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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Can the curvature of a vibrating string be derived from the energy equation?
Arnold’s Mechanical Methods of Classical Mechanics page 17 says the theory of oscillation is $\dot x = -x$ and $E=x ̇^2/2+x^2/2 $. The energy level sets are concentric circles in union with the ...
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Lagrangian and Hamiltonian Mechanics: Conjugate Momentum
I am a physics undergraduate student currently taking a classical mechanics course, and I am not able to understand what conjugate/canonical momentum is (physically). It is sometimes equal to the ...
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Boat-river problem [closed]
A river flows from east to west at 4 km/hr. From the north bank of the river, the first boat starts traveling straight towards the other bank at a speed of 10 km/h. The second boat starts moving along ...
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Impulse imparted into a circular orbit
I am studying classical mechanics and the following problem has come up. I am not quite sure how to approach it.
A particle of mass m moves under the influence of an attractive inverse square law ...
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Understanding the use of Capstan Equation
I'm currently working on the analysis of a current capstan, I want to analyze this system using the capstan equation.
The current capstan I'm working on has been built on the following parameters
...
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Energy landscape of a spring in a potential
What does the energy landscape of a spring that is moving through an external periodic potential look like?
Consider a spring that connects two particles in a periodic potential. Let us say the ...
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How charge interact with mass? [closed]
If mass does not interact with charge, why does the mass of an electron move (means by which mechanism it moves) in an electromagnetic field? It is same like we stick ball on magnet with fevistic and ...
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2 objects heading towards each other at a certain distance and with initial velocity and friction coefficient [closed]
I'm not a physics student. I'm a programmer. But I found this physics problem interesting and I would like to understand how to approach it.
2 objects, A and B, heading towards each other at a certain ...
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In statistical mechanics, why is one "allowed" to treat classical systems probabilistically?
Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental ...
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Derivation of Hamiltonian by constraining $L(q, v, t)$ with $v = \dot{q}$
I am trying to reconstruct a derivation that I encountered a while ago somewhere on the internet, in order to build some intuition both for $H$ and $L$ in classical mechanics, and for the operation of ...
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Does the potential energy $\alpha\ln r$ have closed trajectories for $E>0$? [closed]
Say we've got the following potential energy
$$U(r)=\alpha\ln r,$$
$\alpha$ being positive constant ($\alpha\in\mathbf R^+$) .
To argue whether it has closed trajectories or not we'll have to focus on ...
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Does the acceleration formula from dynamics apply in all cases?
Can the formula for acceleration $$a=\frac{F}m $$ (where $a$=acceleration, $F$=force ,$m$=mass) be used in all cases ? Or is it an isolated formula used only for some cases ?
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Classical Mechanics: How can i find the analytical form of the effective potential? [closed]
Question: Consider the system on the side consisting of two particles with the same mass m, connected to each other by a flexible string with fixed extension l. One of the masses is suspended and the ...
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On the connection between the ocean of physical elements with vacuum and the formation of space - Part 1 [closed]
Abstract:-
I shall put forth in this article a description of the formation of space and its gradual development into a universe while addressing the crucial case of how, why, and when. I will, ...
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Electrical charges and energy
Since we have defined energy as the ability to do work, how come electric charges (-) and (+) be able to do work without using any energy? If lets say I have a big fixed positive charge and if lets ...
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Which is the effective potential energy that derives from the force?
I am having troubles identifying which potential energy is the one that can be expressed as this $$\vec F=-\nabla U.$$ I have in my notebook that in the context of orbits and problems of 2 bodies $$\...
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Why isn't work $Fd \sec \theta$? [closed]
In the following image if force the triangle PAN was right angle at P then the component of force in the direction of displacement would be $F\sec\theta$ so work $F*Displacement(AC)*\sec \theta $.
I ...
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Calculate rotation from net torque and inertia matrix
I am trying to grasp the concepts of forces applied to a rigid body resulting in a net change of the rotation of the object.
This is not a home assignment and I read some resources on both the web and ...
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Meaning of a Constant in the Unbound Orbit Equation
The solution to the radial equation for two celestial bodies with eccentricity $\varepsilon$ greater than 1 can be expressed as
$$
\frac{(x-\delta)^2}{\alpha^2} - \frac{y^2}{\beta^2}=1,
$$
where
\...
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Question about distribution of mass
I recently began taking my first university-level physics course after having studied quite a bit of pure mathematics. While I think that my math background has helped me grasp some concepts a bit ...
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Doubt Regarding Noether's theorem for time-dependent systems
I'm having problems showing Noether's theorem when the lagrangian is time dependent. I'm trying to do it not using infinitesimal transformations from the beginning, but continuous transformations of a ...
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What is the amplitude in c) part and why is the phase difference not $\pi$? [closed]
So this is from OCW
First part is fairly easy natural frequency comes out to be 10 Hertz,Gamma came out to be 1/2 for two traffic signals and 1 for a single traffic signal, In second part I am ...
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What are good books to study mechanics to quantum physics? [closed]
I'm currently in my senior year of high school. I already have a solid foundation on the basics of differentiation and integration (including some techniques: by substitution, by parts, and by trig. ...
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Particularity of symmetries generated by the action variables of a classically integrable system
Background
I was reading this article on the unviersal $SO(4)$ and $SU(3)$ symmetries in all central potential problem. Turns out every bounded planar motion in any smooth central potential will all ...
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Difficulties understanding the procedure behind Hamilton-Jacobi equation variable separation
i'm having difficulties understanding how to proceed when facing an Hamilton-Jacobi equation through separation of variables. I'm currently following Fasano's book (pdf here: http://homepage.sns.it/...
