views

Meaning of centrifugal term in the mechanical energy of a orbiting planet [duplicate]

For a planet under the effect of gravitational force the mechanical energy can be written as $$E=\frac{1}{2}\mu {\dot{r}}^2+\frac{L^2}{2\mu r^2}-\gamma \frac{m M}{r^2} \tag{1}$$ Where $\mu$ is the ...
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2answers
45 views

Position, velocity and acceleration vs time graphs

I'd like to draw graphs of a vehicle and I have a position vs time table. I can set the points but how am I supposed to join them, straight or hyperbole ? If the object is accelerating which is yes ...
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0answers
37 views

Are physical functions always differentiable [duplicate]

I know that physicist usually don't really think too much about differentiabillity of functions. Usually there are at most finite many points where functions aren't differentiable and if there are ...
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72 views

Derive Galilean transformation. (The meaning of the relativity)

In the book The meaning of the relativity Einstein says that in classic mechanics two postulates are previously supposed: 1.- The time is absolute. 2.- The longitude is absolute. And this implies ...
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69 views

Free particle and harmonic oscillator coupled

I'm currently playing with a toy model given by the Lagrangian $$L=\frac{m\dot{x}^2}{2}+\frac{m\dot{y}^2}{2}+\frac{1}{2}m\omega^2x^2+x y,$$ which is basically a free particle (described by $y(t)$) and ...
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Why are vibrations so common? [closed]

Why are vibrations so common? We all know, or pretend to know, that symmetries and the least action principle lead to conservation laws.Is there something more fundamental behind the fact that ...
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1answer
38 views

Newtons corpuscular theory

I am learning about the history and evolution of certain physics theories, one being Newtons corpuscular theory. I am reading that Newton predicted the corpuscles, which make up light would travel ...
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1answer
51 views

2D Momentum question

I am working through some questions in practice for a mechanics exam and I cant seem to find a solution to the following problem; Two objects, one of which is initially at rest, undergo a perfectly ...
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36 views

Why does the shock in viscous flow occur sooner than non-viscous one?

Why does the shock in viscous flow occur sooner than non-viscous one? If we want to discuss about drag, which one has bigger drag? This figure may help.
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2answers
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Does the position-time graph have to be a smooth function?

If at some time $t$ there were a discontinuity in the velocity-time graph, then the acceleration would be infinite at $t$. So intuitively, it seems that the velocity-time graph must be continuous. I ...
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1answer
74 views

Why do two rolls with the same mass but different moments of inertia roll different distances?

Imagine two rolls with the same diameter and mass. The mass of one roll is concentrated to the center of the roll while the mass of the other roll is concentrated to the edge of the roll. If the two ...
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When will a moving vehicle stop faster: when the brakes are applied and the wheels are slipping, or just before? [closed]

When will a moving vehicle stop faster: when the brakes are applied and the wheels are slipping, or just before the wheels start slipping? Explain why.
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93 views

Physical Relevance of Classical Limit to QFT's

We know the physical relevance of the classical limit of quantum mechanics quite well. However, if I take the classical limit of a quantum field theory, the answer is not so clear. Suppose I take the ...
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11 views

Why Flow meters are some times showing -ve fluctuating Values in Pressurized Pipe lines [closed]

In our Underground Water reservior we are pumping water by Hydro-pneumatic pumps to maintain same pressure till last connection. in order to measure the flow we have installed precise electromagnetic ...
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4answers
288 views

Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
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31 views

How to derive kinetic energy from the Lagrange equations? [duplicate]

I'm having trouble deriving the kinetic energy from the Lagrange equations. For reference, I'm following Landau and Lifshitz book, "Mechanics," which can be found for free at Archive. In any case, ...
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33 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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Pressurizing a circular toroidal shell

Consider a toroidal elastic, isotropic, homogeneous shell with a circular cross-section that is initially not pressurized. Under an internal pressure $p$, the shell might become more straight, but the ...
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1answer
72 views

Multiplying Lagrangian by a constant

Does a Lagrangian of a system multiplied by an arbitrary constant still work? If if I apply the Euler-Lagrange equations, do they still guarantee that the action is extremal? I arrived to the ...
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1answer
64 views

Wave equation in classical mechanics!

We represent the wavefunction of any wave on the string as $$y=f(x-vt),$$ where $v$ is velocity of the wave and $x$ is distance from origin and $t$ is time taken to reach the given point and $y$ ...
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1answer
56 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 ...
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5answers
124 views

Airplane on a treadmill - Variant Thought Experiment

This thought experiment is in a way related to the (in)famous airplane on a treadmill problem. If you take a ball and place it on a treadmill, will the ball: Move backwards relative to the ground ...
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1answer
32 views

How the mechanical equivalent of heat is employed in this situation?

Reading a little about the "mechanical equivalent of heat" what I understood is that we can convert units between calorie and $J$ by setting $$1\mathrm{\ J} =4.1860 \mathrm{ \ cal}.$$ Now, I saw a ...
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1answer
41 views

water stream cut off abruptly; why there will occur sprinkling?

Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the ...
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3answers
149 views

What happens to the coefficient of friction as the normal force increases?

Does the frictional force increase as the normal force increases, or does the coefficient of friction get smaller in value?
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1answer
50 views

What to do when you're hit by another car? [closed]

I have a question about what's the "best" thing to do if you're about to be hit by another car. Imagine you're in your car, and you're at rest. There's another car coming at you, and they're going ...
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1answer
134 views

A mass hanging under a table: a problem from Goldstein [closed]

I'm trying to solve Problem 1.19 from Goldstein's Chapter 1 (2nd edition), and am getting bogged down in trigonometry (?). Please help me figure out what I'm doing wrong! Two mass points of mass ...
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5answers
326 views

In the Principle of Least Action, how does a particle know where it will be in the future?

In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
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25 views

Computing the value of an Action given some boundary conditions

Having being dealing with Actions for a while I have come across a question in which I am required to calculate the value for $S$ an action in the form of a function for some given boundary ...