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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Intrinsic angular momentum in classical mechanics

Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics. Inspired by this question: Is Angular Momentum truly fundamental? My question ...
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1answer
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Amplitude at distance from source

So, there is a sound at $S$, whose intensity $I$ obeys the inverse square law ($I \sim \frac{1}{x^2}$). At point $P$, at a distance $r$ from $S$, the air molecules oscillate with an amplitude of ...
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1answer
411 views

Mass fixed to a wheel - mechanics problem [closed]

I am struggling with a problem from classical mechanics. Imagine a massless wheel (to make it simpler) with a mass $m$ fixed to it rolling without slipping on a horizontal ground. If we now try to ...
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7answers
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What properties do you need for building a tower?

When I was a boy I used to daydream about building a tower so tall that the top of it would stick out of the top of Earth's atmosphere project into near space. There would perhaps be a zero gravity ...
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1answer
868 views

Brachistochrone Problem for Inhomogeneous Potential

This recent question about holes dug through the Earth led me to wonder: if I wanted to dig out a tube from the north pole to the equator and build a water slide in it, which shape would be the ...
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1answer
1k views

Fractal nature of turbulence

Someone described to me the difficulty of numerically simulating turbulence as that as you look at smaller length scales you see more structure like you do in a fractal. Searching on google for ...
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1answer
741 views

How do anti-lock brakes know when to brake?

When you come to a stop normally, the brakes don't pulse when you stop. Since the car can only know its speed by the rotation of the wheels, how can it distinguish between the car is stopped normally ...
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4answers
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what energies do the wheels of a moving car posses?

I saw this question in a test. I would have answered kinectic energy due to rotation and translation. It that correct. Else what is the answer? Oh no, i forgot to mention it was objective type ...
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1answer
4k views

Water rocket physics

According to this page, the current record for greatest altitude achieved by a water and air propelled rocket is 2044 feet (623 meters). In this connection, i had one question: How the greatest ...
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3answers
182 views

Are there measurable effects to scaling the action by a constant?

Classically, we obtain the equations of motion by finding a path which has an action that is stationary with respect to small changes in the path. That is the path for which: $\delta S =0$ Scaling ...
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3answers
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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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1answer
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Find velocity and displacement from force equation

How to find velocity and displacement equations from a given force equation? For instance, it was given the following 1-D equation: $$F = b_1(v_1-v) - b_2 v$$ $v_1$, $b_1$ and $b_2$ are constants. ...
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2answers
1k views

Rigid body dynamics joints

I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
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2answers
629 views

“Work” when biking up a hill

So, when biking, I noticed that when going up hills, it was less tiring if I went up them more quickly. This is not total Work done as is Force * Distance, as that should be the same. But the longer ...
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4answers
3k views

How can earthquakes shift the earth's axis?

One often comes across news articles that claim that an earthquake shifted the earth's axis. http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis If you ignore the ...
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5answers
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Are water waves (i.e. on the surface of the ocean) longitudinal or transverse?

I'm convinced that water waves for example: are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
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2answers
1k views

Calculate stainless steel pole necking limit

Background Trying to determine how much weight a post can support without necking when a monitor is attached to an articulated arm: a cantilever problem. Problem There are three objects involved in ...
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16answers
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Can a car get better mileage driving over hills?

Two towns are at the same elevation and are connected by two roads of the same length. One road is flat, the other road goes up and down some hills. Will an automobile always get the best mileage ...
4
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1answer
164 views

Chaos and continuous flow

What needs to be the case for a dynamical system with a continuous flow to exhibit chaos? It looks like 1D systems with a continuous flow can't exhibit chaos. Are two dimensions enough or do you need ...
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3answers
4k views

Convert running speed uphill to equivilent speed on flat

Given a certain running pace uphill, I want to be able to determine an equivalent pace running with no elevation change. Assumptions: similar effort in both cases (say for example running at 90% max ...
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4answers
3k views

Meaning of the Poisson bracket as a coordinate transformation

Well, the Possion bracket: $ \{ A(q,p),B(q,p) \} \equiv \sum_{s} \left( \dfrac{\partial A}{\partial q_{s}} \dfrac{\partial B}{\partial p_{s}} - \dfrac{\partial A}{\partial p_{s}} \dfrac{\partial ...
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3answers
701 views

Most elegant/fundamental formulations of the laws of classical mechanics?

Newton tried to do it with three laws/statements. While the first can be derived from the second, the three form a pretty nice framework. Later on, I've encountered Lagrangian Mechanics, which ...
6
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1answer
901 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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2answers
1k views

How the Lagrangian of classical system can be derived from basic assumptions?

It is well known that the Lagrangian of a classical free particle equal to kinetic energy. This statement can be derived from some basic assumptions about the symmetries of the space-time. Is there ...
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2answers
1k views

Dynamics of moment of inertia

I'd like to be able to determine the angular acceleration of a system of two rotating masses, which are connected so as to have a variable mechanical advantage between the two. My background with ...
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3answers
719 views

What does it mean, when one says that system has N constants of motion?