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Is the invariance of the Lagrangian under some transformation equivalent to the covariance of the motion equation? [duplicate]
Take the Lagrangian $L=\frac{1}{2}m{{\left( \frac{{\rm{d}}}{{\rm{d}}t}x \right)}^{2}}-\frac{1}{2}k{{x}^{2}}$, for example.
The equation of motion of this system should be given by $m\frac{{{{\rm{d}}}^{...
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Can I find $\frac{dm}{dt}$ where $m$ is the relativistic mass of a particle?
So, recently I learned the basics of Special Relativity, and I found out that the mass of a body increases with the increase in its velocity as given by the Relativistic Mass equation:
$m=\frac{m_0}{\...
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Mean and higher moments of final position of particle subject to time dependent central force along x
I would like to find the expected value and higher moments of the x and y components of the final position of a particle moving in the xy plane, subject to a central force, centered on a positive x ...
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How do I analyze the cue tip at impact with a billiard ball?
this is not a homework problem, it is something I've been trying to understand in billiard physics (because I'm a big pool fan)
When we hit the cue ball off-center to impart spin, we still don't know ...
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Understand the definition of frame and inertial frame in Arnold's Galilean spacetime definition
In Arnold's Mathematical Methods of Classical Mechanics, we define the physical space time as a four dimensional affine space with associated Galilean structure. I understand this part.
Now what I'm ...
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Bloch Wave Solution to the Oscillating String
I am taking a graduate-level mechanics course right now, and we are working with the continuous limit of coupled harmonic oscillators. My professor mentioned that he prefers the "bloch wave ...
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The frequency is off by a factor of $2 \pi$?
I was reading morin's intro to mechanics, and the following material came up:
At equillibrium point $x_0$ expanding the taylor series, we see $V(x)=\frac12 V"(x_0)(x-x_0)^2$ so comparing this with $V$ ...
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Causality in formulas in general physics
Follow-up on this question about causality for Newton's second law.
In $F=ma$, the $=$ sign signifies proportionality, not causality. It makes sense, as the equal sign is invertible, whereas causality ...
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Is $F=-\nabla V$ a form of the least action principle? [closed]
Only for conservative systems, of course.
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Work of friction along a circular path using dot product
Good day guys, I was working on circular motion and was wondering about the following:
I have seen that the work done by friction along a circular path is given by
$$W = F_fS$$
I was wondering if it ...
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Buoyancy in the hydrostatic equation
I have a question regarding the fundamental equation of hydrostatic, namely:
$\vec\nabla P=\rho \vec g$.
Why do we not take into account in Newton's 2nd law (used to prove this equation) the buoyancy? ...
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Reaching a closed form solution for $S$ in the Hamilton-Jacobi equation
I am trying to solve this problem
Discuss the use of parabolic coordinates to obtain separable Hamilton-Jacobi equations for the potential $V(\rho, \phi, z)=\frac{\alpha}{r} - Fz$ and give a closed ...
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Energy Loss of a Ball which Splits into Pieces
It is well-known that one can analyse the loss of kinetic energy when an inelastic ball falls and bounces back up from the ground in terms of the coefficient of restitution
$$E_f - E_i= \frac{K_i - ...
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Conservative forces and Variation
I am currently studying "Classical mechanics by Goldstein" and have just started. The book introduced something simple. For a conservative force, the work done in taking a mass from one ...
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Problem while calculing the bending torque of internal air pressure in a soft actuator
this is a question I cant resolve while looking a paper I needed for my undergraduate thesis.
In this image (from Modeling of Soft Fiber-Reinforced Bending Actuators, Panagiotis Polygerinos et al.), ...
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Can a body be in both static and dynamic equilibrium simultaneously?
I was just studying statics when I realized that a body can be in both static or dynamic equilibrium at the same time but I am not so sure.
My textbook says that an object at rest is in static ...
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How to determine whether an object is a point object?
I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks ...
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In the equation of wave (mechanical) : $y (x,t) = a \sin(kx-wt+\phi)$;
Does the $x$ show the displacement of the particle and the $y$ shows the displacement of the wave?
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HW: particle subject to central force with exponential logarithmic orbit
I've been working on this exercise for some time now and although I've almost got it I can't seem to make it to the end of it. Here is the exercise:
A particle subject to a central force is orbiting ...
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What happens if the impulse of a collision results in the change in velocity being greater than the speed of sound?
It is my understanding that impulse travels through materials at the speed of sound through that material (i.e. impulse through steel travels through the steel at ~5000 m/s which is the speed of sound ...
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Connection Helmholtz free energy and $H,M,B$ fields
Consider a magnetic system subject to a magnetic field. Here we work with the fields $H,M,B$.
Now, how does a change in the Helmholz free energy depend on $H,M,B$? I have three sources that seem to ...
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If the Lagrangian depends explicitly on time then the Hamiltonian is not conserved?
Why is the Hamiltonian not conserved when the Lagrangian has an explicit time dependence? What I mean is that it is very obvious to argue that if the Lagrangian has no an explicit time dependence $L=L(...
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Kinetic energy of a rotating body
On my own, I tried deriving the rotational kinetic energy for a rotating body with an arbitrary changing axis of rotation. What I did is use the formula:
$$T = \frac{1}{2}\omega^2 (\hat{n}^{T} \mathbf{...
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Find the acceleration of a block sliding down on an accelerating inclined place [closed]
I don't understand the solution provided in the image. Using Newton's second law for forces along the x-axis (parallel to the inclined plane), shouldn't the equation be $ma = mg\sin \theta+ mb\cos \...
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Confusion regarding spherical coordinates
I have a few dots in my brain that I need to connect, one of them is:
Is $\dot{\vec{r}}=\vec{v}$ true always? But $\dot{r}=v$ isn't always true? If so, in which cases both are true or not?
Regarding ...
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