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; ...

learn more… | top users | synonyms (1)

15
votes
2answers
340 views

Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
2
votes
0answers
59 views
+100

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
5
votes
1answer
77 views
+50

Why was the Stark effect discovered much later than the Zeeman effect?

This is strange. The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical ...
2
votes
1answer
132 views

Which way to lean when driving a gokart?

Given a car that has two lines of wheels, the center of gravity at constant height above the ground, constant turn angle and given surface and wheel material. What is the maximum speed the car can ...
2
votes
1answer
50 views

Why does a system have to be holonomic?

So I'm doing some work from Taylor's mechanics book. He says for the problems in the book, we require the system to be holonomic - that is the number of generalized coordinates = number of Deg. of ...
2
votes
2answers
61 views

The action of a relativistic point particle, the meaning of its parametrization invariance and possible potential terms

i am currently toying around with the behaviour of a classical relativistic point particle a bit. For a free one we get the action \begin{align} S =\int_\tau - m\sqrt{- \dot X_\mu \dot X^\mu}. ...
-1
votes
0answers
23 views

Practical uses of superfluids [on hold]

I am wondering whether and how superfluids (possibly at room-temperature, if that is possible at some point) can be of any practical use in mechanical or electrical engineering or other fields. I ...
6
votes
4answers
171 views
+50

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
0
votes
3answers
104 views

Forces Create Angular Acceleration And “Straight” Acceleration - But How Much Of Each?

Let me set up the following problem for a rectangle floating in space: We know its dimensions. We know its mass. There's a force pushing it for a known amount of time - we know the angle & ...
2
votes
1answer
26 views

A system of particles interacting via conservative forces, will also respect $U_2+K_2=U_1+K_1$

Studying vector calculus you learn to prove that a particle moving in a gravitational field will that field that $dU=-dW$ from which you can conclude $U_2+K_2=U_1+K_1$. This is easy to prove in this ...
2
votes
1answer
28 views

Deriving velocity after elastic and inelastic collision via the Principle of Least Action

I am reading on the Principle of Least Action from a historical perspective. I am also trying to make sense of it from a contemporary point of view -- though my training in contemporary physics is ...
0
votes
1answer
25 views

Why must an inertial navigation system take the Coriolis effect into account?

I read somewhere that an inertial navigation system, in order to be accurate, must take the Coriolis effect into account. Why is this so? If I go a 500 mph velocity in a given direction, I'm going 500 ...
0
votes
1answer
62 views

The EFE - The 'Mother' of all equations of motion in the universe?

This question addresses the scope of general relativity. Scientists and engineers solve all sorts of physical problems in all sorts of fields and often to solve these problems a 'system' is defined ...
0
votes
1answer
42 views

Allowed Virtual Displacements

I am having trouble understanding the kinds of virtual displacements which are permitted for a given constrained system. I have a specific example in mind: A block of wood resting on a table parallel ...
0
votes
1answer
126 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
2
votes
1answer
62 views

How can we obtain equations of motion from $\iota_{X_{H}}\omega =dH$?

I don't know if this is an obvious result and I am just missing a trick, so please forgive me, but how do we obtain equations of motion from the following equation. \begin{equation} \iota ...
2
votes
0answers
74 views

The tested scale of classical mechanics

I was reading this, but I was wondering actually how good an approximation is classical mechanics in very large chosen scales? Which makes me would like to ask a question here: to what scale, order ...
0
votes
2answers
64 views

Is the universe a Turing machine?

Reading about Computable numbers I wondered if there is any physical experiment that returns non-computable numbers or if there is any physical theory that needs non-computable numbers. Because if ...
5
votes
6answers
5k views

Difference between torque and moment

What is the difference between torque and moment? I would like to see mathematical definitions for both quantities. I also do not prefer definitions like "It is the tendancy..../It is a measure of ...
2
votes
0answers
31 views

Classical probability of harmonic oscillator

I am trying to derive the classical probability density function to find the harmonic oscillator at position $x$. I am confused between the random variables involved here $x, t$ and not able to ...
0
votes
0answers
27 views

First integrals for a particle in a central-force field

Consider an arbitrary dimension $n>3$. What are the independent first integrals for a particle? The Hamiltonian is $$ H = \frac{p^2}{2m} +V (|r|) . $$
-1
votes
0answers
25 views

Will water vapour rise in vacuum?

