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].

Filter by
Sorted by
Tagged with
0 votes
1 answer
19 views

How to find the direction of acceleration if an object is changing its direction of velocity but not magnitude then how we can find the direction

I am new at this topic so please do mind if my question doest make sense to you.I am trying to find out that what will be the direction of acceleration if object changes Direction of velocity but not ...
user avatar
0 votes
0 answers
17 views

Why do we solve for $\theta_2$ here [closed]

Two non-identical charged spheres, the first one has a mass $m_{1}$ and a charge $q_1$ and the second one has a mass $m_2$ and a charge $q_2$ . They hang by two strings in equilibrium as shown in ...
user avatar
0 votes
0 answers
46 views

Necessary and sufficient conditions for periodic motion

Let us fix a reference frame $S$ with origin in $O$ in the euclidean space $\Bbb R^3$, then let us also define a periodic motion in the following manner: A motion is periodic if and only if the time-...
user avatar
0 votes
0 answers
18 views

Estimate the revolutions per minute for which the engine will experience the greatest vertical vibrations

A freely rotating motor rests on a thick rubber floor to reduce vibrations (vertical oscillations). The motor, due to its weight, sinks $10$ cm into the floor. Estimate the revolutions per minute for ...
user avatar
0 votes
0 answers
25 views

Minimum Potential energy required to behave like a turning point in relativistic case?

Inspired by this question a normal extension would be to ask: What is the minimum potential energy required (to behave as a turning point) for an elastic collision between $2$ point particles $A$ and $...
user avatar
0 votes
2 answers
17 views

What are the implications on the mechanics of connected particles over a pulley if the connecting string is not considered to be light?

In high-school level mechanics, whenever we solve problems involving pulleys, we assume that the connecting string is light. But how would the mathematics be affected if the string is not considered ...
user avatar
0 votes
0 answers
27 views

How to put angular momentum in individual equation of motion in two body problem with moving centre of mass (at origin) at constant velocity

How to put angular momentum in individual equation of motion in two body problem with moving centre of mass (at origin) at constant velocity. Equations are in polar coordinates. $$ {r_{1}}^{2} \dot{\...
user avatar
2 votes
0 answers
35 views

Why do we discount higher-order variations when applying variational methods in analytical mechanics? [duplicate]

In No-Nonsense Classical Mechanics, the calculus of variations is introduced with what I'm sure is a standard example. We try to find the minima of function $f(x) = x^2$ by evaluating it at $x + \...
user avatar
0 votes
0 answers
46 views

(Classical) Probability distribution of momentum for a harmonic oscillator (Griffiths problem 1.12)

I am trying to solve problem 1.12 in Griffith's Introduction to Quantum Mechanics, but when I compare my answer to the solutions online it is wrong. We want to find the probability distribution of ...
user avatar
  • 131
1 vote
2 answers
92 views

Minimum energy required to behave like a turning point?

So I've managed to confuse myself. We know if the energy equal to the potential energy then point at which the energy exceeds the potential energy it behaves like a turning point (slide 2). Usually in ...
user avatar
0 votes
1 answer
27 views

What's the relationship between the positions of each mass in this concentric pulley? [closed]

Reference image at the end of the post. This is supposed to be solved using lagrangian formalism, but I'm struggling to find a relationship between $x_1$ and $x_2$ (there has to be one: the discs are &...
user avatar
  • 227
2 votes
0 answers
74 views

The tilting of solar cells and their efficiency

This is a thought experiment I am considering. It concerns putting solar panels on a flat roof. The question is whether one should tilt them. Whilst there are more mundane reasons for tilting them (eg ...
user avatar
  • 21
1 vote
0 answers
128 views

How to use GR instead of QFT (or vice versa), if possible at all, in the sense that we can use SR instead of CM even for low-speed cases? [closed]

I asked a question on the philosophy SE - here. However, I realized this question is better suited in a Physics SE but I would rephrase it and explain my question very precisely. First, I'll mention ...
user avatar
  • 109
0 votes
2 answers
101 views

Why is Hamilton's equations sometimes written with a gradient? [closed]

I am used to seeing Hamilton's written as: $$\frac{dq_j}{dt} = \frac{\partial H}{\partial p_j}\\ \frac{dp_j}{dt} = - \frac{\partial H}{\partial q_j}.$$ However I have also seen it written as $$\frac{...
user avatar
  • 187
0 votes
2 answers
88 views

When to apply $I_c \underline{\omega} = \underline{M_c}$?

I was solving an exercise the other day, about a rolling cylinder on an inclined plane. Initially the cylinder slides, but then it begins to roll and the problem wanted to know the velocity of the ...
user avatar
2 votes
1 answer
77 views

What do you think about this particularization of the Euler-Lagrange equation that resembles Newton's 2nd Law?

