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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Angular velocity $\omega$ by $v$

We have two girls, with mass ($M$). They become close to each other in speed of $V$. The distance between them is $3L$. I was asked to calculate the Angular velocity ($\omega$) of the two girls. So ...
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4k views

Artificial gravity on rotating spaceship?

One of the possible ways to simulate gravity in outer space is to have a rotating spaceship, so that the centrifugal force experienced provides a gravity-like force. My question is: shouldn't this ...
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2answers
157 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
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10answers
3k views

What is the Earth truly rotating about/revolving around?

Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
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Yield Strength versus Ultimate Strength

What is the qualitative difference between these two: As seen on the table Typical yield and ultimate strengths. I am trying to resolve the meaning of the phrase "contact yield stress" from C. ...
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2answers
85 views

Damped Coupled Oscillations

I'm currently revising for a vibrations and waves module that I am taking as part of my physics degree. One of the our final questions involved finding equations for the displacements of the two ...
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42 views

Question about resolving forces

Say, in the example below, the weight $mg$ of the object is $800N$. To find $R$, the conventional method is to use $R\sin(28^\circ) = 800$. But why isn't it possible to use instead the component of ...
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0answers
39 views

Is there quantitative theory of cutting with edge or blade

I wonder if there is some simple theory of what determine efficiency ( speed, energy end force required ) of cutting by edge ( blade , knife, sword ) At least something phenomenological like in ...
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2answers
98 views

How to derive energy expressions thinking of it as a conserved quantity only?

By now I understand that "energy is a conserved quantity" and that's all we need to know. Then, the idea of work comes as the change in kinectic energy of a system and we realise that having energy is ...
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252 views

How do we know if a formulation of classical mechanics is correct?

For example, the Lagrangian formulation. I may be missing something, i.e. not having done it in enough detail, but here is my issue: from the definition of the lagrangian ($\mathcal{L}$) and from ...
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26 views

Modulus of action-reaction forces

I read somewhere that action-reaction forces satisfy the form $$ \mathbf{F}_{12}=-\mathbf{F}_{21}=f(|P_1-P_2|)(P_1-P_2) $$ meaning that the modulus can only depend on the distance between the two ...
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2answers
6k views

Determining the center of mass of a cone

I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..! I know the required equation. But, ...
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220 views

Euler-Lagrange equation for continuous systems

I'm having a little trouble with wrapping my head around a part of a method which is fairly 'new' in some fashions to me. I imagine it should be fairly obvious, but I am not seeing something at the ...
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5answers
3k views

Physics behind Wheel Slipping

Lets say that I'm in a car and I apply full acceleration suddenly. Now, the wheels would slip and hence the car doesn't displace much. But If I start with some constant acceleration, slipping doesn't ...
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0answers
23 views

Normal modes of two wires fastened together

The problem is to find the normal frequencies of the system formed by two fastened wires of length L, and different mass per unit length. I already wrote the boundary conditions, but I need to know ...
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6answers
402 views

How do traveling waves pass through a standing wave node, if the node doesn't move?

I'm having trouble with the explanation that a standing wave in a string is the superposition of traveling waves. The nodes in the diagram above are points where the particles of the string's ...
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0answers
59 views

Classical/ Quantum mechanical view of magnetic monopoles

Is there any classical/ quantum mechanical proof for the non-existence of magnetic monopoles? Or is it just lack of experimental evidence that has led us to the conclusion that monopoles do not exist, ...
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0answers
118 views

Trying to solve 2D Toda Lattice Equation with Lax Pair Approach

I am working on this Hamiltonian: $$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$ Thank you for the hint that it is a modification of the Toda Lattice Equation. Let me sketch ...
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4answers
423 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
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1answer
70 views

Why does shape of elements matter in finite elements analysis? [closed]

I have used FEA for a couple of years now, but using it and using it correctly are two different things, safety factor is not the solution to everything. I have the feeling I won't be using it right ...
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0answers
105 views

Why and how will the string break?

While i was searching on the identity discussed earlier that is $$1 + 2 + 3 + 4 + 5 + ... = -\frac{1}{12}$$ I found a similar identity applied to physics concept. It started by arranging long ...
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7answers
4k views

Why the Principle of Least Action?

I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
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1answer
99 views

Conjugate momentum is not gauge invariant

The conjugate momentum of a charged particle moving in a uniform magnetic field is given by $$\vec p=m\vec v+q \vec A$$ This expression is not unique because $\vec A$ is not unique. $\vec A$ is not ...
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2answers
169 views

Liouville's theorem and conservation of phase space volume

It can be proved that the size of an initial volume element in phase space remain constant in time even for time-dependent Hamiltonians. So I was wondering whether it is still true even when the ...
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1answer
81 views

Confusion with curl of Lorentz magnetic force

Since the magnetic force is a no work force, $dW=\vec F\cdot d\vec r=0$ for $\vec F(\vec r)=q(\vec v(\vec r) \times \vec B(\vec r))$, therefore $\oint \vec F \cdot d\vec r=0$ by Stoke's theorem. ...
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75 views

Can the Lorentz force stabilize the Hydrogen atom?

