# 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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### Pendulum Circular Motion query

Using two different approaches, I appear to recieve contradictory information about the tension force in a simple pendulum. Under the idea of a centripetal force, the tension - component of mg in that ...
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### How to calculate time when I have a equation of acceleration dependent on displacement?

I know how to calculate in case of varying acceleration.But there a equation of acceleration dependent of time is required. But I have a equation dependent on displacement. If I be more specific, ...
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### Brachistochrone applied to Fibonacci sequence

In a medium, if a particle is allowed to fall from origin (0,0) under gravity force field given by F=-g, and assuming that it can steer its motion to minimize time taken, then the Brachistochrone ...
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### Is minimizing the action same as minimizing the energy?

When we differentiate the total energy with respect to the time and set it to zero (make it stationary), we get an expression as similar to what we get while we minimize action. Also putting the time ...
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### Physics of “force spreading” on impact on a surface

Consider a plate $P$ of thickness $d$ (for example a plate of wood) laying on a hard surface $S$ (for example on concrete floor). Suppose you have a maximum value of pressure $p_{\mathrm{max}}$ $S$ ...
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### Find tension forces and distance from centre of mass [closed]

A straight rod of 30 cm and 600 g mass is horizontally hanged on two upright, parallel, and light threads, both of them attached with distances of 5 cm and 10 cm from its ends. Find tension forces of ...
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### Find the velocity of $a$ relative to $b$ [closed]

Particles $a$ and $b$ move in opposite directions around a circle with angular speed $ω$, as shown in figure 2. At $t = 0$ they are both at the point $\vec{r} = l\hat{j}$, where $l$ is the radius of ...
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### Why do se use $U$ for potential energy? [migrated]

I am unaware if someone has asked this before, but I am studying classical mechanics and I don’t know why do we use $U$ for potential energy. I have read that Rankine used it first, but I can’t find ...
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### In a Lagrangian, why can't we replace kinetic energy by total energy minus potential energy?

TL;DR: Why can't we write $\mathcal{L} = E - 2V$ where $E = T + V =$ Total Energy? Let us consider the case of a particle in a gravitational field starting from rest. Initially, Kinetic energy $T$ is ...
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### $E\times B$ drift in strongly nonuniform fields

Potential is defined as $\{\phi,\, 0,\, A,\, 0 \}$; fields are static and depend only on the axial coordinate $x$: $E_x=-\partial_x\phi$, $B_z=\partial_x A$. Charged particle moves in the $\{x,y\}$-...
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### Is action maximized for a system in stable equilibrium?

Others have asked in general about cases in which the action integral is not minimized, but my question is specific: Can we show that the conventional action integral is always maximized for a system ...
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### Symmetry Condition in Noether's Theorem

Suppose $q = \{q_1,\cdots, q_i\}$ is a coordinate system for Lagrangian $L(q,\dot q)$. In this text by David Morin, on page 16 in chapter 6, it states that a symmetry is a transformation of the ...
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### Difference between eigenvalues of the potential energy Hessian vs. “generalized” eigenvalues with respect to a kinetic energy “metric”

Simple version Consider if we have a Lagrangian defined by $$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$ where the potential energy $U(q)$ has a single minimum at $q=0$ (...
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### Can the Lagrangian be written as a function of ONLY time?

The lagrangian is always phrased as $L(t,q,\dot{q})$. If you magically knew the equations $q(t)$ and $\dot{q}(t)$, could the Lagrangian ever be written only as a function of time? Take freefall for ...
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### Discrepancy between two calculations for the power provided by pump [duplicate]

I am a high school student and I am very confused in a question related to power. I was able to get the right answer but i am not satisfied with the results I get. The question is A motor pumps liquid ...
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### Disintegration of many particles Landau (Mechanics 3rd Ed page $43$)

On page $41$ Landau states that the total momentum in the C system is $0$. On page $43$ for the disintegration of many particles, Landau states: In the C system... every resulting particle (of a given ...
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### Conserved Quantities and Integrability in the $N$-Body Problem

Under my understanding of integrability, a system with $2n$-dimensional phase space is integrable when there are at least $n$ constants of motion satisfying some conditions (e.g., they are in ...
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### How can classical relativity explain the Michelson–Morley experiment?

If we suppose that light is made of small elastic particles, does the classical Galilean relativity explain the Michelson-Morley experiment? I would greatly appreciate any point of view.
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### Why does a body not rotate if force is applied on the centre of mass?

The definition of centre of mass on Wikipedia is given as This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. How can I prove that such ...
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### Change in potential energy after infinitesimal variation in position

The a particle with the potential $V(x^2+y^2)$ undergoes an active transformation where $x\rightarrow x+y\delta$ $y\rightarrow y-x\delta$ The exercise was to prove that the Lagrangian of the system ...