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Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

2097 questions
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A-Level Mechanics: Finding the Weight of a Non-Uniform Rod

A non-uniform rod has length 2m. The rod is placed on a support at its midpoint. It is in equilibrium when a particle of weight 50N is placed at one end and a particle of weight 30N on the other end. The particles are then removed and the rod is…
AOD
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Motion on a slope - A Level

A particle P of mass 5kg and particle Q of mass 1kg are connected by a light inextensible string. P lies on a slope inclined at a 60 degree angle to the horizontal. The string passes from P parallel to the line of greatest slope, and runs over a…
AOD
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Verify that $r=a(1-e\cdot \cos(\theta))^{-1}$ is a solution of the central force equations

A particle of mass $m$ moves under the influence of an attractive central force of magnitude $mk/r^2$ where $r$ is the distance from the origin. I have the equations $$ r^2\cdot \frac{d\theta}{dt} = h$$ and $$ \left(\frac{dr}{dt}\right)^2 +…
Tom
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How do I solve for the reaction force at the hinge

The question given is A uniform rod, of mass $m$ and length $2a$ smoothly hinged to a vertical wall is connected to a point on the wall above the hinge by a light inelastic string. Find the magnitude and direction of the force on the rod from the…
Filthyscrub
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Simple Harmonic Motion

A particle moving with simple harmonic motion starts from rest at a distance $3m$ from the center of oscillation. If the period is 2$\pi$ seconds: a) Find the time taken to move to a point $2m$ from the origin b) Find the velocity and…
Taylor Barton
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Algebra step for Noether theorem

In Tong’s preliminaries for QFT, he makes the following step while showing Noether’s theorem: $(\frac{\partial L}{\partial q}\delta q + \frac{\partial L}{\partial \dot q}\delta \dot q) = \left(\frac{\partial L}{\partial q} -…
Urdatorn
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Torque, beam problem.

The length of the beam is L, mass of the beam m, there is a hinge at the origin O Equilibrium conditions gives $\sum\limits_{i=1}^n \textbf{F}_i=0$ and $\sum\limits_{i=1}^n \Gamma_i=0$ Position vectors are $\textbf{r}_R=0$,…
rebekkah
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How does $F_p$ genrated?

Leaning pole A pole of negligible mass leans against a wall, at angle $θ$ with the horizontal. Gravity is directed down. (a) Find the constraint relating the vertical acceleration of one end to the horizontal acceleration of the other. (b) Now…
Unknown x
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Mechanics question (requiring SUVAT formulas)

An elevator ascends from rest with an acceleration of 0.6 m/s^2, before slowing down with a deceleration of 0.8 m/s^2 for the next stop. The total time taken is 10 seconds. Find the distance between the stops. I have tried this problem over multiple…
Mathematician
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Why does the velocity gradient tensor have additive decomposition but the deformation gradient does not?

In describing the decomposition of the deformation gradient tensor given by $\mathbf{F}=F_{iJ}=\partial x_i/\partial X_J$, Malvern (1969, Introduction to the mechanics of a continuous medium) mentions that due to the finite nature of the…
Rodrigues
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Two OCR A Level questions on $F=ma$

I just asked this on Physics.se, but the question was closed on there for "Homework-like questions and check-my-work questions are considered off-topic here, particularly when asking about specific computations instead of underlying physics…
Adam Rubinson
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Central orbit differential equation problems

I have a problem with the highlighted step in the example, i couldn't quite understand how did he integrate that ?
trytryandtry
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Equivariant moment map. Equivariant with respect to what?

I'm a physicist who occasionally likes/needs to read math papers. In these, the definition of the a moment map is as follows: We have a symplectic manifold $(M,\omega)$ with a symplectic action of a Lie group $G$ on it. If it exists, a moment…
mike stone
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poisson brackets?

Calculate the Poisson brackets {$f, g$} for (a) f = q, g = $p^{3}$ + p - 1 (b) f = sin q , g = cos p I am trying to do this via the definition of Poisson brackets (not sure who to write this in Latex) I got 0 for both but but both answers are…
mathsnerd22
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Smooth table/smooth pulley question problems

I'm struggling with the above question. As it is a smooth table, there should be no friction, so I came up with the two equations (using $F=ma$): $T=5a$ and $T=(2*9.8)+2a$. This solved out to give me the answer of $a = 6.5333333$; however, the back…
Corsaka
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