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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Understanding the phrase "Classical mechanics corresponds to the high frequency limit of quantum mechanics"

Recently I have taken an interest in mathematical physics and as my background is mostly in math itself, I have quite a lot of catching up to do regarding my knowledge of physics. One phrase that I ...
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Phases of vectors

This maybe because I am missing a whole concept itself, but how can vectors have a phase? I have been studying forced oscillations and I read that when multiplying a vector with i (sqrt(-1)) , the ...
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Rayleigh's Dissipative Function in Lagrangian Mechanics

What exactly is the derivation of Rayleigh's dissipative function? How does one know what to assume the function to be while dealing with a problem in Lagrangian mechanics? These two questions have ...
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Independence and ambiguity of holonomic constraints

I've got a couple of questions concerning constraint equations: Suppose I've got $n$ holonomic constraint equations for a particle, how can I be sure those are all the ones there are and I didn't ...
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Does the direction of angular momentum of a table fan different for two people standing behind the fan and in front of the fan?

Does angular momentum of a table fan depend on place of observation? What is its direction of angular momentum of a fan when I stand behind a table fan? In front of a table fan? And along the same ...
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What's a good simple model for wind attacking drone?

I'm trying to simulate a drone on https://rapier.rs/. My idea is to do an X shaped object, with a force $P$ on each end of the X, always perpendicular to the drone plane. I want to simulate wind, ...
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Is there a difference between a pattern's results and its processes? [closed]

Is there a difference between a pattern's results and its processes? The following link will send you to Wikipedia site where they define Pattern
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Question regarding Energy Interaction of two particles

https://imgur.com/s6RGUKb To give a context as to what I'm asking here ,I am talking about the energy of a two particle system (section 4.9 Taylor's Classical Mechanics) . My question is what does $\...
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Linear drag for pendulum in air, justifiable or not?

So, when trying to measure the gravity constant $g$ at home through a pendulum I realized I wanted to try to model drag on the pendulum, to get a more accurate result. I am asking how we can justify ...
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Vortex generated as a result of Newton's third law

This books states this process as a result of Newton's third law. However I just can't find ways to graps how the "vortex" is generated, is it a fundamental law? (The question emerges on the ...
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Are any points at rest on a globe spinning both horizontally and vertically?

Suppose there was a globe which could be spun about polar and horizontal axis. It is first spun about the polar axis, then promptly spun about the horizontal axis. Would any points be at rest?
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Velocity addition and Thomas precession

In Goldstein’s classical mechanics, section 7.3, there's an approximation (7.19) that I do not understand, in particular $\beta''_y=\beta'_y/\gamma $. Worse, even if I accept the approximation, it ...
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Why is angular momentum involved in a spinning ball hitting another?

One ball has a certain velocity and is spinning. It hits another ball, and each have a certain friction constant which kind of roughly defines how their surfaces interact. Now, when I was in high-...
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Starting point/references to understand infinitesimal canonical transformations? [closed]

So I just got done with my second year of my physics undergrad and I'm currently going through a course on Lagrangian and Hamiltonian mechanics on my own. I was getting everything just fine until the ...
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How do we visualise multiplication and division (reciprocal multiplication) in physical equations?

All formulas have terms generally multiplied or divided to represent another physical quantity. Like $F=ma$, $I=Q/t$, $W=F.s$ etc. Technically this is so because of ratios and proportionalities, the ...
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How to add a potential to a wave equation?

Imagine you have the wave equation: $$ \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}= \nabla^2 u$$ And you have your solution wave is "confined in a box" (or with the extremes of the ropes ...
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About a form of general solution to the coupled harmonic oscillators (Marion's book)

I'm reading Thornton, Marion, Classical Dynamics, section 12.2 and stuck at undersating some point : My question is, how can we take a general solution of (12.1) as of the form (12.9) (underlined ...
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Dynamics: why do physicists include derivatives like $\dot{\theta}$ in the state space for a system like a pendulum?

I come from statistics, so my experience with physics is spotty, especially on some simple stuff. I have been working on some applications related to control theory lately, and was looking at some ...
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Goldstein's derivation of Noether's theorem

This is a followup to my previoucs question: Translation invariance Noether's equation In Goldstein's derivation of the Noether's theorem in chapter 13, we have the infinitesimal transformation $$...
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Translation invariance Noether's equation

In chapter 13 of Goldstein's classical mechanics, on page 591 when talking about Noether's theorem, Goldstein says we need condition 3, which is $$\tag{13.133} \int_{\Omega'}\mathcal{L}(\eta_\rho'(x^\...
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Deducing equation of motion for a free particle using the form of the Lagrangian

This is in reference to the question: Deriving the Lagrangian for a free particle My question is specifically in regards to QMechanic's answer to this question, and I have quoted the relevant part of ...
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How did Noether use the total time derivation to get her conservation of energy? [duplicate]

I was informed by @hft that by combining the total time derivation: $$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} + \frac{\partial L}{\partial \dot{x}}\ddot{x} + \frac{\partial L}{\partial t}$...
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How to compute the eigenvalues and eigenvectors of the pseudo inertia matrix?

The pseudo-inertia matrix is defined as $\widetilde{\Xi}=\left(\begin{array}{cccc}\frac{1}{2}\left(-I_{x x}+I_{y y}+I_{z z}\right) & -I_{x y} & -I_{x z} & m c_{x} \\ -I_{x y} & \frac{1}...
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Where do these expressions in this "block on an inclined plane" problem come from? [closed]

I'm a returning physics student after nearly a decade being away from the subject matter. I'm doing some self-study to refresh myself on the material and am starting with reading through David Morin's ...
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How can you figure out when inertia or momentum is keeping the object in motion?