For example for an isolated system the energy $E$ is conserved. But then any function of energy, (like $E^2,\sin E,\frac{ln|E|}{E^{42}}$ e.t.c.) is conserved too. Therefore one can make up infinitely ...
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3answers
476 views

Consistent theory of continuum

Why is there a consistent theory of continuum mechanics in which one just consider things like differential elements and apply Newtons laws? Is there a deeper reason for it. Is it the nature of ...
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2answers
2k views

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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3answers
377 views

How does solar activity affect the ISS?

Currently the sun is launching some intense solar flares. http://www.guardian.co.uk/science/2011/feb/17/solar-flares-northern-lights-uk Th article I've linked also mentions how a "coronal mass ...
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1answer
809 views

converting force from spherical to Cartesian coords

So I am working on my assignment, and have a question about converting coordinates. I dont know whether I should ask here or the math SE, so lets give it a try here. The force in question is ...
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2answers
2k views

Why an object travels a circular path?

It might sound stupid but seriously I couldn't find why? We have a mass with a constant speed, which is acted on by a unit force which is always at right angles to its direction of motion. Why do ...
0
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3answers
2k views

Impulse - distance question [closed]

What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ? Thanks! Update 14.02.2011: I still wasn't able to find an answer to this. ...
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0answers
688 views

Do symmetries increase the number of conserved quantities? [closed]

Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential ...
2
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3answers
625 views

How long for a frictionless top to fall over?

We've previously discussed why it is that spinning tops do not fall over, see: Why don't spinning tops fall over? However, as the highest rated answer notes, the angular momentum of the spinning top ...
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3answers
1k views

Is the total energy conserved in a moving reference frame? [closed]

I have a ball attached to a spring and the spring is attached to a wall. There is no gravity for simplicity. In the rest RF the oscillating ball energy is conserved: T + U = const. In a moving RF it ...
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1answer
741 views

How to determine velocity and mass of asteroid 2011 CQ1

As you may have seen, a small asteroid had a near miss with the earth a few days ago. As a physics teacher teaching momentum, I think this could be an excellent problem for my students, however, I ...
14
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3answers
2k views

Significance of the second focus in elliptical orbits

1.In classical mechanics, using Newton's laws, the ellipticity of orbits is derived. It is also said that the center of mass is at one of the foci. 2.Each body will orbit the center of the mass of ...
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1answer
4k views

Finding the steady state solution of a damped oscillator

A damped harmonic oscillator with $m = 10$kg, $k = 250$N/m, and $c = 60$kg/s is subject to a driving force given by $F_0\cos(\omega t)$, where $F_0 = 48$N. (a) What value of ...
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2answers
284 views

Under what conditions do the Galilean transformatons become more accurate?

For S and S' in standard configuration, the Galilean transformations are: x' = x - vt, y' = y, z' = z, t' = t From the Lorentz transformations for v << c: x' = x - vt, y' = y, z' = z, t' = t ...
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2answers
2k views

How long does it take a block to slide up and down a plane with friction? [closed]

So I am studying for my exam on monday for analytical mechanics. I am kind of stuck on a question, so wondering if someone can give me a pointer. I am actually looking for some pointers and some ...
2
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3answers
2k views

Torque homework

We have learned that Torque is equal to a force that is perpendicular to a radius (displacement); however, I just cannot grasp one of the study questions we received: A hammer thrower accelerates ...
1
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5answers
708 views

Conserved quantities in generalized n-body problem

Given a collection of point-particles, interacting through an attractive force $\sim \frac{1}{r^2}$. Knowing only $m_1a=\sum_i \frac{Gm_1m_i}{r^2}$ and initial conditions we can deduce the motion of ...
5
votes
4answers
360 views

Is a periodic force capable of transporting a particle to large distances?

I have a particle at rest. At $t = 0$ a periodic force like $F_0 \sin\omega t$ starts acting on my particle. Can such a force transport my particle to infinity when $t \to \infty$? Please answer this ...
8
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2answers
414 views

Shaking a jar of balls

A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$. If initially the balls are randomly placed throughout ...
16
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3answers
4k 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?
2
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3answers
1k views

Could life survive a pole shift caused by an asteroid collision?

Could life on earth survive a large pole shift caused by an asteroid collision? I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
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2answers
3k views

Homework Help - Physics / Calculus III / Force-Work Problem [closed]

I have tried to answer the problem correctly, and I have found similar (and even an identical) problem in my textbook, yet I still can't seem to yield the correct answer with this specific problem. ...
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2answers
532 views

max velocity of SHM

So I think my algebra is wrong somewhere. Lets say you have an object that goes under SHM with some initial conditions (amplitude is 5m. The piston is at 5m at t = 0 and period is 20 seconds). Okay ...
8
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4answers
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Examples where momentum is not equal to $mv$?

I am aware that momentum is the thing which is conserved due to symmetries in space (rotational symmetry, translaitonal symmetry, etc). I am aware that in some systems, the generalized momentum, ...
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2answers
1k views

Mechanical energy problem

Question goes: "An anvil hanging vertically from a long rope in a barn is pulled to the side and raised like a pendulum 1.6 m above its equilibrium position. It then swings to its lowermost point ...