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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Period of swinging incomplete hula-hoop

I was working on a problem where I had to calculate the period of a swinging incomplete hula-hoop given its center of mass and radius. It only swings with very small amplitude so I considered the ...
7
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1answer
293 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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3answers
152 views

What forces are at work in a loose ball bearing bicycle hub?

I've landed in a physics debate amongst bike mechanics. In a typical bicycle hub you have a simple bearing; the cups are set in the hub, the race (cone) threads onto the axel and there are just loose ...
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1answer
64 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
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2answers
348 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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2answers
94 views

Coupled ODEs that model a quad rotor

I am working on modeling the vibrations of a quad rotor. The arms that support the rotors are fixed to a center plate; that is, it is pretty much a cantilever beam with an end load. Since this is the ...
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1answer
65 views

Why do some objects tend to change their axis of rotation while rotating?

This question struck me a few minutes back, I was at a table with a pear. It was more narrow than round.I proceeded to rotate this pear in one swift movement. It rotated for a few seconds, and ...
2
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1answer
117 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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1answer
696 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
524 views

Classical analogue of Heisenberg and Schrödinger pictures?

What do the Heisenberg and Schrödinger pictures in quantum mechanics correspond to in classical mechanics (if they correspond to anything)? It's kind of weird, because (if I understand it well) in ...
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2answers
46 views

Net work done for rubber bands

I know that work is done on a rubber band to extend it, and then the rubber band does work to contract. However, then what is the net work done? If it returns to its original length, is the area ...
2
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1answer
49 views

Does Special Relativity require a “ruler postulate” analogous to the “clock postulate”?

It's fairly well known that the clock postulate is needed in Special Relativity when dealing with accelerated clocks, so does something analogous exist when dealing with accelerated spatial ...
3
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1answer
234 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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3answers
572 views

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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1answer
50 views

Analytical Mechanics [closed]

This is one of my three homeworks. I see that $W_a(1) = \dot U_a(1)=\ddot{X_a}(1) = 0.3 $ Since $U_{O'}=0 $ then O' is Instant centre of rotation. Then $U_b = 2U_a = 0.6$ I tried a lot, about a ...
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0answers
33 views

Symplectic Structure without predefined Hamiltonian

Here there is a link which has helped me understanding the relationship between symplectic geometry and classical mechanincs. In short, the symplectic form transforms the derivative of the ...
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3answers
115 views

Unstable equilibrium in a pendulum

Consider a pendulum with a bob and a massless, rigid, hinged rod attached to the bob. The bob is at rest at the bottom most position. Neglecting friction, is it possible to impart such a velocity ...
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4answers
5k 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 ...
4
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1answer
102 views

Liquid Column “Recoils” in a Sealed Cylinder When Hit by a Piston — Is it Possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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2answers
473 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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1answer
3k views

Floating Objects and Weight

The Situation: A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string. The Question: The ball is attached to the beaker, thus ...
2
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2answers
127 views

Is static friction an impulsive force?

For example: let's consider a static sphere on an horizontal rough surface. I apply an impulse $J$ parallel to the ground and in the middle of the sphere. If, like my book says, the friction is not an ...
1
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1answer
22 views

How to calculate when an object will fall over

TL;DR Given the point of centre of mass, width of base and height, is there a way to calculate the angle where the object will fall over? The TL;DR of this question pretty much sums it up, however I ...
2
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1answer
248 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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1answer
73 views

How can the Gallilean transformations form a group?

In class my professor said the Galilean transformations form a group of order 10. $$ x'=x-vt\\ y'=y\\ z'=z\\ t'=t\\ $$ But how do these form a group? I don't see 10 things to interpret as elements. I ...
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2answers
697 views

Find generating function $F_1$ for canonical trasformation

I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation. For example, considering the transformation $$q=Q^{1/2}e^{-P}$$ $$p=Q^{1/2}e^P$$ ...
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1answer
52 views

Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
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3answers
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What is the physical meaning of diffusion coefficient?

