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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203 views

Definition of Kinetic energy

In class we had that $ T= \frac{1}{2}T_{ij}v_iv_j$ where we used the Einstein summation convention. Hitherto we only discussed examples where the kinetic energy was dependent of the square of one ...
7
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0answers
740 views

Mechanical similarity in Landau

I've read this very short paragraph from Landau & Lifshitz's Mechanics (Chap.2, Par.10) (that you can find here) about Mechanical similarity. I was looking for some more detailed explanations of ...
2
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1answer
538 views

Dynamics of controlled overdamped inverted pendulum

I wonder how to properly write the motion equations for the inverted pendulum on a cart in case of overdamped dynamics. Imagine the system illustrated in Wikipedia placed in a liquid with high ...
16
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3answers
1k views

Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory

I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
9
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1answer
5k views

Derivation of differential scattering cross-section

I'm trying to follow the derivation of the Boltzmann equation in my Theory of Heat script, but have a little trouble understanding the following: The cross-section $d\sigma$ is defined as: The amount ...
2
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0answers
123 views

Derivation of impact free Boltzmann equation

When deriving the impact-free boltzmann equation ( $\frac{\partial f}{\partial t} + \vec{v} \cdot\frac{\partial f}{\partial \vec{x}} + \vec{a} \cdot \frac{\partial f}{\partial \vec{v}} = 0$) I have a ...
8
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5answers
367 views

Why can't we obtain a Hamiltonian by substituting?

This question may sound a bit dumb. Why can't we obtain the Hamiltonian of a system simply by finding $\dot{q}$ in terms of $p$ and then evaluating the Lagrangian with $\dot{q} = \dot{q}(p)$? Wouldn't ...
4
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1answer
627 views

Principle of Least Action [duplicate]

Is the principle of least action actually a principle of least action or just one of stationary action? I think I read in Landau/Lifschitz that there are some examples where the action of an actual ...
12
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1answer
560 views

What makes a Lagrangian a Lagrangian?

I just wanted to know what the characteristic property of a Lagrangian is? How do you see without referring to Newtonian Mechanics that it has to be $L=T-V$? People constructed a Lagrangian in ...
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4answers
9k views

Would a pendulum swing indefinitely in a frictionless vacuum?

I am attempting to settle a friendly bet. Would a pendulum swing indefinitely in a hypothetical vacuum (i.e. no air resistance) having a hypothetical frictionless bearing (i.e. no energy lost due to ...
16
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5answers
2k views

Is my boss wrong about our mechanical advantage from our pulley system?

I work on a drilling rig as a roughneck and we had a lecture today (at the office) about mechanical advantage in pulley systems. Now, I know that my boss is well educated in oil drilling, but my ...
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1answer
224 views

Einstein Notation for Strain Energy Function

I encounter the following formula (for strain energy function) a lot in physics literature: $$ W(\epsilon_{kl}) = \int_0^{\epsilon_{kl}} \sigma_{ij} \textrm{d}\epsilon_{ij} $$ where all indices ...
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2answers
383 views

Bertrand's theorem

I found in Goldstein's Classical Mechanics that the condition for closed orbits is given by $\frac{d^2 V_{eff}}{dr^2}>0$.(bertrand's theorem). Can somebody explain to me, how this inequality is ...
2
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0answers
317 views

The correspondence between Poisson bracket and Commutators in Quantum Mechanics

I don't understand canonical quantization. In passing from classical to quantum, one replaces the Poisson brackets with the commutators. I don't really understand this. How can we generally show that ...
2
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4answers
2k views

rope wrapped around a pole

I would like to solve this question without using conservation of angular momentum(because of some reason I'll elaborate later). So imagine that we have a pole with radius $r$ and a ball attached to ...
20
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2answers
602 views

How to combine these equations of constraint?

I want to model a nonholonomic system of an arbitrary rotating disk in 3D, which rolls without slipping, and doesn't have to stay vertical. (think spinning a penny on the table) I want to use the ...
0
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1answer
606 views

Equations of motion for bob-on-a-string — am I missing some terms?

The dynamics of a type of physical system I am currently working on are modeled in most of the literature by replacing the moving parts of that system with an equivalent set of pendulums. Parameters ...
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2answers
124 views

Need an intermediate resistivity part/material

I need a part or material for a planned experiment (the experiment is similar to those described in my articles http://arxiv.org/abs/1208.0066 and http://arxiv.org/abs/1109.1626 ). The problem is that ...
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1answer
82 views

Energy in a wind instrument?

My physics teacher said that he saw a guy playing a very large wind instrument on TV, and the guy apparently calculated that the total energy present in the instrument when he was playing was almost ...
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1answer
172 views

Is there a difference between, static loading and fast loading of a polymer (non linear elastic material) in terms of elastic potential generated?

