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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I am trying to derive an expression for the magnetic field of charged particles travelling at significant fractions of speed of light [closed]
I tried using lorentz transformation , which gives me correct answer for speed of light c but when i try to input any other values nearby c it becomes a constant
B = 10-7 . q/r² ( (v - u)/ 1- uv/c²)
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Justifying that the gold nucleus is at rest in a Rutherford experiment
This is an example on the Rutherford Experiment from Young and Freedman's University Physics.
In the last paragraph of the solution the book states that it is valid to assume that the gold nucleus ...
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Is it possible to understand in simple terms what a Symplectic Structure is?
I would like to understand what a Symplectic Structure is, and its implications in Classical Mechanics (Phase Space), but in pre-grade terms (If that could be possible). I have not taken any ...
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Diffusive momentum transport as overlap of acoustic peaks?
In the context of molecular dynamics simulations of soft or hard spheres in the fluid phase (e.g., with Lennard-Jones interactions), it is known that the velocity autocorrelation function (VACF) ...
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Massless String Having Different Tensions
I'm a student fairly new to physics, and I was working through a textbook (this is not for homework) when I came across a problem involving
Two masses, $m$ and $2m$, hang over a pulley with mass $m$ ...
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Getting an opposite sign for the centrifugal potential energy in the effective potential [duplicate]
Consider a system whose Lagrangian is
$$L = \frac12 \mu\left( \dot r^2 + r^2 \dot\theta^2 \right) -U(r) $$
By the Euler-Lagrange equation,
$$\frac{\partial L}{\partial\theta}=\frac{d}{dt}\frac{\...
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Understanding the “source” of magnetic energy in a bar magnet
I’m an amateur trying to grapple around this problem of what sources the magnetic energy in a bar magnet…
We know that the source of the magnetic force that a bar magnet exerts is due to its magnetic ...
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Problem explanation from Estonian-Finish Physics 2003 olympiad [closed]
I am having trouble understanding problem 5.3 (Vibrations) from the Estonian-Finish 2003 Physics olympiad. Specifically in 5.3 they say "brick is kept in motion along(horizontal) $y$-axis by a ...
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Could you please answer my questions (I have four questions)? [closed]
1.must the positive direction is always upwards when we study systems that have springs in a vertical way and we cannot assume that the positive direction is downwards?
If I understand correctly, how ...
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Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
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Centrifugal Governor Question [closed]
I've been working through Hand and Finch's Analytical Mechanics and have just attempted this question:
My attempt at a solution is as follows:
First, find the kinetic energy of the two masses $m$ by ...
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How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
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How does an object with friction fly off of a disc with angular acceleration? [closed]
Consider the image below
An object is resting on a rotating disc with angular velocity w and it is at rest with respect to the disc. Now if we increase the angular velocity of the disc(give it an ...
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QFT introduction: From point mechanics to the continuum
In any introductory quantum field theory course, one gets introduced with the modification of the classical Lagrangian and the conjugate momentum to the field theory lagrangian (density) and conjugate ...
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Designing a thought experiment on Noether's Theorem [closed]
By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation.
So logic says "if" there exists closed ...
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Is my solution for Morin 3.7 Correct [closed]
I already posted this question on PF and wanted some opinions from stack exchange. Essentially I want to know if my approach is correct.
Reference: https://www.physicsforums.com/threads/morin-3-7-...
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Non-inertial frames in quantum mechanics
In classical physics, non-inertial frames necessitate adjustments to Newton's laws due to acceleration and rotation, yet in general relativity, Einstein successfully incorporates such frames. Why does ...
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In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?
Here are the equations. ($V$ represents a potential function and $p$ represents momentum.)
$$V(q_1,q_2) = V(aq_1 - bq_2)$$
$$\dot{p}_1 = -aV'(aq_1 - bq_2)$$
$$\dot{p}_2 = +bV'(aq_1 - bq_2)$$
Should ...
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Invertibility between generalized and actual coordinates
Chapter $1$, page $13$ of Classical Mechanics by Goldstein ($2^{nd}$ edition), he states the following after defining a transformation equation:
"It is always assumed that one can transform back ...
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Meaning of $d\mathcal{L}=-H$ in analytical mechanics?
In Lagrangian mechanics the momentum is defined as:
$$p=\frac{\partial \mathcal{L}}{\partial \dot q}$$
Also we can define it as:
$$p=\frac{\partial S}{\partial q}$$
where $S$ is Hamilton's principal ...
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Why aren't all objects and their images same in size?
Suppose there is an object in front of a convex lens and we know that the light rays from each point on the surface of object will converge at a different point and form an image. So that means that ...
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Prerequisites for studying Lev Landau Mechanics vol. 1 [closed]
Lev Landau Mechanics vol. 1 dives directly into Lagrangians and Hamiltonians. What do you think are the prerequisites in order to study and grasp it?
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Relating Brachistochrone problem to Fermat's principle of least time [closed]
When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time.
So, we could make many glass slabs of high $\mathrm dx$, and every slab has a ...
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Why the interaction between system and thermal bath does not affect the energy levels of the system?
When we write down the full Hamiltonian of a system in contact with a thermal bath, it is as follows:
$$H_{\text{total}} = H_{\text{system}} + H_{\text{system+bath}} + H_{\text{bath}}.$$
As our focus ...