If I put water vapour in vacuum, will it behave normally like a gas? Will it rise up in the vacuum?
1
vote
1answer
73 views

Mathematics of the Virtual Displacement

So I'm pretty certain this question has been asked to death here, but I still can't find a good explanation of a very particular aspect of the virtual displacements in physics. Background For ...
1
vote
1answer
39 views

Intuition about Momentum Maps

I'm studying Classical Mechanics and there is one object that appeared recently on the book I'm not being able to get a physical intuition about it. The mathematical definition goes as follows: Let ...
9
votes
4answers
492 views

When/why does the principle of least action plus boundary conditions not uniquely specify a path?

A few months ago I was telling high school students about Fermat's principle. You can use it to show that light reflects off a surface at equal angles. To set it up, you put in boundary conditions, ...
1
vote
1answer
37 views

Find the separation distance for a line of oil being squashed between two flat plates [on hold]

I was wondering if someone could give me some help on how to start this problem, I'm really struggling to get my head around it. A long line of oil is being squashed between two flat plates of length ...
1
vote
0answers
34 views

What is special about quantum entanglement? [duplicate]

Get two pieces of paper. In secret write the same number on both papers. Transfer one paper to the Moon. Look to the paper which is left at the Earth. Voila! We know what is on the Moon paper. The ...
1
vote
1answer
456 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
0
votes
1answer
27 views

Efficiency of a gravity feed hose

If I am trying to fill a large cylindrical container with a gravity feed hose, would it be more efficient, time-wise, to drill a hole in the bottom of the container for a greater initial pressure ...
0
votes
2answers
37 views

Where does the energy go when you stretch a rubber band?

There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same ...
2
votes
1answer
182 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
12
votes
3answers
3k views

What exactly is a virtual displacement in classical mechanics?

I'm reading Goldstein's Classical Mechanics and he says the following: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
2
votes
2answers
191 views

How do waves have momentum?

A question on a practice test I'm taking is as follows: By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries: A. mass B. energy C. momentum D. ...
0
votes
0answers
47 views

Hausdorff spaces and finite elements

Must the shape functions and the interpolation functions (which are the same in an isoparametric element) in a finite element model be elements of a Hausdorff space? If so, is this necessary to ...
2
votes
0answers
76 views

Poisson brackets and magnetic field [closed]

I'm a maths student trying to teach myself some physics so sorry if I'm missing something simple here. I think the main problem is lack of experience with the Levi-Cevita symbol. We have a particle ...
0
votes
2answers
134 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
5
votes
4answers
103 views

How can we explain the difference in change of kinetic energy, due to different frames of reference?

Imagine a ball ($m= 1\,{\rm kg}$) moving at a velocity $2\,{\rm m}/{\rm s}$ towards a wall. When it hits the wall, it suddenly stops, thereby liberating all its ${\rm KE}$ as heat. Here, the initial ...
4
votes
1answer
311 views

Does a thermally expanding torus experience internal stress?

I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic ...
0
votes
3answers
68 views

What was the motivation behind the work formula?

Surely there must be a reason we decided to use this as a metric for mechanical energy.How was it developed and what made it more acceptable than other work formula candidates (Like force over time, ...
4
votes
1answer
112 views

Scaling arguments for the Contact mechanics between two elastic spheres

I am studying a bit granular dynamics and I have seen that two spheres of radius $R$ in contact with a contact area of radius $a$ would need an applied force $F$ on this two spheres that is nonlinear ...
4
votes
1answer
82 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
3
votes
3answers
129 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 ...
1
vote
1answer
93 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 ...
3
votes
4answers
301 views

Liouville's theorem and the preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? By Liouville's theorem, the total phase space volume is ...
1
vote
2answers
36 views

Is configuration space in any similar to vector spaces?

The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else. I have just learned about vector spaces and their properties and on the other hand have also ...
2
votes
1answer
134 views

Physics of a cold and hot top

Imagine two tops made up of exactly one thousand atoms. One is kept at 4 degrees Kelvin, the other at room temperature. 1. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
2
votes
2answers
560 views

Standing wave velocity

My question is simple: How is it that a standing wave has velocity? I mean, it's not travelling... A lot of equations depend on this concept, for example: $f_n = \frac{nv}{2L}$ Here we're ...
0
votes
1answer
335 views

Speed of sound in air

Quick question. I thought that the speed of sound in air was constant, say in the right conditions of pressure and temperature, and humidity... 300 m/s. Now, if I have a sound source that moves ...
0
votes
2answers
300 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
8
votes
1answer
397 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...