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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Why do two rolls with the same mass but different moments of inertia roll different distances?

Imagine two rolls with the same diameter and mass. The mass of one roll is concentrated to the center of the roll while the mass of the other roll is concentrated to the edge of the roll. If the two ...
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36 views

When will a moving vehicle stop faster: when the brakes are applied and the wheels are slipping, or just before? [closed]

When will a moving vehicle stop faster: when the brakes are applied and the wheels are slipping, or just before the wheels start slipping? Explain why.
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98 views

Physical Relevance of Classical Limit to QFT's

We know the physical relevance of the classical limit of quantum mechanics quite well. However, if I take the classical limit of a quantum field theory, the answer is not so clear. Suppose I take the ...
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Why Flow meters are some times showing -ve fluctuating Values in Pressurized Pipe lines [closed]

In our Underground Water reservior we are pumping water by Hydro-pneumatic pumps to maintain same pressure till last connection. in order to measure the flow we have installed precise electromagnetic ...
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294 views

Noether's theorem for space translational symmetry

Imagine a ramp potential of the form $U(x) = a*x + b$ in 1D space. This corresponds to a constant force field over $x$. If I do a classical mechanics experiment with a particle, the particle behaves ...
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How to derive kinetic energy from the Lagrange equations? [duplicate]

I'm having trouble deriving the kinetic energy from the Lagrange equations. For reference, I'm following Landau and Lifshitz book, "Mechanics," which can be found for free at Archive. In any case, I'...
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33 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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Pressurizing a circular toroidal shell

Consider a toroidal elastic, isotropic, homogeneous shell with a circular cross-section that is initially not pressurized. Under an internal pressure $p$, the shell might become more straight, but the ...
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77 views

Multiplying Lagrangian by a constant

Does a Lagrangian of a system multiplied by an arbitrary constant still work? If if I apply the Euler-Lagrange equations, do they still guarantee that the action is extremal? I arrived to the ...
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68 views

Wave equation in classical mechanics!

We represent the wavefunction of any wave on the string as $$y=f(x-vt),$$ where $v$ is velocity of the wave and $x$ is distance from origin and $t$ is time taken to reach the given point and $y$ is ...
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56 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 r}\...
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138 views

Airplane on a treadmill - Variant Thought Experiment

This thought experiment is in a way related to the (in)famous airplane on a treadmill problem. If you take a ball and place it on a treadmill, will the ball: Move backwards relative to the ground ...
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34 views

How the mechanical equivalent of heat is employed in this situation?

Reading a little about the "mechanical equivalent of heat" what I understood is that we can convert units between calorie and $J$ by setting $$1\mathrm{\ J} =4.1860 \mathrm{ \ cal}.$$ Now, I saw a ...
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1answer
41 views

water stream cut off abruptly; why there will occur sprinkling?

Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the ...
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3answers
159 views

What happens to the coefficient of friction as the normal force increases?

Does the frictional force increase as the normal force increases, or does the coefficient of friction get smaller in value?
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50 views

What to do when you're hit by another car? [closed]

I have a question about what's the "best" thing to do if you're about to be hit by another car. Imagine you're in your car, and you're at rest. There's another car coming at you, and they're going ...
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1answer
142 views

A mass hanging under a table: a problem from Goldstein [closed]

I'm trying to solve Problem 1.19 from Goldstein's Chapter 1 (2nd edition), and am getting bogged down in trigonometry (?). Please help me figure out what I'm doing wrong! Two mass points of mass $...
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337 views

In the Principle of Least Action, how does a particle know where it will be in the future?

In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
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25 views

Computing the value of an Action given some boundary conditions

Having being dealing with Actions for a while I have come across a question in which I am required to calculate the value for $S$ an action in the form of a function for some given boundary conditions....
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1answer
93 views

Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
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112 views

Quantum systems without a classical analogue? [closed]

I am now reading the quantum mechanics textbook by Dirac (chap. 4, $\S21$, p. 88). He says that his quantization procedure does not include all possible systems in quantum mechanics and there are ...
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1answer
44 views

Atmospheric pressure below sea level

If I go up in the air the amount of oxygen decrease and the atmospheric pressure gets lower. What would happen if i dig a hole 100 km down? does atmospheric pressure go up? when is the pressure so ...
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55 views

The coffee ring effect

Would spin coating a homogeneous solution of colloids also result in a coffee ring structure? Or is it just naturally drop casted evaporation methods that lead to the same.
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55 views

Solenoidal forces

As far as I know a solenoidal vector field is such one that $$\vec\nabla\cdot \vec F=0.$$ However I saw a book on mechanics defining a solenoidal force as one for which the infinitesimal work ...
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1answer
24 views

Can cyclic acceleration/deceleration be worse for fuel consumption?

Recently I have started to drive my car slower on the highway in order to save money on gas. However, I feel like I am spending at least as much fuel as before. One possible explanation that I thought ...
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33 views

Does vehicle tire mass effect efficiency?

