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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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 ...
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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 ...
0
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2answers
203 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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3answers
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?
4
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1answer
462 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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1answer
2k views

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 ...
2
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2answers
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
624 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 ...
7
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2answers
752 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
484 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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2answers
655 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)? ...
4
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2answers
1k views

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, ...
2
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0answers
218 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 ...
1
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2answers
995 views

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 ...
1
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1answer
314 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
197 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 ...
6
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1answer
1k views

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 $\alpha L$ ...
2
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2answers
516 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
292 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
votes
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
416 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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2answers
532 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 ...
3
votes
2answers
418 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 ...
7
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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?
2
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1answer
488 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.
2
votes
2answers
200 views

Mechanical work to required battery power

I have a very practical question where I've calculated the mechanical work needed by a simple mechanical system by solving the line integral $W = \int_C \ F \ dx$. However, since I have a black spot ...
4
votes
6answers
1k views

Stronger than Newton's laws?

According to the Newton mechanics, the force is responsible for changing the body velocity, and the body mass is the body inertia - a property to resist to the applied force. These two things make a ...
5
votes
2answers
1k views

Two spheres (A physics olympiad problem)

Browsing an archive of problems of a local physics olympiad, i stumbled upon a problem which seems not a very trivial. Given two identical metal spheres in vacuum, with mass $m$ and radius $R$. One ...
7
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2answers
908 views

Forget Hooke's law. Why does a spring exert a force?

Forgetting Hooke's law for a minute why, from a microscopic perspective (preferably quantum) on up to a macroscopic one, does a spring under tension exert a force? I was thinking that there might be ...
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2answers
690 views

Simulation of physics of chains/ropes in force fields resources?

I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting ...
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1answer
339 views

purely hypothetically, could a quantum being appear to be human? I ask for the purpose of research on a novel [closed]

I am a budding novelist, and im researching a few things for a fictional narrative. the characters are from other dimensions and i want to present a coherent scientific structure. any suggestions ...
5
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3answers
473 views

How fast do I need to go in order to avoid being seen by the Police?

I was driving down the road at roughly the speed of traffic. I saw a police officer parked on the side of the road, and also noticed that a Semi was traveling in the lane right next to him. This got ...
4
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3answers
725 views

Does decoherence explain all instances of wave function collapse?

Specifically, how can decoherence explain the appearance of flecks of metallic silver on a photographic plate when exposed to the very weak light of a distant star? EDIT: Perhaps the advocates of ...
4
votes
3answers
542 views

Why trimming the mainsail gives a larger torque to head up

I am learning sailing on a 5m catamaran (Nacra 5). I am familiar with basic aerodynamics and the physics of the sail and keel. We learned that when sailing closed hauled, too tight a mainsail tends ...
1
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1answer
446 views

Upper equilibrium point of a pendulum with small perturbations

I remember the following fact about a rigid pendulum: The point when the pendulum weight is lowest is a stable equilibrium while the point where the pendulum weight is highest is an unstable one. ...
21
votes
3answers
771 views

Equations for bent paper

I have a paper which lies on a flat surface. The paper is fixed on one side and the opposite side can slide in the direction of the opposing side. As side end slides toward the other, a "bump" forms. ...
-1
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1answer
1k views

Modeling and Simulating Pendulum Motion

I've been having difficulty creating a mathematical model of a pendulum in my code. While there is plenty of info on general equations describing a the motion of a pendulum, I seem to be having ...
0
votes
1answer
820 views

Distance traveled by a projectile into a block

This problem is part of one of the free response questions on the 2011 AP Physics C Mechanics exam [PDF of free-response questions] that was administered last week. (Sorry the problem statement is so ...
8
votes
3answers
810 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. ...
5
votes
2answers
2k views

Shape of Fan Blades

How is the shape of the blades of an air fan determined? Trial and error, or is there a theory behind it? What are they trying to maximize, volume of air dislocated per rotation?
3
votes
1answer
595 views

Phenomena which are incorrectly declared as resonance phenomena?

In standard college physics text books, high-school books and popular level physics books, the collapse of the Tacoma Narrows Bridge is often taken as an example of resonance. However a more detailed ...
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1answer
198 views

How should I REALLY have done this continuous moment formula derivation?

One of my more recent hobbies is making "swords" out of PVC conduit, foam, and duct tape. As all the weight is forward of the cross guards, I needed to put some amount of some substance inside the ...
6
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5answers
3k views

Maximum speed of a rocket with a potential of relativistic speeds

Ultimately, the factor limiting the maximum speed of a rocket is: the amount of fuel it carries the speed of ejection of the gases the mass of the rocket the length of the rocket ...
4
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3answers
1k views

Formula for implementing a simulated weighing scale

Background: I'm on the pledge drive committee for a non-profit group, and there is an issue that is always contentious within this group; thankfully the group is amicable, although competitive, about ...
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8answers
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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. ...