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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27 views

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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1answer
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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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31 views

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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42 views

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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2answers
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Are partial derivatives in the context of Action-Angle variables different from partial derivatives of functions?

Let's say I have a system with two degrees of freedom and I can find two independent action variables. One action variable is total energy expression, such as is often used in classical mechanics. $$...
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How the optical CD disc gets drawn in when we gently push it? what is the mechanism behind it? [closed]

We have seen CD drives that have slits. The CD gets drawn inside upon a gentle push. how the CD gets drawn inside upon a gentle push? How it's mechanism works?
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How can we describe the path of a projectile fired from the ground using the principle of least action? [closed]

If a similar question were asked in Newtonian mechanics, the answer would be rather simple. But in Lagrangian mechanics, how can we say that the parabolic path taken by a projectile has a stationary ...
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Potential inside a hollow sphere [closed]

How to find the potential at a point at a distance $a/2$ from the center of a hollow sphere of mass $M$ and radius $a$?
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What is the process of finding a good canonical transformation to describe a system? How do I choose the correct generating function?

Supposedly, canonical transformations are used to provide a general procedure to transform a Hamiltonian such that all coordinates in the new frame are cyclic. I have done the proofs and derivations, ...
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GEARS- Does mechanical efficiency affects transmitted force [closed]

Does mechanical efficiency affects transmitted force between the gear teeth or it only affects transmitted power?
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4answers
411 views

Time quantization [closed]

There is no evidence to support that time is quantized. So wouldn't the use of discrete values like $dt$ in calculus suggest time is quantized and comes in discrete durations of $dt$?
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Question on fluid and basic mechanics

The question given is : Two vertical cylindrical vessels A and B of horizontal cross–sectional areas S and 2S are connected at their bottoms with a horizontal tube of cross sectional area 0.5S. An ...
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2answers
130 views

Derivation of the catenary equation [closed]

I’ve seen two derivations of the catenary equation: one involving Lagrange multipliers and another using a balance of forces on a segment of the cable/rope. I’m trying to derive the catenary equation ...
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1answer
34 views

Hamiltonian flow generated by angular momentum

Hamiltonian flow generated by angular momentum function $ J(\mathbf{x}, \mathbf{p})=x_{1} p_{2}-x_{2} p_{1} $ is given by: $$ \begin{array}{r} {\left[\begin{array}{l} x_{1}(t) \\ x_{2}(t) \end{array}\...
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1answer
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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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1answer
66 views

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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52 views

How to understand the 2D Harmonic Oscillator in Polar Coordinates with Action-Angle Variables? [closed]

The 2D Harmonic oscillator in polar coordinates (r,𝜃) has this Hamiltonian $$H = ½ (p_r² + (p_𝜃/r)² + r²)=E.$$ I'm thinking of two action variables, the total energy (E) and the angular momentum $(...
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Pushing out a coil spring from a straight pipe

A ∅0.32mm NiTinol thread is trained or "shape-set" into a coil spring. If you are unaware of the properties of NiTinol, let me brefly describe the shape-setting feature. If you place the ...
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2answers
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Air Pressure Acting Below Object

Consider an object resting on a surface. If I had to find the net force on the object, I would write an equation as follows: weight = normal force. But what about the air pressure that's acting on the ...
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2answers
103 views

Lagrangian mechanics formulation of a simple free motion of two masses in uniform gravity field

As a part of larger project, I decided to test my Lagrangian formulation of simple system of two rigidly connected point masses as indicated below. I introduce the generalized coordinates vector $\...
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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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2answers
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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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26 views

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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1answer
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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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Inertial Torque Exerted By Engine on Crankshaft

In Shigley(5th Edition), in Chapter 14. Dynamics of Reciprocating Engine ,Section 14.7 Inertia Forces, the inertia torque exerted by the engine on the crankshaft is given as $$ \mathbf{T}_{21}^{\...
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2answers
110 views

