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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Diffraction through the slit

In book "Quantum Mechanics and Path Integral", 3-2 Diffraction through the slit: Under the fig. 3-3, why did Feynman say that we cannot approach the problem by a single application of the free-...
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230 views

A particular case when Lagrange equation is equivalent to equation of motion on a Riemannian manifold

Suppose a particle is moving on a surface of a sphere,then it contains a holonomic constraint and so the three Cartesian co-ordinates are available with a constraint equation(equation of surface in ...
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238 views

Clarification on a Goldstein formula steps (classical mechanics)

At page 20 of Classical Mechanics' Goldstein (Third edition), there are these two steps given between eqs. (1.51) and (1.52): $$\sum_i m_i \ddot {\bf r}_i \cdot \frac{\partial {\bf r_i}}{ \partial ...
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4k views

What is the relationship between mass, speed and distance of a planet orbiting the sun?

After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star. Given the mass of the sun and star,...
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115 views

Complex part of the solution for physical values

What's a physical meaning of, for example, complex part of the solution for coordinate change of the anharmonic oscillator? Why after substitute (for diff. equation solve) for real x we can earn $x = ...
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229 views

On the Discretization of Energy Levels

We consider a system of "n" particles whose total energy E and net momentum $\vec{P}$ are fixed are fixed.There no net force on the system(assumed) $$\Sigma \epsilon_i= E$$ $$\Sigma\vec{p_i}=\vec{P}$$...
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441 views

Euler's buckling formula applicable for impact calculations?

$$F = \frac{\pi^2 EI}{(KL)^2}$$ Is Euler's buckling formula applicable for impact calculations, considering speeds relevant for a car or aircraft crash? If there is a level where the formula ...
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83 views

Does this relation about direction of particles make sense?

Maybe I've just stared at this statement too long and I've missed something obvious. Nevertheless, here's the problem: Landau-Lifshitz vol. 1§16, problem 1. Consider (classical) collision of two ...
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182 views

Linking two balls together

I have a physics simulator that simulates a bunch of balls moving and colliding with each other, and I would like to be able to "link" two balls together so they stick to each other (are always ...
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413 views

How to determine n equidistant vectors from point P in three dimensions

As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces. For the first part of the assignment, the particle has mass $m$, ...
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27k views

Difference b/w Kinetics & Kinematics w/concrete example

(I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
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554 views

What techniques can be used to analyze a rod rotating about the edge of a table?

A uniform rod of length $4x$ is rotating about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making an ...
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139 views

How to find the value of the parameter $a$ in this transfer function?

I am given a transfer function of a second-order system as: $$G(s)=\frac{a}{s^{2}+4s+a}$$ and I need to find the value of the parameter $a$ that will make the damping coefficient $\zeta=.7$. I am not ...
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546 views

What conditions must be met for a ball to roll perfectly down an incline without slipping?

What conditions must be met for a ball to roll perfectly down an incline without slipping? A mathematically rigorous definition, please. I honestly don't know where to begin with answering this ...
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887 views

Problem based on Rotational Motion [closed]

A spool of mass $\mathsf m$ and inner radius $\mathsf r$ and outer radius $\mathsf{2r}$, having moment of inertia $\Large\mathsf{\frac{mr^2}{2}}$ is made to roll without sliding on a rough horizontal ...
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535 views

Spin angular momentum of a system of particles : Is there any energy associated with it?

Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
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283 views

Is the number of independent constants of a system equal to the number of degree of freedom of it?

Maybe the question is not very clear myself since I am not a physics major.But can you help me make this question clearer and then give me some comments on it? I got that this holds in gravitional ...
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402 views

Proof of the Hydrostatic weighing equation?

