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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Theorems on instability of classical systems of charged particles?

Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
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831 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 ...
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1k views

Mechanics + Thermodynamics: Bouncing Ball

In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated: A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 ...
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2answers
359 views

Tracking photon color in Bell experiments

In parametric down-conversion, it is said that a driving photon is converted into two entangled photons whose frequencies add up to the driving frequency. Yet in discussions about entanglement ...
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323 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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How do we explain accelerated motion in Newtonian physics and in modern physics?

Maybe my question will seem stupid, but I am not a physicist so I have some problems understanding a classic Newtonian experiment: in the bucket experiment, why does he have to introduce the absolute ...
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3k views

How to calculate the exit velocity of a coil gun projectile?

First off, what quantities need to be factored in? Voltage and current through the coils, the magnetism of the projectile, the magnetic fields, etc.? Next, how would you calculate the speed of the ...
4
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1answer
181 views

Name of the guy that Feynman mentioned during a lecture: the diagram is of a chain hanging over a triangle

In a Feynman book, he talks about a man (I believe he lived 400-500 years ago) that discovered something about the dimensions of triangles (I think)by hanging a chain around the triangle. I've ...
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487 views

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface?

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface? The question I am working on is: A projectile is launched vertically from ...
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4answers
346 views

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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2answers
1k 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?
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589 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
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Why can't we feel the Earth turning?

The Earth turns with a very high velocity, around its own axis and around the Sun. So why can't we feel that it's turning, but we can still feel earthquake.
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232 views

Lagrange's equations: What is $\dot{q}_j$?

I'm looking at the solutions to a problem about a uniform thin disk. For the sake of this question, I start with $$L=\frac{1}{2}m\left( r\omega \right)^2$$ Then we plug it into Lagrange's equations: ...
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3answers
433 views

D'Alembert's Principle: Where does $-Q_j$ come from?

This is a follow-up question to D'Alembert's Principle and the term containing the reversed effective force. From the second term of Eq. (1.45) $$\begin{align*} \sum_i{\dot{\mathbf{p}}_i \cdot ...
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822 views

D'Alembert's Principle and the term containing the reversed effective force

For our Classical Mechanics class, I'm reading Chapter 1 of Goldstein, et al. Now I come across Eq. (1.50). To put it in context: $$\begin{align*} \sum_i{\dot{\mathbf{p}_i} \cdot ...
3
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1answer
273 views

Coincidence detectors in Bell tests: How close is close enough?

When is a coincidence a coincidence? We know that to identify entangled photons, the electronics is set to look for simultaneous clicks at opposite detectors. The size of the window is to some degree ...
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2answers
264 views

Why isn't pressure used for flight?

Why isn't pressure used as flight? I've heard that 2L bottles can hold a pressure of up to 90 PSI safely. Since $F = PA$, if the nozzle of a pressure rocket is about 4 inches squared in area, that ...
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2answers
567 views

Non-Linear Density Shell Problem

I'm trying to understand Newton's Shell Theorem (Third) http://en.wikipedia.org/wiki/Shell_theorem However this applies to a sphere of constant density. How is this formulated for sphere of varying ...
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1answer
197 views

Is it theoretically possible for the orientation angle of a projectile to remain exactly equal to the orientation of velocity?

This question is sparked by my answer to this question: Is this simulation following real physics? After examining the math, I don't see how it is theoretically possible for the situation simulated ...
14
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4answers
6k 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 ...
5
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1answer
2k views

Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time

My question is in reference to Landau's Vol. 1 Classical Mechanics. On Page 6, the starting paragraph of Article no. 4, these lines are given: If an inertial frame $К$ is moving with an ...
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2answers
204 views

How could pinion in automatic quartz watch be rotated at 100K RPM?

Wikipedia article on automatic quartz watch describes the watch mechanism as follows: a rotating pendulum is attached to a pinion and when the wearer moves his hand the pinion is rotated at up to 100 ...
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3k views

A spinning bullet

I know the rifling in a gun or rifle puts a spin on the bullet along the axis of trajectory. Now I don’t understand exactly what does it make the trajectory more stable and the travel grater?
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1answer
464 views

Invariance and forms of the Lagrangian

I have been doing Landau and due to its concise style been facing a few problems. I hope you can help me out here somehow. 1)Does the "homogeneity of space and time" essentially talk about the ...
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what is uniform velocity?

i have a very basic question from school days. what does it mean to say an object is moving with uniform speed? it seems to me now that it should be an unit dependent concept. for example if speed is ...
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82 views

In a gas of particles, how is the displacement vector related to the number density?

Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector ...
2
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2answers
2k views

Stress vs Strain for mild steel

After Yield point on stress strain diagram the under curve occurs what does it mean what will happen for the mild steel at that particular time and again why the curve goes to up and reaches ...
4
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1answer
628 views

Collision between a rod and a bullet

There lies a homogeneous rigid rod of mass $M$ and of length $H$ on a frictionless table at rest. A small bullet of mass $m$ moves toward the rod with velocity $v_0$, perpendicular to the rod and ...
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764 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 ...
2
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2answers
494 views

Wave equations & propagation theories

I'm interrested in making computer simulation but I've run into rather physics oriented problem. I have to choose how to propagate my wave. Though I've found technique called FDTD (finite-difference ...
2
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1answer
207 views

Church–Turing Thesis

Can the Church–Turing Thesis be proved assuming classical mechanics, how is the proof or disproof? Edited: I was looking for a proof of "everything computable by a device obeying CM is computable by ...
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676 views

Spinning bucket of water in zero gravity

Everyone knows how the surface of a spinning bucket of water would look like on earth - parabolic. But what if we turned off gravity (for instance by doing the experiment in a freely falling lift)? ...
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Why are generalized positions and generalized velocities considered as independent of each other?

I'm confused how $$\dot{\mathbf{r}}_{j}=\sum_{k}\frac{\partial\mathbf{r}_{j}}{\partial q_{k}}\dot{q}_k+\frac{\partial\mathbf{r}_{j}}{\partial t}$$ leads to the relation, ...
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0answers
223 views

Displacement due to sinusoidal load on a finite strip in an infinite plane

From a paper on tunnel design I've been reading: (http://www.sciencedirect.com/science/article/pii/0886779887900113) In the present application, the solu- tion corresponding to a sinusoidal load ...
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2answers
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What, if anything, makes forces the “cause” and acceleration the “effect”? [closed]

We typically say that forces cause acceleration inversely proportionate to mass. Would it be any less correct to say that acceleration causes forces proportionate to mass? Why? (Note that the ...
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1answer
316 views

Artificial Gravity - Spinning Station Questions II

In an answer to Artificial Gravity - Spinning Station Questions Vintage wrote: A theoretical space station of radius 900 meters, doing a complete rotation every 60 seconds (in order to generate ...
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3answers
198 views

Constrained particles under distance dependent force

This question is from the 1975 Canadian Association of Physicists Exam. No solutions are posted and I am quite lost on how to proceed with it. A particle is constrained to move along the x-axis of a ...
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1answer
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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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2answers
529 views

How do you find conserved quantities for linear second order ODEs?

I have a differential equation of the form $ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $ where $f$ and $g$ are known functions of time. Is there a systematic (or otherwise) way of ...
3
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4answers
1k views

What do we consider “Perpetual Motion”

I know this is a bad question to most serious Physics but I have a question about what is considered “Perpetual motion.” The Foucault pendulum in the UN consists of sphere that passes directly over a ...
2
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2answers
293 views

a question on Lagrange's equation when the time derivative of the generalized co-ordinates is constant

Consider a system whose generalized co-ordinates are $q_i$ and is under the constraints $\dot{q_i} = K_i \forall i = 1,2,3,...$ where $K_i$ are constants. I have a problem in writing the Lagrange's ...
2
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2answers
2k views

Do we know exactly how fast we are going relative to the center of the galaxy

I mean total inertial on my body siting here at my computer "California US." Ok so the earth is rotating on its axis and in turn around the sun and the sun around the galaxy. The object the question ...
5
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1answer
121 views

Sum of angular momentum of all electrons in a magnet

Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
3
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2answers
5k views

Analyzing the motion of a ball rolling without slipping inside a hemispherical bowl

Consider a solid ball of radius $r$ and mass $m$ rolling without slipping in a hemispherical bowl of radius $R$ (simple back and forth motion). Now, I assume the oscillations are small and so the ...
2
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1answer
431 views

significance of maxima and minima of time varying kinetic energy of a system

Consider a system of particles where the kinetic energy of the system is varying with time. I'd like to know the significance (or meaning) of the time derivative of the kinetic energy being zero at a ...
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592 views

In a 2D problem with a thrown object, why is the acceleration along the x-axis equal to 0?

I'm starting Physics, and I don't understand why the acceleration along the x-axis is zero for an object thrown near the surface of the Earth. This may be problem specific, but I wouldn't know since I ...
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2answers
423 views

A tunnel inside the Earth (but not an ordinary tunnel)

I decided to dig a tunnel inside the Earth. In equatorial plane. It should be designed in such a way that it follows the Coriolis effect. That means if, say a stone is dropped from rest into the ...
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3answers
2k views

How do you produce electricity from a wind mill?

How does a spinning windmill produce electricity?What is the principle behind the windmill?
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1answer
492 views

What are examples of Solutions of Newton's Laws that have analogs to Solutions of the Wave Equation?

The idea is to give examples of processes that deal with properties of a particle that have clear wave analogues.