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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17 views

Why does Gauss' Law appear to neglect charge outside the Gaussian surface

Suppose I have an infinitely tall solid cylinder with radius $R$ and charge density $\rho$. Then, a portion of that cylinder is enclosed by a Gaussian surface, in this case another infinitely long ...
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Parabolic, elliptic and hyperbolic dynamical systems

In dynamical systems people often classify (groups of) dynamical behaviours with the terminology of conic sections. Hyperbolic, elliptic and parabolic dynamics all presumably have some kind of meaning ...
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3answers
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Why position of an object is unique?

Position in physics is defined as the location of an object w.r.t some reference point. I conceptualized it as the description of the path from the reference point to the location of the object. My ...
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1answer
62 views

How is mechanical energy conserved when a ball is thrown?

Suppose someone is holding a ball at some height,the ball will have some potential energy and 0 kinetic energy then, if the ball is thrown both the potential energy and kinetic energy will increase ...
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1answer
31 views

Does the elasticity of a collision depend partially on the initial speed

If I have an object and a wall (assumed to not be able to move) and collide them, the elasticity is the percent of the objects kinetic energy right before impact that exists right after the impact. If ...
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2answers
37 views

What is the unit for modulus of elasticity?

I've previously asked a question regarding the modulus of elasticity which I am still unsure about. I've been told various formulae to calculate the modulus of elasticity, some of which give answers ...
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1answer
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Time stepping in Rigid Body Dynamics

When simulating the interaction of 3d rigid bodies, how do you decide what object you advance the state on first? If you advance all bodies at the same time there will be intersection/constraint ...
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What is the equation for calculating magnetic field for two coils when the currents in the coils have opposite orientation?

So I was wondering what the equation is to calculate the magnetic field when the two coils are separated by a distance d, with the currents in the coils in opposite orientation? Any help would be ...
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2answers
72 views

Why is angular momentum conserved in a central field?

I am trying to understand how a gyroscope works, which in the broad strokes is due to conservation of angular momentum. I understand the case when the angular momentum passes through the origin of ...
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1answer
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What if angular velocity is parallel to linear velocity

Hello I want to ask you a question about rotational movement. Say I would consider a system and the center of mass is moving with a velocity $\dot{\mathbf{R}}$ and the system is rotating with an ...
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10 views

Analytical mechanics resource recommendation [duplicate]

Is there any book on analytical mechanics that covers all the materials in-depth as in Goldstein but in a more organized way?
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Rotational motion in special relativity

From analysis of translational motion and transformation of reference frame, one conclude the upper limit of velocity cannot exceed the speed of light. In classical mechanics, the velocity by rotation ...
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Is fundamentals of physics by Halliday enough for the GRE physics test? [closed]

Is fundamentals of physics enough to enter the GRE physics test or no? If no what books should I read more?
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What limits the maximum reaction force that can be exerted by the table?

Suppose I have an object placed on a table which exerts a force $$W=mg$$ on the table. The table provides a reaction force which is $-mg$ if the table does not accelerate. However if the table breaks,...
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Physical significance of infinite flow velocity at leading edge of flat plate?

In our fluids lectures we used a conformal map of a complex potential to transform a flow around a cylinder into a flow around a flat plate. We showed that the velocity of the flow was infinite at ...
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Why the volume of a cell in phase space should be equal to $(2\pi \hbar)^s$?

We want to properly define the concept of entropy using the Boltzmann's Definition of it. But there is a big problem: the coarse graining problem (Id est: How do we count the number of microstates in ...
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2answers
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How to fully understand the Definition of Entropy?

In the context of Thermodynamics and Statistical Mechanics we encounter, basically, three different definition of entropy: First definition: Consider an isolated macroscopic system, it has a ...
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Motion of Particle Pushed By Flow of Liquid

If I were to slide an ice hockey puck into a constant headwind, the puck would slow down and start sliding back towards me. If it continued past me and beyond, it would reach a terminal velocity ...
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1answer
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Canonical transformations - sufficient & neccessary argument

I see in many textbooks that for a transformation of coordinates $P=P(q,p,t), Q=Q(q,p,t)$ it is sufficient & neccessary to check: $$[Q_i,Q_j]_{q,p} = 0$$ $$[P_i,P_j]_{q,p} = 0 $$ $$[Q_i,P_j]_{q,p}...
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What if 1st law of motion and 2nd law of thermodynamics contradict?

