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Questions tagged [classical-mechanics]

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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Motion of the center of mass of rigid bodies in space

For the classic two body problem, I know that the motion of the center of mass is a straight line (with respect to an inertial frame), provided that the bodies are considered as point particles. Now ...
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Rigorous definition of generalized coordinates

In Goldstein's classical mechanics and in many other books I haven't seen a rigorous definition of generalized coordinates. In a system of $N$ particles described by $\textbf{r}_1, \dots, \textbf{r}...
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Eddy Currents and magnet's orientation with respect to motion

I am doing a report on an experiment on harmonic oscillators. We added magnets to the cart (they move with it) to provide magnetic dampening, placing the magnets once horizontally and once vertically (...
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Physics mystery : why does it rotate?

In the beginning this thing was floating still and the candle was out. Then someone lit the candle and the flame somehow Made the object spin on the water. See the picture. I know a little bit about ...
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A particle moves on the outside of a smooth ellipse in a vertical plane.The major axis of the ellipse is vertical & its eccentricity is e [on hold]

A particle moves on the outside of a smooth ellipse in a vertical plane. The major axis of the ellipse is vertical & its eccentricity is $e$. If the particle starts from rest from the highest ...
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Why does the instantaneous axis of rotation pass through the metacentre?

When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of ...
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In this cart-and-pulley problem, why is the tension multiplied by a factor of 2?

I got an exercise to solve but I can't understand something and need your help. First of all, I want to apologize for my English and I'll try to explain myself in the best possible way. As shown on ...
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1answer
31 views

beta velocity notation in Galilean matrix

I was looking at the Galilean transformation matrix and came across a matrix for Galilean of the form. $$\begin{pmatrix}x'\\ y'\\ z'\\ t'\end{pmatrix}=\begin{pmatrix}1&0&0&-\beta c\\ 0&...
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Calculation of drag coefficient of a square plate oscillating in water

I am currently reading up on fluid mechanics and was reading up on the drag force equation, and it come to my attention I am not sure how one can find the coefficient of drag of and object without ...
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1answer
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Is the barycenter always at the same position?

I am currently preoccupied with the Two Body Problem and I was wondering whether the barycenter, or center of mass, is a static point or if it is moving, and how to calculate its position.
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1answer
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How come $\frac{d}{dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}$ in Lagrangian mechanics? [duplicate]

It is written in the Goldstein's Classical Mechanics text that $$\frac{\mathrm d}{\mathrm dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}=\sum_k \...
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Why charged particles moving in an electric field deflect less at higher velocity?

According to coloumb's law, particles of the same charge should experience the same force, however, when moving at higher velocities, they deflect less. Can this be explained in terms of classical ...
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A short question regarding Hamiltonian [duplicate]

Can any one please tell me in what cases the hamiltonian is not Equal to Total energy. My guess, albeit educated, is if the potential is either a function of time explicitly or a function of velocity, ...
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2answers
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Deriving effective potential energy from the Lagrangian of a two-body system [duplicate]

I'm having some issues understanding how the effective potential energy of a two-body system is derived from the Lagrangian of the system. Specifically my issue is with one step... Suppose we are ...
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2answers
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Is there a fundamental efficiency limit for generators?

Im currently interested in the theoretical efficiency limit of a generator, ie any device transforming kinetic energy to electrical energy. In particular, id be interested in turbines, that convert ...
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1answer
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What does Ehrenfest's theorem actually mean?

I am told that Ehrenfest's theorem, applied to a physical observable $\hat A$, is: $$\frac{d\langle\hat A\rangle}{dt}= \frac{i}{\bar h}\langle[\hat H,\hat A]\rangle$$ I don't understand how to use ...
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How do I calculate the tension in the string of a yo-yo with Lagrange? [on hold]

I can not figure out, how to solve the last equation for λ. I know the moment of inertia is $1/2·m·R^2$ Can somebody please help?
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Pressure in a fluid and force of gravity

I have this moving fluid in a pipe. Let's consider the force P1A1 in the left face of the fluid portion before the movement. In a real scenario does the pressure P1 also contain a component of the ...
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1answer
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Solutions to an Underdamped Oscillator

In many of the books talking about damped Simple Harmonic Motion, the underdamped Oscillator is treated as follows: We have Newton's Second Law Equation as - $$m\ddot{x} + r\dot{x} + sx = 0 $$...
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Is it possible to create Poincaré sections using a Lagrangian?

I have a triple pendulum Lagrangian and equation of motion, and now I'm thinking of creating Poincaré sections. Do I have to find the Hamiltonian first?
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30 views

Logic about Tap water and Hot water calculation [on hold]

Let's say, Temperature of Flame is 50. In each pass, the water will get 77.8% of temperature difference between water and flame. The tap water temperature is 20. and the valve controls % of cool/...
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1answer
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Mechanics of a spinning cup

Has anyone noticed how if you have a plastic cup on its side, and you spin it from either side, you can get it to stand upright? Well you can see some guy try it on this (fairly odd) video. Depending ...
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What is the physical interpretation of the action integral, without the stationary action principle?

