Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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Quantum mechanics and Classical limit(s)

I have tried to make sense of this and i am not sure i get it. What i gather from this page about the classical limit is: You need coherent states something like $\hbar \to 0$ is not really enaugh. ...
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27 views

Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
2
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0answers
43 views

Particle moving under force $F=-cx^3$ [closed]

A particle with mass $m$ moves under influence of a force $F=-cx^3$, with $c$ a constant. What is the potential energy function $V(x)$? And if it starts to move from rest from position $x=-a$, what ...
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3answers
103 views

Does the second law of thermodynamics take into consideration of attractive interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...
2
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1answer
71 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid?

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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1answer
4k views

Floating Objects and Weight

The Situation: A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string. The Question: The ball is attached to the beaker, thus ...
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1answer
71 views

Normal force, work and conservativity

I have searched very much on line, both in this site and elsewhere, but found no proof of whether the normal force is conservative or is not, in general. Clearly, if the force is orthogonal to the ...
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50 views

How does one find the phonon frequencies for a 1D anharmonic interaction potential?

Suppose there is a one-dimensional crystal with an anharmonic interaction potential between particles (e.g. $U = ax^2+bx^3$ where $x = d-a$ with $d$ as the distance between two particles and $a$ as ...
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0answers
38 views

Rain falling into a cart on an incline [closed]

I have a practise question in which a cart on and incline of angle $\alpha$ and starts initially at velocity $v_ 0$. Just as the cart moves off it starts raining vertically and the mass of the rain ...
3
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1answer
47 views

Limits for the linear wave equation

In acoustics and continuum mechanics the following wave equation (for Speed of Sound $c$) for the pressure field $p$ is well-known: $\partial_t \partial_t p = c^2 \Delta p$. This wave equation can be ...
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0answers
48 views

How did Lord Rayleigh find the volume fraction of argon to air?

In order to isolate for pure nitrogen, Lord Rayleigh and his colleagues took some air and removed oxygen, carbon dioxide, and water vapour, leaving behind what he believed to be pure nitrogen. In ...
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0answers
11 views

Good reference on angular motion especially on linear and angular velocity? [duplicate]

I am currently using a book called "Classical Mechanics" by Goldstein, which is a very good text and has amazing introdution to Lagrangian mechanics. Unfortunately not too much is said about angular ...
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2answers
62 views

Why does the period/frequency of a fan slow down significantly when I taped a piece of rubber band to it?

All of this was done with a standing fan set horizontally on a table. During an experiment, I had to tape a piece of rubber band to one of the standing fan's blade and measured the period of the fan. ...
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1answer
42 views

Which of the Physics textbooks would you recommend I read this quarter (Analytical Mechanics)? [duplicate]

My Analytical Mechanics class this quarter has one required textbook: "Classical Dynamics of Particles and Systems" by Thornton & Marion and three recommended readings: "Mechanics" by Landau ...
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1answer
61 views

Determine the equation of motion [closed]

The problem is the following. A ring of mass $m=1$ is moving along a circle of radius $R$ without friction. It's tied to a spring (coefficient $k$) of natural length $0$. The other end of the spring ...
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1answer
64 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
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1answer
66 views

Definition of kinetic energy without the second Law of Newton

As I see it, the definition of kinetic energy $$T= {1\over2} m u^2 \text { where $u<<c$}$$ comes by using the definition of work $$W= {\int F\cdot\ dx }$$ and we use for the meaning of ...
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2answers
70 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
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71 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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181 views

Is it possible to write explicitly the exact solution for forced damped harmonic oscillator?

Preamble Consider a damped harmonic oscillator, with his well know differential equation \begin{equation*} m \ddot{x} + c \dot{x} + kx=0 \end{equation*} and let's find the solution that satisfies ...
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2answers
88 views

What is the significance of angular frequency $\omega$ with regards to wave functions?

What is the physical significance of $\omega$ in a function like $$ f(x) = Asin(kx + \omega t) $$ The only place that I am familiar with angular frequency is when dealing with circular motion, but ...
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1answer
135 views

What is the physical interpretation of the Poisson bracket [duplicate]

Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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36 views

Ratio between power of chaotic and regular airflow

Turbulent field is created as a result of an impact of an airjet on an edge (the flow velocity is high enough). The field of velocities have a regular and a chaotic component. What I need is to ...
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2answers
172 views

Can we describe the classical laws of physics in a frame-of-reference-independent way?