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Work performed by hydrostatic pressure
One should be able to show mathematically that the hydrostatic work done by an environment on an object undergoing a volume change $\Delta v$ should be $p \Delta v$, where $p$ is the (constant) ...
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How to compute the vector field from a potential in the complex plane?
I am watching this Youtube video and I have the following dumb question around 1:18:00: How do you draw the vector field for a given potential in the complex plane? He gives the potential $V(x) = x^4-...
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Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?
This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
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Zero stress in $z$ components for thin surfaces
We can write the stress tensor as:
\begin{equation}
T= \left [
\begin{array}{ccc}
\sigma_r & \tau_{r\theta} & \tau_{rz} \\
\tau_{\theta r} & \sigma_\theta & \tau_{\...
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Would a nearby electron be attracted/repulsed due to the oscillating $\vec E$ and $\vec B$ field of a passing electromagnetic wave? [closed]
I had just read up on the propagating electromagnetic wave equation, and realized that I do not know how to apply it in practice beyond knowing the equation...
Suppose
$$\vec E (x, t) = \begin{bmatrix}...
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The conservative force [closed]
I read about the definition of the curl.
It's the measure of the rotation of the vector field around a specific point
I understand this, but I would like to know what does the "curl of the ...
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Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates
I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is:
A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
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Can a translational torque cause a change in rotational angular momentum? gyroscope example
Please confirm if my understanding is correct: The example of a gyroscope suspended from a pivot is a case in which translational torque causes a change in the direction of rotational angular momentum:...
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Vanishing virtual work done by non-holonomic constraints
I was reading classical mechanics by NC Rana. I was reading a topic on vanishing virtual work done due to constraint forces. How do you prove that the virtual work done by non-holonomic constraint ...
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Why does my curry "bounce back" after stirring?
I recently cooked a big pot of curry, consisting largely of coconut milk, a bit of chicken stock and some vegetables. You can probably imagine that it was somewhat thick in consistency. The cooking ...
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Is the Virial Theorem dependent on the classical Equipartition Theorem?
The Wikipedia entry for the Virial Theorem states:
"*The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems ....
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Generalized momentum
I am studying Hamiltonian Mechanics and I was questioning about some laws of conservation:
in an isolate system, the Lagrangian $\mathcal{L}=\mathcal{L}(q,\dot q)$ is a function of the generalized ...
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What's the need for 2 separate laws of motion when the first law is an special case of the second one? [duplicate]
The first law of newton tells us that a body shall remain unaccelerated when the net force acting on it is 0, but the second equation gives us the relation F=ma so, ain't the first law just an special ...
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Finding Exterior Confining Pressure from Interior Pressure Point for a Solid Disk
Essentially, I've been wrapping the pictured object tightly with string to exert a confinement pressure on its exterior. It's been difficult however to make a good estimate of how much pressure is ...
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Consider a car going to a level curve while coasting(by disengaging clutch) is there any situation in which the speed of the car will increase?
Consider a car going to a level curve while coasting(by disengaging clutch) is there any situation in which the speed of the car will increase? (neglect the air resistence, assume the coefficient of ...
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Larmor precession - analogy with gyroscopic precession
Almost everywhere in scientific literature, Larmor precession is introduced via an analogy with a spinning top.
I understand that in a quantum framework, precession can be explained considering the ...
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Temperature as a frequency
In Arnold's Mathematical Methods of Classical Mechanics, he leaves as an exercise to show that if $S(E)$ is the area enclosed by a closed phase curve of energy $E$, then $T:=S'(E)$ is the period of a ...
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Confusing Goldstein Statement about Magnitude of the Lagrangian
On page 345 of Goldstein's Classical Mechanics 3rd Ed., he writes:
...the Hamiltonian is dependent both in magnitude and in functional form upon the initial choice of generalized coordinates. For the ...
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Is it possible that work is being done on an object, it's kinetic energy doesn't changes and still the body is transferred from one point to another?
Recently, I read a book about Electrostatics which stated that "Electrostatic Potential at a point is defined as the work done to move a unit charge from a reference point (generally taken as ...
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The specific heat of an EM wave in classical physics
I'm reading Dirac’s Principles of Quantum Mechanics and, in the first chapter, he states:
… There must certainly be some internal motion in an atom to account for its spectrum, but the internal ...
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Distribution of forces on bolts in mechanical joints - what factors affect the uniformity of loading? [closed]
I have a question about the distribution of forces on bolts in mechanical connections. Suppose we have a flat bar bolted to a flat surface with three bolts along the longer edge. An equally ...
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Understanding gauge in Lagrangian mechanics [duplicate]
I know given a Lagrangian $\mathcal{L}$ satisfying the Euler-Lagrange equations, then the Lagrangian $\mathcal{L}'=\mathcal{L}+\frac{d}{dt}f(q,t)$ is also a solution of said equations. Nonetheless, I ...
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Dipole radiation of a non-relativistic electron in elliptic motion [closed]
I'm trying to solve the following problem:
A non-relativistic electron is moving in elliptical motion inside a positively charged cylinder of homogenous charge density $\rho$. The initial radius ...
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Evolution of rigid body system using Impulse Based integration [closed]
I have been reading about physics engines, I have a reasonably OK understanding force based models and 6 dof integration.
I'm still confused on how impulse based models work.
What define the equations ...
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