If we consider the case of Earth, inertia carries the Earth forward (inertia alone will make the Earth go out of orbit so gravity keeps it in orbit around the sun), but if we consider the case of a ...
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Intuition behind space-average velocity

Time-average velocity is easy to visualize. But I am struggling with the concept of space-average velocity. I know the formula and definition for these two measures: Space-average velocity = $ \frac {\...
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Why do we apply a Legendre transform to the Lagrangian in the first place? [duplicate]

I understand how the legendre transform of the Lagrangian with respect to $\dot{q}$ yields the hamiltonian, but I do not understand why one would think to do this in the first place? what is the ...
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Why is the action guranteed to have unique extrema in classical mechanics? [duplicate]

Reading any classical mechanics book which introduces the Lagrangian formalism of mechanics, a one particle system is introduced to show that we obtain the euler-lagrange equations from Newton's ...
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Why is the action guranteed to have one unique extrema in classical mechanics? [duplicate]

Reading any classical mechanics book which introduces the Lagrangian formalism of mechanics, a one particle system is introduced to show that we obtain the euler-lagrange equations from Newton's ...
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Equations of motion of a car with variable mass and drag [closed]

Lately, I've been trying many ways to attain these equations, yet I've not succeeded in any. I'm basically using Newtonian mechanics because it's the most suitable for this case with dissipative ...
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Multiplying non-constant acceleration by a constant on every point - would the total path be multiplied by the same constant?

If the non-constant acceleration is multiplied by a constant (on every point), would the total path also be multiplied by the same constant over the same time? Both starting and ending speeds are zero ...
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Do all objects in a system need to have the same acceleration? [closed]

What is the definition of a system? Could multiple objects accelerating at different magnitudes and directions still be considered a system?
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Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement. Rudder ...
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What are some examples of microscopic quantities?

Mass, volume, energy, entropy, temperature, pressure are some macroscopic quantities. Which means we can think of them even without considering the molecular nature of matter. What are some examples ...
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Does the force that need to be applied to pull the weight out of a well by string is more at the start?

One way to estimate depth of the well is attaching a weight to a string then throwing it into the well until it touch a hard surface then pulling the string out of the well and evaluate its length. ...
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Yet another perpetual motion machine: does this imply large selective membranes are not possible? [closed]

So I was just thinking about the buoyant force and came up with what seemed like a simple perpetual motion based on it. Obviously such things are not physically possible so I'm trying to figure out ...
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Necessary torque calculation for rotating a heavy object?

I'm trying to create something like the image below, where a motor will be connected to a gate/big piece of wood, which will be hinged so that the motor can rotate the gate. I know the weight (4lbs) ...
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Why classical mechanics is not able to explain the net magnetization in ferromagnets?

Why classical mechanics is not able to explain the net magnetization in ferromagnets? why does exchange interaction can explain net magnetization in Ferromagnets, which is purely quantum mechanics??
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3 votes
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Stress and equilibrium

By newton's third law, all internal forces in a portion of volume must be zero. Thus the total force is due to other volume portions exerting force onto the surface of said portion. However, if one ...
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Where does the excess energy go in this problem?

Two identical plastelin balls were suspended on a non-extensible weightless string with the same length L, which are fixed at the same point. One of the balls was deflected 90 degrees from the ...
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Do Legendre transformation form a group?

In my classical mechanics class, my professor asked if Legendre transformations form a group, and in my little knowledge about groups, I know that a transformation group consists of a set of ...
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Why is the potential energy of a suspended rope proportional to the stretch?

In A. Zee Einstein Gravity in a Nutshell, when he is talking about variational calculus on page 113, he gives an example of a suspended rope. To calculate the total potential energy due to tension, it'...
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How to show that the Hamiltonian $H$ is invariant under flow generated by $F$?

I know usually if I have a transformation of phase space $Q(p,q), P(p,q)$ it is defined to be canonical if and only if its Jacobi matrix is part of the Symplectic Group or equivalently $\{Q^{i}, P_j \}...
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Relativistic Particle theory [duplicate]

I have read relativistic field theory and non-relativistic particle theory. My question is How to derive Lagrangian for Relativistic Particle theory (not field).
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Largest feasible Crooke's Radiometer?

I will be working with a scientific glassblower to make a large demonstration Crooke's Radiometer. I would like it to be as large as possible. We will be using jewel pivot bearings to keep the ...
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How do I calculate the force applied on an inner surface of a tube?

This is a one piece button. the point in the middle is not necessarly the center, and the r1,r2,r3 are not necessarly the radius . d- is the shank between the button and the middle point. How do I ...
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1 vote
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Truck with leaking sand - How can it not have a change in momentum?

If we have a truck filled with sand moving at a velocity "v", and the truck is leaking sand vertically downwards at a rate of $\frac{dm}{dt}$, if we ignore friction and air resistance, why ...
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Books of classical mechanics exploring non-holonomic constraints

I would like to know books of classical mechanics exploring non-holonomic constraints examples in depth. I know some common examples as when a rigid body is rolling but I would like to read more about ...
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How do we calculate the required mass when we have a height and area of the impact? [closed]

we have a steel bar, chisel, and hammer. when the hammer hits the chisel which is in contact with the steel bar what is the force required. after hitting the chisel it makes an impression of the ...
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2 votes
2 answers
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Why $\dot{r} \neq v$?

I am solving the same problem as the person in this link was solving. But I am having a different kind of doubt, i.e related to the derivative of radius. then differentiating $\dfrac{dE}{dt} = \dfrac{...
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