First of all, I am not a physicist, so I cannot guarantee things I say will make sense. I will try my best, though. In classical mechanics we have the notion of inertial frame of reference. If my ...
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4answers
437 views

Is this solveable? Simultaneous elastic collision of 4 objects in XY plane

I'm writing a computer program/game and can't figure something out; I want to be able to calculate the resulting velocities of 4 particles (hexagons, specifically) after they simultaneously ...
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1answer
79 views

Relative kinematics and laws of Newton

I am an engineering student and currently taking a class on kinematics and dynamics. I study at a German university so it may be that I don't translate everything correctly. In the first module of ...
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2answers
110 views

Maximum Extension of a Spring [closed]

In the given figure: m= 5kg, F = 30N, K = 700N/m In the figure shown above. the surfaces are friction-less. The blocks are initially at rest and the spring is initially in its natural length. What ...
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2answers
79 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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2answers
458 views

Heisenberg picture of QM as a result of Hamilton formalism

Consider the formula for the total time-derivative of a physical value in Poisson's formalism: $$\tag{1} \frac{dA}{dt} = -\{H, A\}_{P.B.} + \frac{\partial A}{\partial t}, $$ where $\{A, B\}_{P.B.}$ is ...
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2answers
102 views

Phase space Lagrangian?

Reading out of this lecture series we define a phase space Lagrangian $\mathcal L$ to be a function of $4n+1$ variables namely $q,\dot q,p,\dot p,t$. My question is, what space is this function ...
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4answers
2k views

How far does a trampoline vertically deform based on the mass of the object?

If a baseball is dropped on a trampoline, the point under the object will move a certain distance downward before starting to travel upward again. If a bowling ball is dropped, it will deform further ...
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1answer
79 views

Can we disconnect an object from the pull of gravity using some material? [duplicate]

I have once come across a material/ substance/ compound, or something, that cuts off objects from Earth's gravitational pull. In other words, it would keep the object suspended in the air and will ...
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3answers
4k views

Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
2
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1answer
61 views

When can an autonomous system be written using a Hamiltonian?

If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all ...
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1answer
64 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
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2answers
527 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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1answer
77 views

How to find equations of motion when potential is given by inverse-square? [closed]

When potential is $U=-\dfrac{a}{r^2}$ ($a>0$), how can I find $r=r(\phi)$? I'm trying to solve this problem during several hours. From $E=T+U$, and constant angular momentum $L$, I can get the ...
16
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6answers
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Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin ...
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0answers
48 views

Higher order principle of isotropy

Let us work with classical mechanics in the substantivalist metaphysics, that is, space and time are seen as absolute. Call $n$-th order of motion any observer such that $n$ is the biggest order of ...
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99 views

When to use Hamiltonian vs Lagrangian?

I currently studying the Lagrangian and Hamiltonian formalisms in classical mechanics, but something I'm not seeing is how do I know which one to use in a given problem? After I find the Lagrangian, ...
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2answers
154 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
2
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1answer
241 views

Lagrangian, Kinetic & Potential energy with two masses connected to three springs

Two masses $m_1$ and $m_2$ are on a frictionless surface. They are connected by three springs with constants $k_1,k_2,k_3$. $k_1$ and $k_3$ are attached to walls and $k_2$ is between the masses. $k_1$ ...
0
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1answer
62 views

Does it take more effort to move against earth's rotation?

I know that if we stand still, we are traveling at 0 m/s relative to the Earth. But if we move against the rotation of the Earth we lower our speed, so, wouldn't we have to fight against the ...
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1answer
46 views

Continuity Equation for Momentum

Momentum is a conserved quantity, which makes me wonder if we can write an equation for the local conservation of momentum in the form of a continuity equation. If we're considering a system of ...
3
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1answer
2k views

Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
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23 views

Optimal “Blow up” Configuration

Suppose you have three balls glued together. Two are red and one is blue. The system of balls is blown up by an explosion of pure energy (that conserves the center of mass frame) exactly at the ...
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1answer
56 views

Lagrangian formalism (demonstration)

My question is about the multiplicity of the Lagrangian to a Physics system. I pretend to demonstrate the following proposition: For a system with $n$ degrees of freedom, written by the ...
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2answers
201 views

Adding a total time derivative term to the Lagrangian

This is proof that $L'$ represents same equation of motion with $L$ through Lagrange eq. I understand $L'$ satisfies Lagrange eq, but how does this proof mean $L'$ and $L$ describe same motion of ...
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1answer
62 views

What is a point transformation?

This problem comes from Goldstein. What does $s=e^{\gamma t}q$ mean? Do I just put $q=e^{-\gamma t}s$ into the Lagrangian? But I don't know what that means. I think the point transformation may ...
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1answer
62 views

Effect of Eath's rotation on a ball thrown upwards

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...