I've been trying to derive this equation for about two hours: But I can't seem to get it. In my class, we are using it to accurately measure the volume of irregulary-shaped objects, but I ...
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419 views

centrifugal force in static frame of reference

The other day we derived Kepler's third law. $$ \left( \frac{T_1}{T_2} \right)^2 = \left( \frac{r_1}{r_2} \right) ^3 $$ In order to derive this, you can look at a given planet that revolves around ...
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276 views

Impulse situation

I am wondering if a physical system subjected to an impulse $=A\delta(x-a)$ makes any sense. I reckon that a force could take that form -- thought of as a finite impulse applied over an infinitesimal ...
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276 views

Is the pressure at the outer hole on a pitot static tube equal to atmospheric pressure?

I'm looking at a pitot static tube question right now and I just need some clarification. There is the outer hole on the pitot static tube, not the hole that the air stream goes through, but the other ...
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391 views

Modellng mechanical behavior of heat shrink film

Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or radiation)...
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564 views

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface?

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface? The question I am working on is: A projectile is launched vertically from ...
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340 views

Artificial Gravity - Spinning Station Questions II

In an answer to Artificial Gravity - Spinning Station Questions Vintage wrote: A theoretical space station of radius 900 meters, doing a complete rotation every 60 seconds (in order to generate ...
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207 views

Constrained particles under distance dependent force

This question is from the 1975 Canadian Association of Physicists Exam. No solutions are posted and I am quite lost on how to proceed with it. A particle is constrained to move along the x-axis of a ...
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54 views

On the Stability of Circular Orbits

Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the ...
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31 views

Electric Field under Time reversal

We know under time reversal electric field does not change direction. I am doubtful about it. Imagine an electric field parallel to x-axis (in positive x direction) and a charge moving parallel to ...
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41 views

Reason behind $L = T - V$ (Lagrangian formalism) [duplicate]

I've been learning about the Lagrangian formulation recently, and while I'm with the process, I am still struggling somewhat with the theory behind it. As I (rather poorly) understand it, the ...
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123 views

When does a Trebuchet Shoot Its Projectile?

Consider the following sling trebuchet: While researching I found that what controls the release angle of the projectile is the angle between the 'finger' and the extension of the beam $r_b$, as ...
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47 views

Lagrangian in a system with a specific velocity dependent potential

I have a system of a particle moving under the generalized central potential $$ V= \frac{1}{r}(1+\dot{r}^2) \tag{1} $$ The general Euler-Lagrange equations for such type of potentials are: $$ \frac{...
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37 views

Homework exercise: a ball hits a rigid bar [closed]

I need a hand with the following exercise: A rigid bar of mass $M$ and length $L$ is hanging vertically from it's upper side, from which it can rotate freely. A particle of mass $m$ hits the ...
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64 views

Tractrix - velocity pointing to pulling point

It is said the tractrix is the curve described by a mass being pulled by a string, where the end of the string being pulled moves with constant speed, and the mass suffers a friction force. What is ...
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60 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
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37 views

Photon transmission

I want to know exactly how light travels. Are each photon in a light beam traveling in a cosine function? I'm confused because only when it goes through polarization that it starts to show this type ...
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34 views

change of energy in changing frame of reference

Let's imagine a car that can jump onto, or off a moving train. The train moves at 10m/s. The car, on a road next to the train, accelerates to the same 10m/s, jumps off a ramp and lands on the train, ...
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35 views

Confused about shear elasticity and complementary shear stress

I am a self learner of continuum mechanic. I am confused about simple shear stress in situation similar to figure 1, in case $F_\textrm{ext}$ is caused by external perturbation by i.e., human, what ...
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39 views

Why we can use partial derivatives to tell if a force is conservative? [duplicate]

Let us, initially, analysis only a two dimension situation. Assume that $F(x,y)$ is a force dependent on the particle position (give by $x,y$) is proposed that if \begin{equation} \frac{\partial \...
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63 views

Normal reaction [closed]

Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H? I don'...
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17 views

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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49 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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91 views

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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1answer
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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52 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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36 views

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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57 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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37 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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38 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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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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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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32 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, I'...