# Tagged Questions

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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### Rigid body dynamics of tossing of a coin

While tossing a coin, it is commonly experienced that you get a head, if you toss it up with the head side up, and a tails if you toss with the tails side up. Is there a mathematical proof of this ...
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### Small Oscillations and matrices: suggestion about text

I'm undergraduate and I'm looking for a text about Small Oscillations in which matrices are used. Could you suggest me a book or a PDF file?
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### Non-Integrable systems

Integrable systems are systems which have $2n-1$ time-independent, functionally independent conserved quantities (n being the number of degrees of freedom), or n whose Poisson brackets with each other ...
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### Finding an efficient strategy for walking

Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...
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### Bernoulli's equation and reference frames

So I was thinking about this while driving home the other day. I've never been quite clear on why when you drive with the windows down air rushes into your car. I thought this might be explained by ...
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### Flat poster on a wall gaining curvature over time

Assuming you have a flat poster with no curvature, why is it that when you pin it to the wall (with thumbtacks) it gains curvature as seen in the picture below. When I put the poster up it was ...
556 views

### Two masses with interacting forces and an external force

Two masses in 3d space attract each other with a potential relative to the distance between them. There is also an external force on each particle based on the distance from a origin. I want to find ...
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### Normal Forces and Ferris Wheels

At the moment, I am reading an example problem regarding what was alluded to in the title. In this example problem, they say, "Based on experiences you may have had on a ferris wheel or driving over ...
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### Why does leaning back make a kicked ball go higher?

It's relatively common knowledge that when one kicks a football, if they lean back the ball usually goes higher, and if they lean forward slightly it goes at a more desirable height. Why does leaning ...
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### Fresco in his “Future By Design” introduces drawing of underwater vessel and its front system of generating air bubbles. Is idea energy efficient?

I recently saw Fresco's Future By Design and noticed something miniature to investigate. My notice regards about one of his illustration he describes in the documentary. Here is the link on youtube, ...
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### Car accident, put in park or neutral?

I was waiting on a red light the other day and was wondering. If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if ...
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### Generalized momentum conjugate and potential $U(q, \dot q)$

On Goldstein's "Classical Mechanics" (first ed.), I have read that if $q_j$ is a cyclic coordinate, its generalized momentum conjugate $p_j$ is costant. He obtained that starting from Lagrange's ...
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### Question about de Broglie Waves?

Is photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves ? and CAN be identified as with the de Broglie waves ? I ...
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### Is the geometric formulation of Hamiltonian mechanics really necessary? [duplicate]

Possible Duplicate: Why is the symplectic manifold version of Hamiltonian mechanics used in Newtonian mechanics? I was sitting around with some friends the other day trying to come up with ...
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### Reference for the predictability of rigid body dynamics

I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely predictable. A view coming from the background ...
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### To find whether a particle is in equilibrium or not

Actually the following question came in an exam i gave yesterday. I know the site does not allow home-work type questions, but as I am having a conceptual problem in solving the question, I am posting ...
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### How accelerometers sense constant velocity movements

There is something I don't understand about accelerometers. I know it's possible to make an Inertial Measurement Unit (IMU) by using "three" accelerometers. So with that, I could calculate the $x$, ...
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### By how much will water resistance and upthrust slows down a fully submerged object?

Consider the following example: While running, I do work and I have a certain velocity and acceleration. When I'm in a pool (my feet are touching the bottom), I do the same work but, I have less ...
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### Determine the maximum height a pump can suck up water

I am working on a homework problem that presents the scenario of trying to raise water from a small reservoir of depth 8 m whose surface is 25 m below a pump that can maintain a pressure differential ...
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### Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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### What are the fields in this problem?

In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement: Which components of momentum and angular momentum are ...
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### Is it reasonable for a heavy door to “open by itself” (ie from differences in air pressure) if it had already been slightly ajar?

If you consider a basically uniform massive door (say, 300 N) where there is some coefficient $\mu_{s,k}$ of static and kinetic friction between the thing on the inside of the door, and where the ...
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### Landau Mechanics: why does adding Lagrangians remove the indefiniteness of multiplying each Lagrangian by a different constant?

In Landau Mechanics (third edition page 4), why does adding Lagrangians of two non interacting parts remove the indefiniteness of multiplying each Lagrangian by a different constant? If both systems ...
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### Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?

I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude: $$F(r, t) = \frac{k}{r^2}e^{-at}$$ ...
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### Coriolis force in free fall

Does the coriolis force has any measurable effect in free fall from large heights? Take for example the sky diving experiment by F. Baumgartner who started from a height of about 40 km above New ...
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### What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?

I have a problem with one of my study questions for an oral exam: The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
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### What is the relationship between mass, speed and distance of a planet orbiting the sun?

After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star. Given the mass of the sun and ...
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### Charge, velocity-dependent potentials and Lagrangian

Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
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### Differences between classical, analytical, rational and theoretical mechanics

Can you explain me what are the differences between the four following subjects? analytical mechanics rational mechanics classical mechanics theoretical mechanics
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### Stacking gold Bars

I once heard that because gold is so malleable, while also being very heavy; that if one were to stack several layers of bars on top of on another (like is so familiarly depicted in movies & TV), ...
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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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### Problem in Hamiltonian

I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation  \hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
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### Determining friction for unbalanced wheel to roll without sliding

I'm trying to model a weighted wheel rolling without slipping. I understand that friction, by virtue of being an off-center force, affects both linear and angular acceleration. So my train-of-thought ...
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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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### Particles as a limit of classical field theory

A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$. Similarly is it possible to show that a limit to field ...
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### Is it possible to find out the distance traveled by a car if the force applied on it is given?

Say you have car which produces $F$ amount of force which is transferred to the wheels directly. Now assuming that there is air friction which is causing a retarding force proportional to the ...
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### 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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### Reference request: Classical Mechanics as an Application to Smooth Manifolds [duplicate]

Possible Duplicate: Classical Mechanics for Mathematician Last time I asked a question, but it does not sound specific. I am currently taking graduate topology class (using Lee's ...
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### Microphones, Loudspeaker and their analogies to spring mass system

I have just started studying Microphones and Loudspeakers. I need a good text to refer which can explain their mechanical analogies with simplicity and basics too.
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### 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, ...