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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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 ...
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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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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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752 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 ...
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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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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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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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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 ...
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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 ...
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5answers
717 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 ...
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4answers
363 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 ...
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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 ...
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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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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
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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
580 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 ...
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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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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 ...
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745 views

Does Action in Classical Mechanics have a Interpretation? [duplicate]

Possible Duplicate: Hamilton's Principle The Lagrangian formulation of Classical Mechanics seem to suggest strongly that "action" is more than a mathematical trick. I suspect strongly ...
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4answers
442 views

Will tensile strength keep a cable from snapping indefinitely?

Trying to secure a wall hanging using magnets; me and a coworker came up with an interesting question: When the hanging is hung using 1 magnet, the weight of it causes it to quickly drag the ...
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5answers
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Basic mechanics problems, unsolvable by brute-force numerical integration

I'm looking for simple problems in theoretical mechanics that are impossible or unreasonably difficult to solve by means of "brute-force" numerical integration of Newton or Euler-lagrange equations. ...
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4answers
642 views

Radiation from a pair of charged objects orbiting each other

This question on binary black hole solutions, led to me think about the similar question from the perspective of what we know about the Hydrogen atom. Prior to quantum mechanics, it was not ...
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2answers
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Non Classical mechanic answer to : length of time a thrown object spends in rest before falling down? [closed]

When an object is thrown upwards, when it eventually comes to rest and starts falling, for how long is it stationary? What about an particle in electric field having an initial velocity towards it's ...
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372 views

Terminal velocity for falling in a shaft

One falls slower in a mine shaft than in free air. This is due to collisions with the walls. How should one model the terminal velocity in the presence of such collisions?
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1answer
487 views

Lagrangian density of linear elastic solid

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
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4answers
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How does a lower center of gravity affect fuel economy?

It's been a couple years since I've taken a physics class, and I have been wondering about this basically since I bought my car: I drive a 2010 Honda Fit, which has a street weight of approximately ...
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Why do rockets have multiple stages?

What is the advantage for rockets to have multiple stages? Wouldn't a single stage with the same amount of fuel weigh less? Note I would like a quantitative answer, if possible :-)
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Rotation angle of a giant lily when a child crawls on its rim

Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...
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Why is the bell, well, bell shaped?

What is the significance about the bell shape, when its hit at the rim it rings/produces sound better than other shaped objects? If so could anyone explain a little bit on it. EDIT: From the ...
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2answers
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Moving from point A to point B in zero-gravity

Here's an proposal on how to get from point A to point B in zero-gravity without using any propellant and the question why it wouldn't work: A closed tube, filled with water and a round (solid) ...
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6answers
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Why does a car engine not do work if the wheels don't slip?

I saw this mind boggling result that if the tires don't slip then the work done by an engine to move a car is zero. Why is this true? Moreover, what does this truly mean? Update: Sorry about not ...
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4answers
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How long it will take for a upright rigid body to fall on a ground

Let's suppose there is a straight rigid bar with height $h$ and center of mass at the middle of height $h/2$. Now if the bar is vertically upright from ground, how long will it take to fall on the ...
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Including air resistance, what is the escape velocity from Earth?

Including air resistance, what is the escape velocity from the surface of the earth for a free-flying trajectile?
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Why does Guillotine have of 45 degreed blade rather than the one parallel to the ground? [closed]

What is the point of having 45 degreed blade in Guillotine? After all, the pressure-Force over Area-blade imposes to the neck is the same either way.
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What happens when I move a very long bar? [duplicate]

Possible Duplicate: Faster than light information Hey there, I just want to make clear that I'm new here and I don't know whether this is the right place to ask such a hypothetical ...
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3answers
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Equivalent spring-constant for infinite square grid of springs

Consider an infinite square grid, where each side of a square is a spring following Hooke's law, with spring constant $k$. What is the relation between the force and displacement between two points? ...
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Oscillate a swing without touching the ground

Is is possible to set a swing into oscillations without touching the ground? This occurred to me while watching the second pirates movie. There is a scene where the ship's crew is suspended in a cage ...
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1answer
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Cheetah prosthesis efficiency

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A ...
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3answers
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Why does the cart move? [duplicate]

A while ago someone proposed the following thought experiment to me: A horse attached to a cart is resting on a horizontal road. If the horse attempts to move by pulling the cart, according to the ...
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2answers
557 views

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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2answers
384 views

Will a wave packet undergo dispersion when traveling down a hanging rope?

Suppose I tie one end of a rope to my ceiling and the other end to a spot on my floor directly underneath it. Because the rope has some mass, the tension varies along the rope, from highest at the ...
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5answers
354 views

Driving on snowy roads

'tis the season as they say! It seems to me obvious that it's better to drive in high gear on snowy roads to reduce the torque. However, there are completely opposite advices being given on ...
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4answers
585 views

Rolling stone on a frictional surface

Consider a spherical rigid stone rotating with angular velocity $\omega$ being dropped vertically onto a horizontal rigid surface with the coefficient of friction $\mu$. Can the stone roll on the ...
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3answers
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If a vehicle is rolling down a hill, will its speed depend on the size of the wheel?

If I am sitting on a skateboard and travel downhill, will the velocity depend at all on the size of the wheel? The skateboard is only powered by gravity. There are a lot of variables to consider. ...
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2answers
771 views

Does the cube stay on the loop-de-loop?

Suppose a cube of mass $m$ enters a loop-de-loop of radius $r$, travelling halfway around and reaching the top. At the top, it has velocity $v$, and the second half of the loop is frictionless. How ...
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2answers
563 views

Physics of a fixed wheel moving on a flat surface held at distance from a center point

Ok, so my boss is trying to make a car turntable. In essence, he has a two boards that sit atop a rotating ring. He wants to put two wheels at the end of each board (8 wheels total). He thinks that ...
3
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1answer
438 views

Soliton mechanics

How much of classical mechanics can be modelled with solitons? What I am aware of is that single solitons behave in a way like free particles: they move along as stable entities with constant ...
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11answers
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Mechanics around a rail tank wagon

Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it): ...
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1answer
129 views

How long does it take a object captured by a star falling to the center?

If the captured object do not have tangential velocity, it's just the free-fall time. But when it has, it may take longer time to fall in, right ? The function should be $\ddot{r} = -GM/r^2 + ...
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Classical mechanics without coordinates book

I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think ...