Assume a large flat surface with a pile of books on it somewhere. Assume this system to be isolated and gravity to be present there. Also assume there to be a flow of time. As now you have ...
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2answers
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Lagrange Multipliers - bead on hoop

In the following question, why is the constraint equation used $x^2+(y-R)^2 = R^2$ rather than just $x^2+y^2 = R^2$?
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Speed in a friction medium [duplicate]

If a 20 kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s? I want the answer in steps
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0answers
25 views

Friction Medium and Terminal Speed [closed]

If a 20 kg object dropped in air has a terminal speed of 60 m/s, what was its acceleration at 30 m/s?
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27 views

Elements of the Galilean group

The definition I have of a Galilean transformation is one that preserves intervals of time and the distance between simultaneous events. But now I can consider a transformation that takes $(t,\mathbf{...
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1answer
32 views

Hamiltonian for closed system describing parametric excitation

I am trying to describe a system with parametric excitation. Usually this is described as an open system where the time dependence of a parameter is explicitly included in this differential equation: $...
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1answer
44 views

Why are velocity dependent forces considered non-central?

I was going through Classical Dynamics of Particles and Systems (Thornton-Marion, 5ed). On page 50 it is stated: Any force that depends on the velocities of the interacting bodies is considered non-...
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What topics are usually cover in a upper level classical mechanics class? [closed]

I will be studying mechanics using Taylor's book; I am wondering what chapters of the book are actually covered in a 2nd year mechanics class.
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71 views

Gram-Schmidt Orthogonalisation for scalars

I'm reading Chapter 11 (Normal Modes) of Classical Mechanics (5th ed.) by Berkshire and Kibble and came across this on pg. 253: The kinetic energy in terms in terms of the generalised coordinates is ...
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How to solve the following exercise? [closed]

On the slope with a height of $2.0 m$ and the horizontal side of the slope of $5.0 m$, a sled descends, they accelerate evenly to the foot of the slope. Calculate the acceleration and final velocity ...
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43 views

Speed of one frame with respect to another in special relativity [duplicate]

To derive the Lorentz transformation we begin with the general relationship between two frames as below: $x' = Ax + Bt$ $y' = y$ $z' = z$ $t' = Cx + Dt$ If frame $S'$ is moving at speed $v$ with ...
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1answer
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How to solve for the velocities when calculating the conjugate momenta in special relativity?

I try to get the momenta $$p_{\sigma} = \frac{\partial L}{\partial \dot{x}^{\sigma}}$$ from the free one particle Lagrangian $$L = -mc\sqrt{-\eta_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$ I got to the ...
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Why identify the Lagrangian as kinetic energy minus potential energy? [duplicate]

When deriving the Euler-Lagrange equations from the Principle of Stationary Action we start by insisting that the actual path of a particle minimizes the action $S$, defined as $$S=\int_{t_1}^{t_2}\...
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1answer
30 views

How to calculate the damping ratio of a structure with a pendulum tuned mass damper?

I'm a highschool student investigating the damping of an oscillating structure by a pendulum mass damper. The structure has an accelerometer at the top to measure the acceleration. Although I know it ...
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1answer
29 views

Power as force times velocity and change in KE

I was noodling over problems and coming up with one for my students. The concept of power as force times velocity shows up on the Regents exam and I was thinking of a baseball. Specifically, a ...
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26 views

Does a piston push harder against its wall with decreasing load force?