In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
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2answers
159 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
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4answers
2k views

Define Pressure at A point. Why is it a Scalar?

I have a final exam tomorrow for fluid mechanics and I was just looking over the practice exam questions. They do not provide solutions. But pretty much I have to define pressure at a point and also ...
0
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1answer
39 views

Torque and Car parked on slope [closed]

I have a homework question in which a car of mass $M\ kg$ is parked on a hill inclined at $25^o$ The car is facing up the hill and I am told that the wheels are $3\ m$ apart and the centre of mass is ...
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1answer
32 views

Sum of velocity fields

In hydrodynamics the for a non-viscous flow the velocity (and density) fields are given by the continuity and Euler equations: $$\rho\frac{\partial \vec{v}}{\partial ...
2
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5answers
258 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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2answers
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How does the period of an hourglass depend on the grain size?

Suppose I have an hourglass that takes 1 full hour on average to drain. The grains of sand are, say, $1 \pm 0.1\ {\rm mm}$ in diameter. If I replace this with very finely-grained sand $0.1 \pm 0.01\ ...
5
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1answer
257 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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2answers
2k views

Speed of a fly inside a car

A couple of weeks ago I was travelling in a car (120 km/h approximately) and I saw a fly flying in front of me (inside the car, near my nose, windows closed). I wonder how was that possible. Does it ...
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17answers
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Why does one experience a short pull in the wrong direction when a vehicle stops?

When you're in a train and it slows down, you experience the push forward from the deceleration which is no surprise since the force one experiences results from good old $F=m a$. However, the moment ...
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6answers
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Why does higher acceleration minimize a car's fuel consumption?

I generally try to optimize my car's fuel consumption when driving, using my car's real-time MPG gauge and average-trip MPG indicator. Until recently, I believed the slower the acceleration, the ...
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0answers
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What is the temperature effect on trajectories in phase space in molecular dynamics?

In molecular dynamics simulations or microcanonical ensemble (fixed-energy), what is the effect of temperature on the trajectories of the reacting systems (let's say two reactants react to form two ...
4
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1answer
94 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
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4answers
3k views

Does screwdriver length matter?

Everyone who deals with screws and screwdrivers knows that long screwdrivers are stronger than short ones. However, I can't find any relationship between length of a screwdriver and mechanical ...
0
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1answer
268 views

How is the equation of motion for a real scalar field derived from the Lagrangian?

The Lagrangian for a real scalar field is: $$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$ How can I derive the dynamics of this field from this ...
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2answers
81 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
5
votes
3answers
995 views

Sum of torque from a sphere

A sphere (grey color) turn in rotation at $\omega$ rd/s. There are 2 walls that prevent sphere to escape. Walls can only turn around center of rotation. The sphere turn only at $\omega$ rd/s too. The ...
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2answers
34 views

Derivation of ensemble distribution

I heard that you can derive the canonical ensemble by maximizing $L = \sum_i p_ilog( p_i ) + \alpha (\sum_i p_iE_i-E)$ or for the grand-canonical ensemble $L = \sum_i p_ilog( p_i ) + \alpha ...
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0answers
46 views

Good introduction to classical mechanics with math [duplicate]

Right now, I'm reading "Classical Mechanics" by Kibble and Berkshire. Already in chapter 2, I have found a concept being discussed that assumes you have prior knowledge. Specifically, it describes the ...
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3answers
62 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
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2answers
24 views

Understanding a graph of energy conservation with bounded and unbounded motions?

This graph is from the physics undergraduate text "Classical Mechanics by Douglas Gregory". Above this graph was the statement: What I didn't understand is- as stated in the under [*paragraph], ...
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1answer
85 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose speed is $v_0$ ...
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3answers
3k views

Why should fluids be confined for Pascal's Law to be applicable

When is Pascal's law about fluid pressure propagation applicable? Is it applicable to a closed circular pipe with a pump rotating the fluid, but not to a tub of water. Most statements require only ...