Correspondence between quantum operators and classical formulas

Background From what knowledge of quantum mechanics I have so far, it is a postulate that Hermitian operators corresponding to a certain observable act on a quantum state $\psi$ to produce a new ...
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1answer
110 views

Static or dynamic? [closed]

Long time ago, I found a question in the book Introduction to Classical Mechanics-David Morin. The question was Sliding sideways on a plane: A block is placed on a plane inclined at an angle $\theta$....
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86 views

Understanding constraint for not losing contact

What is the exact constraint for two bodies remain in contact? Consider the case of a rod constrained to move downward on an inclined wedge. It is known that the velocity of the wedge and the velocity ...
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2answers
74 views

What happens to the moving ball that collides with wall and the wall disappears at the instant all kinetic energy of ball becomes potential energy?

Consider a wall and a ball that is traveling towards the wall with uniform velocity. Assuming no friction of any kind in this situation. When ball collides with the ball, the ball gets squished as its ...
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0answers
79 views

2-body spring system confined to a plane [closed]

I'm trying to work out the Lagrangian for the following system: "a mass-less spring has an un-stretched length $b$ and spring constant $k$, and is used to connect two particles of mass $m_1$ and $...
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Why is it impossible to look equal Reynolds number conditions between prototype and model for the big wind turbine?

From the given Screenshot of the book the two equations shows equal Reynolds number both in prototype and model. I am not understanding that red marked line why it is saying so. Why is it impossible ...
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2answers
38 views

Minimum coefficient of the static friction of a pencil rolling on an inclined plane [closed]

A standard six-sided pencil is placed on a notebook as shown. Find the minimum coefficient of static friction $\mu_s$ such that, if the upper cover is raised, the pencil rolls down the incline rather ...
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4answers
127 views

Are there any physical processes of which we have a full understanding? [closed]

Are there any physical processes of which we have a full understanding? For instance, we know that each orbit has a different energy, and electrons can move to a higher orbit by absorbing energy and ...
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2answers
60 views

Free fall vs falling on incline of rotating bodies

When you have a sphere and a hoop on an incline, the sphere will always roll down faster because of the smaller moment of inertia. And this is the case no matter the angle of the incline. But what if ...
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1answer
44 views

Is it possible to imagine a virtual displacement for a simple pendulum?

Because I could not understand the term "virtual displacement" properly I have too much questions with it. I will be helpful with your answer. My question: Can we imagine a virtual ...
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2answers
59 views

The Theoretical Minimum: Lecture 5, Exercise 3. Finding equations of motion from potential energy [closed]

From Leonard Susskind's book The Theoretical Minimum. "A particle in two dimensions, x and y, has mass m equal in both directions. It moves in a potential energy $V = \frac{k}{2(x^2+y^2)}$. Work ...
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1answer
53 views

Why is the Euler-Lagrange equation this in generalised coordinates?

I'm a chemist, first off, and I'm trying to self teach myself some graduate statistical mechanics from "Statistical Mechanics: Theory and Simulation" by David Chandler. The first chapter is ...
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70 views

Conservation of Newton's law

Suppose $F$ is independent of velocity,so Newton's law can be expressed as : $m \ddot{\mathbf{x}}(t)=\mathbf{F}(\mathbf{x}(t)) .$ Then an energy function of the form $$ E(\mathbf{x}, \dot{\mathbf{x}})=...
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2answers
124 views

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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1answer
27 views

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 ...
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30 views

Physical interpretation of mathematical products [duplicate]

In physics when we see formulas they have quantities multiplied to give a product while in other cases these quantities are divided The division of quantities gives the understanding of PER UNIT (E.g ...
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1answer
42 views

Does the Higgs field explain inertia?

As far as I understand it the Higgs field leads to the creation of rest mass for certain elementary particles but does it explain the phenomenon of resistance to acceleration associated with rest mass?...

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