I'm building a force model of a piston for a robot simulation, and I've reasoned that when the piston is not moving, as the load force drops, the horizontal force into the wall seems to increase for ...
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1answer
61 views

Problem 5.2 from David Morin (classical mechanics) [closed]

This problem is from Introduction to Classical Mechanics by David Morin: and this the answer: I cant understand why the highlighted part is obvious (or not obvious) I have no idea!
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Emergence of quantum mechanics [closed]

Usually we obtain quantum mechanics by canonical quantisation or path integral quantisation. Canonical quantisation: $$ \{p,x\} = -1 \;\;\;\;\;\to \;\;\;\;\; [\hat{p}, \hat{x}] = -i\hbar $$ Feynman ...
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1answer
21 views

Energy given to a Coin during a Coin Toss

Suppose I toss a coin by flicking it with my thumb at a point distant $x$ away from its center. Say my finger imparts it a linear impulse $J$ at that point. Correct me if I’m wrong, but then the ...
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2answers
443 views

Conservation of Energy with Chemical and Kinetic Energy

There is a rocket $R_1$ that is traveling with velocity $V$ with respect to another rocket $R_0$ of the same mass. $R_1$ has $J$ joules of kinetic energy with respect to $R_0$. $R_0$ has fuel onboard ...
2
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1answer
37 views

Conditions on $\phi$ and $\boldsymbol{A}$ for when $\boldsymbol{B}$ is uniform

I'm reading "Classical Mechanics" (5ed) by Berkshire and Kibble, in the example for uniform magnetic field on pg.243 (Chapter 10 Lagrangian Mechanics) I came across this A charged particle ...
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1answer
41 views

Will the plane of oscillation of a pendulum change if I rotate the suspension point

I'm having trouble understanding Foucault pendulum and from that I've extracted one of my doubt and here it goes: A pendulum on a fixed platform is shown Now if we rotate the platform as shown Will ...
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1answer
38 views

Equations of the spherical pendulum in different coordinates [closed]

I am trying to derive the equations of motion of a spherical pendulum, but instead of using the angles of the spherical coordinate system $\theta$ and $\varphi$, I want to use the angles $\alpha$ and $...
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2answers
27 views

Pressure in an accelerated container

Let us take a closed container completely filled with some liquid.Let us assume that the container moves with some acceleration in the horizontal direction. Usually when we have such situations,we ...
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0answers
40 views

Classical and Quantum Correlations [closed]

I am just now trying to get started with the idea of classical and quantum correlations in physics. Could anyone provide me with the reference of some introductory material(books/publications/articles/...
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4answers
9k views

Toilet paper dilemma

There are two ways to orient the toilet paper: "over" (left image), "under" (right image). Each has it's pros and cons. For some reason, it's always easier to tear off the paper ...
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1answer
29 views

Reflection on moving mirrors [closed]

Say I have an endless mirror, in a x y plane, at y=1. Situation 1: the mirror is stationary and when we send light vertically from the origin, the light reflects back and returns to the origin. ...
3
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1answer
37 views

Kinetic Energy of a Block-Bullet System [closed]

A bullet of mass $m$ is fired towards a wooden block of mass $M$. At a particular instant of time when the bullet is inside the block, the speed of the block is $V$ and the speed of the bullet, ...
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0answers
38 views

Is there something known as a Tensive Gradient in Quantum Physics? [closed]

Where tension doesn't refer to the conventional definition but it is the ability to induce or polarize interference phenomenon?
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1answer
77 views

How to solve equation of motion for Orbit in Einsteinian Mechanics?

Hi i am trying to solve the following equation using runge-kutta method but it doesn't seem to work. $$\frac{dr}{d\phi}=\sqrt{\frac{2Er^4}{l^2} + \frac{2GM}{l^2} -r^2 + 2GMr}.$$ I have written a ...
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1answer
49 views

Are Poisson brackets preserved during a canonical transformation?

Fix a Hamiltonian $H(q, p, t)$. Definition: A transformation $(q, p, t)\mapsto (Q(q, p, t), P(q, p, t), t)$ is said to be canonical iff for the Kamiltonian $K$ defined as $H(q, p, t)=K(Q(q, p, t), P(q,...

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