For: $$\mathcal{L}=\mathcal{L}(q_j,\dot{q_j},t)=T-V$$ the Euler-Lagrange equation is simply: $$\frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\mathcal{\dot{q_j}}} \right)-\frac{\partial \mathcal{L}}{\...
user avatar
  • 227
0 votes
1 answer
52 views

Problem 6.3 from David Morin (classical mechanics)

I get the lagrangian for the system as $$ \begin{align} \mathscr{L} = \frac{m}{2}(\dot{x}^2 + l^2\dot{\theta}^2 + 2l\dot{x}\dot{\theta}\cos \theta) + mgl\cos\theta \end{align} $$ Where $\theta$ is the ...
user avatar
  • 21
0 votes
0 answers
21 views

Inelastic cord vs inextensible cord [closed]

I know that inextensible means that it can't be pulled outwards but can relax inwards, but I don't quite understand what elastic here means.
user avatar
2 votes
1 answer
31 views

How to solve the Helmholtz equation in damped oscillator BCs?

Given the surface of the vibrating object $\partial \Omega$, I am trying to simulate its outer sound pressure field $p(x)$ by the equivalent source method.[1] For ...
user avatar
2 votes
1 answer
34 views

Why the amplitude of monopole solution in Helmholtz equation is complex?

1. Background Given an surface of vibrating object $\partial \Omega$, I am trying to simulate the outer acoustic field. I use the equivalent source method[1], which ...
user avatar
-1 votes
0 answers
23 views

How can I find the potential form given the particle trajectory? [closed]

Given the angular momentum $L$. Find the potential form $U(r)$ such that the particle trajectory affected by this potential is given by $$r(\phi) = r_0\exp(\alpha\phi)$$ with $r_0$ and $\alpha$ ...
user avatar
0 votes
1 answer
66 views

2DOF robot arm dynamic model

Consider 2dof robotic arm. No gravity. Instead of modeling it with two torque inputs at joints, I want to model it as two forces F1 and F2 applied at distance r (motor radius). Because, I think force ...
user avatar
  • 111
1 vote
0 answers
28 views

Integrability of one-dimensional system of motion?

How can I prove that every one-dimensional system is integrable (meaning that there is a constant of motion)? It is clear that if $H$ does not depend explicitly on time then $H$ is indeed a constant ...
user avatar
0 votes
1 answer
39 views

Integration by Parts in Liouville's Theorem

I am looking at a proof of Liouville's Theorem, which states that for $F, G \in C_0^\infty$ and a Hamiltonian $H$, the operator $$D_H = \sum_{i=1}^n\Big(\frac{\partial H}{\partial p_i} \frac{\partial}{...
user avatar
  • 187
0 votes
0 answers
36 views

A mechanical compass that doesn't use magnets? [closed]

I read about a device that used to always point South, without using any magnets, in my textbook. However, I couldn't find more about such a thing on the internet. I wanted to know this functioned. ...
user avatar
14 votes
3 answers
1k views

Can the value of friction force ever exceed value of applied force?

My teacher taught me that the value of friction force can never be greater than the applied force. But recently, when I was studying rotational motion, I got a dilemma… Suppose I made a stand (from ...
user avatar
1 vote
2 answers
52 views

The Hamiltonian of a system under only the effect of an electric field

I have a maybe silly doubt: in quantum mechanics, we have the Hamiltonian as kinetic energy + potential energy. Now kinetic energy is obtained from the integral of force and displacement. Potential ...
user avatar
0 votes
1 answer
46 views

What quantity can a microstate have?

I confused whether a microstate's chemistry potential is defined. And how about temperature, pressure, entropy? And what is a microstate? A ensemble contain a set of microstates. The microstate is a ...
user avatar
  • 1
0 votes
2 answers
52 views

In an $n$ particle system, why is the Hamiltonian summed over $n$?

Suppose I am working in a system consisting of $n$ particles. Thus the phase space will be $\mathbb{R}^{6n}$, and both the momentum and position space will be $\mathbb{R}^{3n}$ each. Then, for some ...
user avatar
  • 187
0 votes
0 answers
47 views

What is the minimum density required for an object to become a black hole? [duplicate]

What is the minimum density required for an object to become a black hole? I ask this because whenever I research about black holes it is always said to have infinite density or infinite mass. ...
user avatar
5 votes
2 answers
137 views

Proper conceptualization & notation for vectors, $n$-tuples, and matrices in physical space

This is a fairly basic question that I may be making longer than necessary. But it has plagued me for some time. It is essentially this: In what space do abstract physical vectors like a velocity ...
user avatar
1 vote
0 answers
34 views

Velocity of points in a rigid body

I'm trying to derive the following statement: Let $\mathcal{B}$ be a rigid body. Then there is an unique vector $\vec{\omega}$ such that for every pair of points $P,Q\in \mathcal{B}$ the following ...
user avatar
0 votes
1 answer
43 views

Can we deduce the conservation of mass in non-relativist physics or is it just an experimental fact? [duplicate]

It is a well-known fact that mass by itself is not conserved (since, for example, a particle can annihilate with its antiparticle). However, in classical physics, and as long as there is no physical ...
user avatar
  • 571
1 vote
0 answers
25 views

Rolling with slipping along an incline

Here my doubt is about the second question. For the second question I went about using work energy theorem. My thought was that since gravitational and frictional force both will do the same amount of ...
user avatar
-1 votes
0 answers
22 views

How much does the Earth lag behind us when we swing?