I'm still wondering about the physical interpretation of the action integral of some mechanical system (classical theory here, to simplify things): \begin{equation}\tag{1} A = \int_{t_1}^{t_2} L(q, \, ...
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Lagrange function and a differential equation with a cylinder

I need some help with the following task. So I have a cylinder which you get by rotating the curve $z=-\frac{\alpha}{2r^2}$ around the $z$-axis. There is a mass moving on this cylinder. It can move ...
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Slipping of a rod -dynamics

A uniform rod of mass m is placed at right angles to a smooth plane of inclination $\alpha$ with one end in contact with it. The rod is then released. Find reaction of the plane when the ...
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What fields of physics that use abstract math concepts can undergraduates start to look into? [closed]

I’m In my Junior year of my math/physics major and I’m interested in pursuing a graduate degree in mathematical physics. My university requires a Sr Thesis for graduation and I would love to do it on ...
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Basic doubts about dynamics of a rod [on hold]

I have few doubts in the given solution. It says there is no force along the plane but $mgcos\alpha$ is acting along the plane ? As given, $A$ is used as orgin. Then how come x-co-ordinate of $G$ is ...
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Definition of complete integrability

For $n$ d.o.f. autonomous Hamiltonian systems, the complete integrability is defined by the existence of $n$ Poisson commuting, globally defined, independent functions. Is it required that we know ...
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1answer
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Prove that surfaces in Phase space can never cross [closed]

I come across a problem that is related to the surfaces in phase space: For a Hamiltonian of a particle $H$ as a function of its location $q$ and its momentum $p$. Prove that the surfaces in phase ...
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1answer
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“Monochromatic” vs. “Impulse” Force (What are the meanings of these terms?)

In a paper I am reading (linked below), the following is stated: The transient motions of the sphere and the gas bubble in the elastic, incompressible, inviscous medium are investigated in response ...
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1answer
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Santa and conservation of momentum. How is it possible that conservation of momentum doesn't hold here?

Santa wants to deliver his presents but his reindeers are on strike. In order to still be able to get somewhere he decides to sacrifice some of his presents to gain speed. He decides to throw them ...
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1answer
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Gyroscopic precession on a friction-less surface

I am having trouble understanding the total energy for a heavy spinning symmetric top (Gyroscope) on a friction-less surface. I am trying to understand it via the Lagrangian of the gyroscope. My ...
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1answer
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Is it possible to define an energy momentum tensor for classical point particles from a QFT?

I have a question about the semi-classical limit of a QFT that so far I have never been able to solve. Let's start with a second quantized Klein-Gordon field with Lagrangian $$\mathcal{L}(\phi)=\frac{...
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1answer
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Real force analogue names for the coriolis and azimuthal fictitious forces

Consider the following equation (10.10) in Morin's book on classical mechanics, it is meant to provide a correct prediction of the measured acceleration of a particle for someone taking measurements ...
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2answers
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How to calculate materials ability to resist penetration

I would like to ask you this question which I struggle to answer. If I have a plate of some material X to which I am shooting at with a tank main gun with ammunition parameters: weight $= 10\text{kg}...
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2answers
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Roller coaster loop top speed

For a roller coaster loop, if it were perfectly circular, we would have a minimum speed of $v_{min} = \sqrt{gR}$ at the top of the loop where $g=9.8 m/s^2$ and $R$ is the radius of the 'circle'. ...
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Examples of central forces on the path of orbit?

In solving a problem from Goldstein (3.13), I solved for multiple properties of a circular orbit with the attractive central force where the path of orbit crosses the point of the force (at origin). ...
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Why don't brake rotors self level through use? [migrated]

A few months ago my brakes developed a wobble, and the mechanic explained that there is a high spot in the rotor so when I'm braking the brake pads grab that spot more than the rest and it makes the ...
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0answers
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Force of friction between spinning cylinder and two perpendicular surfaces [closed]

There is a spinning cylinder in a 'corner' with radius R, mass m and friction koefficient k. I want to calculate both forces of friction ($F_1$ - wall and $F_2$ - floor).
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At what concentration do dispersed particles begin behaving like a fluid?

Suppose that I have a nearly insoluble metallic compound in a solution, and that what little of this compound does dissolve aggregates to form nanoparticles. The number of nanoparticles is ...
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Period of coupled cycloidal pendula

If you were to couple two pendula following cycloidal paths would they still show similar properties to a single cycloidal pendulum? For example, could you in some sense still say that the period is ...
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0answers
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Shooting flywheel for robots [closed]

I'm a student in FRC robotics and I have a problem I am trying to solve that the two mechanic teachers I had couldn't answer. In fact, the whole department of physics of my school couldn't answer. Let'...
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0answers
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Movement on a cylindersurface by using Lagrange formalism [duplicate]

A particle with mass $m$ moves under the influence of gravity smooth on the surface of a cylinder with radius $R$. The cylinderaxis is horizontal , so orthogonal to the gravity. task: Find the ...
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0answers
21 views

Shortest Time Path for a rocket with simple friction

The problem There is a rocket in space at point $a$ whose final destination is point $b$. Find the path of minimum time that goes from $a$ to $b$. To make the model realistic and avoid infinite ...
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1answer
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Force generated by triceps - Statics [closed]

This is the question I am in need of help with. Above is my try to gather an answer. My thought process is as follows, the origin point is well defined. That force enacting clockwise should equal the ...
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Deriving equations of motion using Lagrangian formalism for inverted pendulum on a cart with friction between pendulum and pin

I know this is a problem with plenty of examples and solutions but I can't find one where the friction between pendulum and pin (I know it's negligible) is taken into account. My main question is if ...
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2answers
53 views

Physical Constraints

In physics, what does one mathematically mean by constraint in classical mechanics? What are the the different types/cases and how do people deal with them?
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What properties must a smoothly spinning toy top have?

It would seem that there is some open source software that would allow you to create objects of a certain volume, even with arbitrary shape (I'm thinking blender and some of it's addons.) Now, I know ...
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1answer
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Stokes' law on non-spherical objects

So I have been thinking about Stokes' law and damped harmonic motions in a fluid. Now Stokes' law is only model on spherical objects and if I model this as a spring mass system and oscillate a ...
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1answer
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Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...