Imagine a non-linear elastic material such as a rubber band, nylon webbing or polyester webbing tensioned between two points. Scenario 1: A large mass is statically (no acceleration) loaded onto the ...
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2answers
202 views

Magnitude of force to keep stick in equilibrium [closed]

Problem statement A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the ...
6
votes
3answers
594 views

Principle of Least Action via Finite-Difference Method

I am reading Gelfand's Calculus of Variations & mathematically everything makes sense to me, it makes perfect sense to me to set up the mathematics of extremization of functionals & show that ...
0
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1answer
260 views

Energy of a cylinder rolling down a path

Problem statement: A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, ...
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2answers
270 views

Examples of “pseudo quantum effects” in history of physics

Are there any examples in the history of physics where a phenomenon was considered by the physics community to be not explainable by classical physics and needed a quantum explanation whereas some ...
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0answers
159 views

Relation between the period of rotation and the period of revolution of a satellite

I read somewhere that the tidal forces between the earth and the moon causes the equality between the 2 periods of the moon and that every planet-satellite system will evolve to this condition (like ...
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2answers
484 views

6 Story Building Swaying, Normal? [closed]

Preface: I'm currently sitting at my desk on a 5th floor in a South Florida office building, as I was earlier this morning when I felt the building sway slightly. It wasn't continuous and the ...
4
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2answers
266 views

Non-local Lagrangian contact interaction

Conside a contact interaction given by a delta function on their worldlines. Use a gauge fixed Lagrangian for two point particles in terms of their proper times $t$ and $t^{\prime}$. Is it possible to ...
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0answers
150 views

Small unclarity in proof of Noether's Theorem

I'm trying to understand the proof of Noether's Theorem in my Classical Mechanics class. We formulated it as follows: A continous symmetry is defined as a flow $\phi^{\lambda}(q(t))$ which leaves the ...
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1answer
609 views

Buoyancy Problem - Cubes in water

I have a tank with water (10 m high) , with an ideal seal at the bottom (water can't fall down, but can enter bodies). I have a system of 6 cubes ( of polystyrene density= 20 Kg/m^3) with dimension ...
10
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1answer
165 views

Is there a trajectory which is not a solution of the equation of motion but satisfies all conservation laws?

I'm wondering whether conservation laws are sufficient to imply equations of motions. Specifically: 1) In classical mechanics of point particles, are conservation of energy, conservation of momentum ...
3
votes
3answers
837 views

Classical/Quantum Coin Toss

I am having a brainfreeze moment and have confused myself, help appreciated! Classical Coin: Heads OR tails. Quantum Coin: Superposition Heads AND Tails. Classical Mechanics: Deterministic (in ...
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0answers
49 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
22
votes
3answers
681 views

How many points are required to make a black box

I have a black box with an arbitrary mass distribution inside it. I want to replace that object with n point masses without changing any mechanical properties of the box (center of mass, total mass, ...
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3answers
3k views

How much torque does it take to turn a doorknob? [closed]

How much torque does it take to turn a doorknob? I'm not looking for an exact answer, just a ballpark for someone who doesn't have a sense of everyday amounts of torque. Here's a very ordinary ...
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0answers
70 views

Hamiltonian system: match transformations and constants of motion

I have a problem about the interpretation of an exercise. Given the following Hamiltonian $$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- ...
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0answers
94 views

A quicker way to verify that a function is a constant of motion?

I have three particles that we can indicate with $\alpha$ ($\alpha$=0,1,2), they are identified by the $r^i_\alpha$ coordinates and $p^\beta_j$ conjugata momenta ($\beta=0,1,2$ and $i,j=1,2,3$). I ...
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2answers
484 views

How to calculate pressure exerted on the wheels of a robotic car?

I need some help in designing my robotic car. So its going to have 4 wheels, each driven by a 12-volt motor. It occurs to me that the weight of the chassis itself will exert some pressure on the ...
0
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0answers
372 views

Dose the gravitational force produces precession in the spinning top?

I'm new at classical mechanics but the text book says there is the torque in the spinning top which generated only by gravitation. It is hard to explain the situation, I've add the link. ...
0
votes
2answers
142 views

Hamiltonian equations: can I divide a solution of motion for a constant?

I'm solving an exercise about Hamiltonian equations. I have followed the proceeding below. The results given by the book are different to mine because its first result is the half of mine (and the ...
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vote
1answer
343 views

Solving equation of motion of two massive particle exerting the gravitational force each other

I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$ $$ ...
7
votes
2answers
5k views

Which is more efficient: a larger wheel or a smaller wheel?

I'm designing a 2-wheeled cart that I plan to rig to a donkey for hauling work around a farm. I'm wondering if there are mechanical advantages to using smaller wheels (like 40 cm diameter) vs. using ...
30
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10answers
4k views

What is the Earth truly rotating about/revolving around?

Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
17
votes
6answers
14k views

Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin ...
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votes
1answer
354 views

What are the physics behind the Coriolis effect? [closed]

What causes the Coriolis effect?
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3answers
937 views

Addes mass forces: can a force depend on acceleration?

My friend and I had a little discussion about added mass forces. I always interpreted $F=ma$ as a cause-effect relationship, so I find rather uneasy to accept that the cause can instantaneously ...
0
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1answer
67 views

Doubt about coordinates and point of equilibrium

I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use. This is the text of the exercise: "A bar has mass M and lenght l. Its extremity A is hooked ...
3
votes
1answer
351 views

A different proof for 6 degrees of freedom

I want a different proof of 6 degrees of freedom of a solid object made of $N$ particles. I am thinking along these lines: The definition of rigid body is $$\left\lvert \vec{r_i}-\vec{r_j} ...
2
votes
2answers
687 views

Rotating spring system: Is my intuition correct?

Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of ...
3
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4answers
3k views

Can Newton's laws be explained by Quantum Physics? [duplicate]

I have only basic knowledge of physics. Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels? I'm having ...
0
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1answer
62 views

Something about collision [closed]

A sphere P of mass m, travelling with speed $u$, makes a head-on collision with a stationary sphere Q also of mass m. After the collision, the velocities of P and Q are $v_1$ and $v_2$ ...