I've recently been working on relative equilibria for some systems of particles. (ie. studying equilibrium solutions in a rotating frame. Saturn's rings for example.) This has evolved into some ...
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57 views

Perceived weight in dumbbell vs. barbell

I had an observation today at the gym when I was lifting weights. Lifting a dumbbell of 10 kg on each hand was as difficult for me as lifting a barbell with 5 kg on either end. It's true that the bar ...
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1answer
95 views

upwind vehicle exceeding the wind speed [duplicate]

Has anyone done any research about the upwind vehicle http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind? I think it is impossible but get a surprising number ...
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0answers
21 views

Solving coupled nonlinear ODEs, controlling numerical instability through numerical viscosity

I'm solving a problem numerically that takes the form $ Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0$, where $(Q_{ij},S_{ijk},V_i) $ are all low order polynomial functions of the dependent ...
28
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1answer
1k views

Why does this object periodically turn itself?

See this video about 30 sec in. http://www.youtube.com/watch?v=dL6Pt1O_gSE Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? Is there a ...
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2answers
1k views

Hamilton-Jacobi Equation

In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
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6answers
3k views

Why is superdeterminism generally regarded as a joke? [closed]

Before anything, I'm sorry for being an outsider coming to opine about your field. This is almost always a stupid decision, but I do have a good justification for this case. I've been reading about ...
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313 views

What's the physical intuition for symplectic structures?

I always thought about symplectic forms as elements of areas in little subspaces because of the Darboux theorem, however I cannot get the physical intuition for it and for the hamiltonian vector ...
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144 views

An intuitive proof of Bertrand's theorem

Is there a way to see that Bertrand's theorem is true intuitively. I mean without getting into too much mathematics ?
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1answer
55 views

What can cause a change in wave's shape - One dimensional wave

what can cause a change in wave's shape of one dimensional wave moving through a rope? It's velocity ? or the wave's length ? What can cause him change his shape.
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48 views

If air was significantly compressed, and then the force compressing it suddenly disappeared (no container), what would happen?

Question: If air was significantly compressed, and then the force compressing it suddenly disappeared (no container), what would happen? Side Question: I'm imagining significantly compressed, but ...
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1answer
48 views

Classical static equilibrium in atomic physics

Consider a collection of $n+1$ mass weighted points in $\mathbb{R}^3$. Suppose we have one mass located at the point (0,0,0) with mass $m\in\mathbb{N}$ and further suppose we have $n$ masses arranged ...
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0answers
29 views

Criteria for stable equilibrium [closed]

A homogeneous wooden bar of length 10 cm, thickness 4 cm and weight 1 Kg is balanced on the top of a semicircular cylinder of radius R as shown below. What is the minimum radius of the semicircular ...
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3answers
3k views

Physical meaning of Legendre transformation

I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
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2answers
103 views

Universal gravity at small distance

Could it be that there is simply a maximum gravitational force that two bodies of finite mass can exert on one another? This would occur at $r=0$, so maybe there is some really really really small $a$ ...
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0answers
54 views

Coupled Oscillation Simulation

I'm looking for an online coupled oscillation simulation. The best I have got so far is this --- https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html But I'm looking for something which ...
3
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1answer
88 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
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1answer
32 views

Two-Body with external force - energy confusion

Setup Imagine a two-body system of masses under a classical mechanics model. The separation and mass-ratio doesn't matter for this example. Presume they are initially stationary. Now suppose that we ...
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1answer
26 views

How to reconcile angular momentum measurements?

Imagine a particle tracing a counter-clockwise circular path on a flat table with a certain speed. The particle is tied with a massless string of length $R$ to a point $P$ at the center of the ...
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3answers
135 views

Law of attraction

Could you please explain that since we know Newton's law of Universal Gravitation says all masses attract each other. Thus, we humans should be attracted as well or any other daily life objects. Why ...
3
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1answer
60 views

Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and ...
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1answer
74 views

Center of mass of a cylinder from which liquid is flowing out

A cylindrical container is of mass M, radius R and height H. The cylinder is filled with a liquid of density D. The base of the cylinder has an outlet tap of radius r through which the liquid can flow ...
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2answers
49 views

Can a force applied to a wheel find the fastest way of getting to the other side?

I haven't studied much about this, so if I am mistaken about something please correct me. From what I have seen around the Internet, a force applied to a object takes time to propagate through the ...
4
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3answers
148 views

Newton's principle of determinacy

I am a mathematician. I have a (somewhat long term) goal of understanding some of the physical insights that have influenced my area of research. To this end I read Arnold's Mathematical methods in ...
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2answers
102 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...