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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The other side of the lever

If I have a lever, but I can see only up to the hinge and not the other half, can I know whether the other half is 1 m long with a weight of 3 kg on it, or 3 m long with a weight of 1 kg on it?
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What sustains the rotation of earth's core (faster than surface)?

I recently read that the earth's core rotates faster than the surface. Well, firstly, it's easier to digest the concept of planetary bodies, stars, galaxies in rotation and/or orbital motion. But, ...
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Classical Mechanics contradicts Conservation of energy?

Imagine a Stanford torus rotating with 1 rpm so that centripetal/reactive centrifugal acceleration provides about 1.0g of artificial gravitational acceleration inside the ring. The picture below shows ...
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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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Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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Why is tunneling not a classical idea?

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely ...
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Simple three-body-problem?

Consider the problem of three bodies two of which having mass M, one of them having mass m. Body m is in the middle between the other two, coupled to them by two equal linear springs in rest. Now fix ...
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556 views

Is there an inconsistency between Quantum and Classic in probability density of harmonic oscillator ground state?

Consider probability densities for a particle in the lowest energy state of a simple harmonic oscillator. The quantum mechanical probability density peaks near the equilibrium point and extends beyond ...
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Derivation of differential scattering cross-section

I'm trying to follow the derivation of the Boltzmann equation in my Theory of Heat script, but have a little trouble understanding the following: The cross-section $d\sigma$ is defined as: The amount ...
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Is instantaneous velocity an abstraction?

In introductory analysis, the discussion the derivative emphasizes that while average rates of change are measurable, instantaneous rates of change are a "limiting abstraction". While this makes ...
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Invariance of Lagrangian in Noether's theorem

Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$. However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ ...
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Why are infinitesimal rotations commutative, whereas finite rotations are not?

Infinitesimal rotations commute and every finite rotation is the composition of infinitesimal rotations which should logically mean they also commute; but they don't. Why?
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Galilean, SE(3), Poincare groups - Central Extension

After having learnt that the Galilean (with its central extension) with an unitary operator $$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + ...
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Why $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
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The Z-Torque: how can it be shown intuitively that it does not work?

There is a new kickstarter project that claims to increase torque and power compared to a normal crank on a bicycle (Z-Torque on kickstarter). If this patented (US Patent Number 5899119) approach ...
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Poisson structure comes from hamiltonian?

I am interested in studying quantization, but it seems I am lacking the basics of classical mechanics. Any help would be appreciated. I would first like to ask what is necessary to have a ...
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898 views

Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
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221 views

The feasibility of a satellite orbiting at a fixed time

I was speaking with some friends of mine, one of whom was an aerospace engineer. He posited the infeasibility of a hypothetical "Margaritaville Satellite" that orbited earth in such a way that ...
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The notion called aether

I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this ...
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How does the distance between two rails effect the speed of a steel ball bearing?

As part of a school science project, I constructed a Rollercoaster using Polyurethane tubing as rails for a steel ball bearing to rest on. In the process of building the coaster I observed that ...
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A pendulum clock problem

Below is a picture of a simple pendulum clock. Suppose that the bob (a rigid disk) on the end of the pendulum can spin without friction about its geometrical axis and is spinning at an angular ...
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851 views

Do we need inertial frames in Lagrangian mechanics?

Do Euler-Lagrange equations hold only for inertial systems? If yes, where is the point in the variational derivation from Hamilton's principle where we made that restriction? My question arose ...
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Do strong and weak interactions have classical force fields as their limits?

Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
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How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
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How much effect does the mass of a bicycle tire have on acceleration?

There are claims often made that, eg, "An ounce of weight at the rims is like adding 7 ounces of frame weight." This is "common knowledge", but a few of us are skeptical, and our crude attempts at ...
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Difference between momentum and kinetic energy

From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
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What are the normal modes of a vertical rope?

