[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
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429 views
How fast do you have to spin an egg to have it standing?
If you take a hardboiled egg and put it on a table and start to spin it, if you spin it fast enough it will start to spin in an upright position. What is the angular velocity needed for this ...
7
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3answers
2k views
When is the Hamiltonian of a system not equal to its total energy?
I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
7
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3answers
1k views
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 ...
7
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4answers
400 views
Why does a ping pong ball change direction when I spin it on a table?
When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward.
Here's a video demonstrating the effect.
...
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3answers
313 views
Force through quantum mechanics
In classical physics force is:
$$F=\frac {dp}{dt}$$
How about quantum mechanics?
In Old Quantum Mechanics momentum is: $p=\hbar \cdot k$ so force will be:
$$F=\hbar \frac {dk}{dt}$$
what does $\frac ...
7
votes
3answers
294 views
Is the quantization of the harmonic oscillator unique?
To put it a little better:
Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit?
I'm specifically, but not only, interested in an ...
7
votes
1answer
504 views
Coriolis force and Newton's third law
I would like to ask a stupid question here.
If a body 'b' moving downward with a velocity v in a rotating frame of reference with angular velocity w, and w and v not being parallel and anti parallel. ...
7
votes
3answers
89 views
Rotationally invariant body and principal axis
Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$).
Is it true that in this case the ...
7
votes
6answers
319 views
How does such strange microscopic behavior at the atomic level (quantum mechanics) lead to the macroscopic behavior at our level?
So, I'm only a high school student researching quantum physics, and I find it very interesting. However, there's one question that keeps nagging at me in the back of my head. How exactly do odd ...
7
votes
1answer
295 views
D-brane Lagrangian?
As I understand it from the threads I read, D-branes are viewed as somewhat secondary to strings: If I know what all the open strings do, then I know what the D-branes do as well. But if the D-brane ...
7
votes
1answer
589 views
Pendulum with water dripping out
Consider a pendulum, consisting of a string of length $l$ tied to a ball of negligible mass and radius $r$. The bob is filled with water, which has density $d$, and the pendulum is given a small push ...
7
votes
1answer
554 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 ...
7
votes
4answers
349 views
Hamiltonian and the space-time structure
I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian.
Space-time structure dictates the form of ...
7
votes
4answers
804 views
How far does a trampoline vertically deform based on the mass of the object?
If a baseball is dropped on a trampoline, the point under the object will move a certain distance downward before starting to travel upward again. If a bowling ball is dropped, it will deform further ...
7
votes
8answers
483 views
Is “Causality” the equivalent of a claim that the future is predictable based on the present and the past?
In classical (Newtonian) mechanics, every observer had the same past and the same future and if you had perfect knowledge about the current state of all particles in the universe, you could ...
7
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3answers
457 views
Boundary layer theory in fluids learning resources
I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
7
votes
2answers
290 views
Physics of scaling up an animal: the neck
Consider an animal like a horse. Now scale its neck longer and longer.
How can a giraffe, or even worse a huge dinosaur, raise its neck without the tendons snapping? The dinosaur case in particular ...
7
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9answers
853 views
How to explain independence of momentum and energy conservation in elementary terms?
I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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9answers
2k views
Book about classical mechanics
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
6
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4answers
347 views
What exactly is “F” in $W = \int_{a}^{b} F dx$?
I am trying to teach myself some basic physics, here is something I do not really understand about the definition of work:
when moving from $a$ to $b$ (in one dimension), the work done is defined to ...
6
votes
8answers
4k views
Which Mechanics book is the best for beginner in math major?
I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through Goldstein's Classical Mechanics. ...
6
votes
6answers
787 views
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 ...
6
votes
2answers
302 views
Why don't we consider centrifugal force on a mass placed on earth?
Let us say a block of mass is placed on the surface of earth. Then while drawing the forces on that body, we say:
Force F = mg acting towards the center of earth
Normal reaction N offered by the ...
6
votes
6answers
814 views
Is rotational motion relative to space?
Let's assume that there is nothing in the universe except Earth. If the Earth rotates on its axis as it does, then would we experience the effects of rotational motion like centrifugal force and ...
6
votes
3answers
199 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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7answers
1k views
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
446 views
Connection between Poisson Brackets and Symplectic Form
Jose and Saletan say the matrix elements of the Poisson Brackets (PB) in the $ {q,p} $ basis are the same as those of the inverse of the symplectic matrix $ \Omega^{-1} $, whereas the matrix elements ...
6
votes
2answers
979 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 ...
6
votes
4answers
960 views
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,
...
6
votes
3answers
349 views
When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?
Lets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation
$U(x_{b},x_{a}) = \int_{x_{a}}^{x_{b}} ...
6
votes
3answers
485 views
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 ...
6
votes
2answers
255 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 ...
6
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1answer
447 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 ...
6
votes
1answer
426 views
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 ...
6
votes
1answer
518 views
How did Feynman derive the physics of medallion vs. plate wobble rate?
I am referring to this:
Within a week I was in the cafeteria and some guy, fooling around,
throws a plate in the air. As the plate went up in the air I saw it
wobble, and I noticed the red ...
6
votes
1answer
253 views
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 ...
6
votes
1answer
226 views
Three Pendulum Rotary Harmonograph
I'm trying to create a simulation of a three pendulum rotary harmonograph, the one you can see in action in this video or in these instructions.
As you can see in the video, there are 2 pendulum with ...
6
votes
2answers
389 views
Fields and Newton's Third Law
I'm studying basic physics. I'm using the text available at http://www.anselm.edu/internet/physics/cbphysics/downloadsI.html. It develops the universal law of gravitation by postulating the existence ...
6
votes
2answers
214 views
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 ...
6
votes
2answers
587 views
Can a force in an explicitly time dependent classical system be conservative?
If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian
$$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$
under what ...
6
votes
2answers
494 views
What are the properties of two bodies for their collision to be elastic?
For example, must the shock wave in each body be of a particular form which influences the shape and material properties of the bodies?
I suspect part of the the answer is that the objects must be ...
6
votes
2answers
906 views
Are there examples in classical mechanics where D'Alembert's principle fails?
D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero.
This is obviously true for the ...
6
votes
0answers
247 views
Classical mechanics: Generating function of lagrangian submanifold
I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation.
One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
5
votes
6answers
971 views
Why F=ma and not F=ma'?
What would happen if instead of $F=m*d^2x/dt^2$, we had $F=m*d^3x/dt^3$ or higher?
Intuitively, I have always seen a justification for ~1/r^2 forces as the "forces beeing divided equally over the ...
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votes
5answers
1k views
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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votes
4answers
6k views
Is pushing actually easier than pulling?
It is generally assumed that pushing a cart is more easier than pulling one. But why?
Is there any difference in terms of force required to achieve the same amount of displacement?
Or is it just a ...
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votes
2answers
123 views
Hooke's Law, Phase Space and Classical Geometry
Hooke's Law tells us that $m\ddot{x} = -kx$. We can apply the chain rule to rewrite $\ddot{x}$ as follows:
$$\frac{\operatorname{d}\!^2x}{\operatorname{d}\!t^2} = ...
5
votes
3answers
449 views
How does one quantize the phase-space semiclassically?
Often, when people give talks about semiclassical theories they are very shady about how quantization actually works.
Usually they start with talking about a partition of $\hbar$-cells then end up ...
5
votes
3answers
612 views
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 ...
5
votes
2answers
739 views
How is angular momentum conserved when a spinning top finally stops spinning?
Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