On a swing, we pull the framework on which the swing hangs. We wriggle our body which has it's effect on the frame, which affects the Earth on it's turn (on it's swing...). It's clear that the ...
user avatar
0 votes
0 answers
24 views

Shape of a water balloon laying on the ground

I would like to know if you are aware of any litterature or any way to solve the following problem: what is the equation that describes the shape of a ballon filled with an arbitrary quantity of water ...
user avatar
1 vote
2 answers
61 views

Why doesn't $\omega = \sqrt{\frac{U''(x_0)}{m}}$ work for a simple pendulum?

In a simple pendulum, we know that the angular frequency of small oscillations is $\omega = \sqrt{\frac{g}{l}}$. However $\sqrt{\frac{U''(x_0)}{m}}$ gives $\sqrt{gl}$ as the angular frequency. Let $l$ ...
user avatar
  • 21
0 votes
0 answers
21 views

Limit from general relativity to Newtonian mechanics [duplicate]

What is the limit of general relativity to Newtonian mechanics? Let me elaborate; from quantum mechanics to classical mechanics regime, we ignore the length of the Plancks $\hbar$, so we reached ...
user avatar
  • 13
2 votes
1 answer
96 views

Proof that the Euler-Lagrange equations hold in any set of coordinates if they hold in one

This is a question about a specific proof presented in the book Introduction to Classical Mechanics by David Morin. I have highlighted the relevant portion in the picture below. In the remark, he ...
user avatar
2 votes
1 answer
61 views

Lagrangian Mechanics - Is the Given Answer Incorrect? [closed]

A heavy symmetric top rotating about a fixed point has Lagrangian $$L=\frac{I_1}{2}(\dot \theta ^2 + \dot \phi^2 \sin ^2 \theta)+\frac{I_3}{2}(\dot \psi + \dot \phi \cos \theta)^2-mgl\cos \theta$$ ...
user avatar
  • 473
1 vote
0 answers
31 views

Potentials that prevent the phase flow of the system [closed]

I am trying to solve a question that my professor gave. When a particle moves in one dimension $x$ in a potential $U(x)$ , the resulting motion over a very short time interval is specified by Newton’...
user avatar
  • 11
0 votes
1 answer
35 views

Small mass on a dome (problems with derivatives)

I was trying to solve the classical problem of finding when a mass sliding on a frictionless dome loses contact with said dome. I got the lagrangian $$L=\frac{1}{2}M\left(r\,\dot{\theta}\right)^2-Mgr\...
user avatar
0 votes
1 answer
57 views

Doubt from Arnold; Mathematical methods of classical mechanics (page 20)

I am trying to do a problem from Arnold; Mathematical methods of Classical mechanics. But I didn't get the desired result mentioned by the author. Let $E_0$ be the value of the potential function at ...
user avatar
0 votes
1 answer
73 views

Covariance of Euler-Lagrange equations under arbitrary change of coordinates

I'm trying to prove that the Euler-Lagrange equation $$\frac{d}{dt}(\frac{\partial L}{\partial \dot{q}_i})-\frac{\partial L}{ \partial q_i}=0$$ is invariant under an arbitrary change of coordinates $$...
user avatar
  • 3,885
-2 votes
0 answers
48 views

How to scale physics simulation but yield same results? (Unity)

I am making a game in Unity where you are small but I want some of the rigid bodies to react as if they where full scale. For 25% scale, do I just multiply gravity, mass, and drag by 0.25? What about ...
user avatar
1 vote
2 answers
53 views

In Hamilton-Jacobi theory, how is the new coordinate $Q$ time-independent when Hamilton's principal function separates?

Following the notation in Goldstein, the solution to the Hamilton-Jacobi equation is the generating function $S$ for a canonical transformation from old variables $(q,p)$ to new variables $(Q,P)$ ...
user avatar
  • 13
1 vote
2 answers
26 views

Work done By Internal Forces Inside a hinged Rotating Rod

Following the previous posted question , I got to know that Normal reaction is not doing any work as it does not displace any particles of the thin rod. But,I got another concept dilemma. There will ...
user avatar
2 votes
0 answers
30 views

Elastic collisions inside a moving fence [closed]

A square, rigid fence of mass $M$ moves on a horizontal, frictionless plane. Inside it a point mass $m$ moves freely without friction. Assume the fence has initial velocity $0$ and that the particle ...
user avatar
  • 33
0 votes
0 answers
10 views

Observable effects close to a binary black hole at coalescence

If an object of finite size (for example a planet) is close to a binary black hole that is coalescing, can the object be disrupted by the emitted gravitational waves from the two black holes? In other ...
user avatar
  • 676
0 votes
1 answer
28 views

Work Done on a rotating thin rod by hinge Forces

So I was studying the concept of rotational energy through a video, and the guy presented a problem, It's like this: "Suppose a thin rod of mass M and length L/2 is hinged from one end. Then, it ...
user avatar

1
2 3 4 5
151