Closely related to this question on traveling waves on a hanging rope, I would also like to know what the normal modes are on a rope that hangs vertically, fixed at both ends. Tension in the rope ...
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Newton's Third Law Exceptions?

Lately I've been brushing up on some of my old Physics texts from college. Most recently, I've been rereading parts of "Classical Dynamics of Particles and Systems (5th ed.)" by Thornton and Marion. ...
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Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line?

I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am ...
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392 views

Why is classical mechanics determinism based on position and momentum only and not forces and scattering rules?

Consider a closed system (say a box) of $n$ particles. There is a well-known idiom/meme/law in classical mechanics that says that the position and momentum of those $n$ particles is all that is needed ...
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Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
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Principle of Least Action via Finite-Difference Method

I am reading Gelfand's Calculus of Variations & mathematically everything makes sense to me, it makes perfect sense to me to set up the mathematics of extremization of functionals & show that ...
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617 views

What's the optimal shape for a continuous Galilean Cannon?

A Galilean Cannon is a toy similar to the famous basketball-and-tennis-ball demonstration. You take a tennis ball, balance it on top a basketball, and drop them both. The tennis ball will bounce up to ...
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What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?

Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties: For a ...
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Point particle moving on a frictionless semicircular hill

Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary ...
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Maximal Gravity

I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin: Given a point $P$ in space, and given a piece of malleable material of ...
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Maximum speed of a rocket with a potential of relativistic speeds

Ultimately, the factor limiting the maximum speed of a rocket is: the amount of fuel it carries the speed of ejection of the gases the mass of the rocket the length of the rocket ...
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268 views

Why absoluteness of time implies galilean transformations?

In Landau course, vol.1 Mechanics, one finds the statement: ...the absoluteness of time necessarily implies that the ordinary law of composition of velocities is applicable to all phenomena. I ...
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Two carts connected by spring on frictionless track

I have the following homework problem: Consider two carts of equal mass m on a horizontal, frictionless track. The carts are connected by a single spring of force constant k, but are otherwise ...
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Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is ...
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782 views

How do I calculate electric fields due to currents of magnetic dipoles?

Short version of my question: Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the ...
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Drag on a spinning ball in fluid

I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I ...
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Why are the solution coefficients for a harmonic oscillator proportional to minors of the determinant?

I'm studying the oscillations of systems with more than one degree of freedom from Landau & Lifshitz's Mechanics Third Edition (for those who have the book, my question corresponds roughly to ...
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321 views

Physical Interpretation of a Scalar Quantity Related to Currents/Conservation Laws

Let $Q_{ab} = (\psi_{;a})(\psi_{;b}) - (1/2)g_{ab}|\nabla \psi|^2$ be the energy-momentum tensor of the wave equation in some space time. I will use semicolons to refer to covariant differentiation ...
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920 views

The Coriolis force bending a railway

Suppose a very long railway line goes from South Africa to Sweden, and then it's decided to move the entire railway line, sliding it 1 km to the north (leaving aside the difficulty of moving and ...
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323 views

Why don't clouds fall? [duplicate]

Well I do know that they sometimes fall as rain, but my question is why don't the droplets fall as soon as they condense from steam to cloud. Clouds are white by the process of Mie scattering so the ...
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339 views

How to find zero-point oscillations for this system?

Consider the following Hamiltonian which is absolutely relativistic literally: only sensitive to absolute pairwise relative phase space variables of objects for a system of $N$ objects moving in one ...
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The gravitational potential of ellipsoid

In the literature (Kirchhoff G. - Mechanic (1897), Lecture 18 or Lamb, H. - Hydrodynamics (1879)) one can find the following analytical closed form expression for the gravitational potential of ...
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Circular motion when F=ma'

I apologize in advance if this question is deemed too general or too similar to this and this question. How would mechanics be different if $F=mx'''$ instead of $F=ma$? I feel like I have ...
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Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i} $$ where $\rho$ is the mass density, $p$ is ...