This question has an interesting origin: A tire salesman was recommending tires (aka tyres) for a highly fuel-efficient vehicle. He said the vehicle was light (compared to most production cars), and ...
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Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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34 views

Does a ball thrown down exert less force on the ground when we walk? [closed]

Scenario A: You stand still and throw a ball vertically down. When the ball hits the ground it exerts a specific force on the ground. Scenario B: While walking you throw a ball vertically down. When ...
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1answer
61 views

How can we tell the potential from the orbit?

The orbit is $$r(θ) = a(1+\cos θ).$$ The orbit of the particle is in polar coordinates. How can we tell the potential $U(r)$ from this? $U(r)$ goes to zero at infinity.
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62 views

Cylinder rotating without slipping on an accelerating slab [closed]

I am very confused by the following problem asked in my first year physics class: Please let me know if you can assist in any way! I've spent hours and hours on this question and gained absolutely ...
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31 views

Relation between linear and rotational motion of molecules?

The temperature of a substance, such as an ideal gas, can be related to the root mean square speed of the molecules. For example, for gases the molecules travel at about 480 meters per second. If we ...
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3answers
116 views

Conversion of angular momentum to linear momentum in free space

If two objects both with angular and linear velocity collide in free space, can the total linear velocity of the objects increase at the expense of a loss in angular momentum? In other words, imagine ...
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0answers
36 views

In what cases do we use the Routh Function? [duplicate]

As many of you, I studied Lagrangian Mechanics and Hamiltonian Mechanics, with the so famous functions called Lagrangian $\mathcal{L}$ and Hamiltonian $\mathcal{H}$ related by: $$\mathcal{H}(q_i, p_i,...
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30 views

What is the displacement between highest points on a pendulum with discontinuous forcing? And is this dependent on gravity?

I know the question is worded horrendously, but my professor gives strange badly worded problems, so I've started to speak that way. It'll take a paragraph to pose this question properly. Consider a ...
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190 views

Is this a fundamentally relativistic phenomenon?

This question was inspired by some silliness in other threads but is independent of that silliness. Say that a train car sitting on a track is accelerated uniformly along its length if each point on ...
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1answer
41 views

How do I calculate the work done on standing an object upright?

So I was trying to figure out how much work someone does when they do a sittup or crunch. I guess to make things simple, I'm imagining a really really thin rod with some uniform mass lying on the ...
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0answers
29 views

General approach to Mechanics? [duplicate]

So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie... Lately, I am trying to find a way to "generalize" my ...
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1answer
94 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
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27 views

Which are the path variables in an intrinsic coordinate system?

This question concerns "path variables" or "intrinsic coordinates" or "normal and tangential coordinates" whichever you like to call it, in 3D. We have the three $path~~variables: (\alpha_1,\alpha_2,...
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46 views

Good books for understanding Lagrangian formulation of classical fields?

I want to understand Lagrangian formulation for classical fields and apply it to understand constrained dynamics. Currently I am referring to "A modern approach: Classical Mechanics" by ECG Sudarshan, ...
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1answer
46 views

Note and homework organization [closed]

I am currently in a mechanics class and have some trouble trying to figure out how I should structure my lecture notes and my homework. I recently began rewriting my notes after class but I am still ...
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1answer
68 views

Is the Impulse-Momentum Theorem True? [closed]

This is just a general question I want to throw out there, and see arguments from both sides... Is Impulse-Momentum Theorem True? Well in my opinion I would say yes because it is a derived equation: ...
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2answers
63 views

Can we measure the exact position and momentum of a ball by hitting it with other balls?

Imagine a billiard table that's is covered we can't see what's happening under the cover. Now imagine we throw in a ball whose throw in time, mass, size, position and velocity is unknown. To measure ...
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0answers
31 views

Energy-Momentum tensor for classical field with nontrivial boundary conditions

Question: Is there a energy-momentum tensor for the potential flow equations with a free surface under the action of gravity (ie the equations governing some types of surface water waves)? ...
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1answer
38 views

Internal energy. Mechanics and Thermodynamics

Internal energy is defined in thermodynamics as a function of state, in such a way that, in an adiabatic process, the variation of internal energy equals to the work done, regardless of the way it has ...
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1answer
109 views

Is there conservation of momentum if there's conservation of energy? [closed]

The equation for conservation of momentum: $$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{u}_1 + m_2\vec{u}_2$$ The equation for conservation of energy: $$\frac 12m_1v_1^2 + \frac 12m_2v^2_2 = \frac ...
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1answer
68 views

Torque and Force of Pulley fixed on side

If you had only 1 pulley that is connected to a rotating shaft, and which has a rope circled around it once, with a mass M on one side and with the rope fixed on the other end, how would you then ...
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14 views

Scattering in Higher Dimensions

In 2 dimensional scattering, if the scattering situation is reflexive about the beam axis then we can relate the differential cross section to the impact parameter via $$\frac{d\sigma}{d\Omega}=\left|...
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4answers
209 views

Is it correct to say Newtonian mechanics is a subset of Quantum mechanics?

I grew up in a three dimensional (3D) reality described quite well by Newtonian mechanics as opposed to the reality described by Quantum mechanics. That is I could go to bed at night without worrying ...
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3answers
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Why is response of system same frequency as driving force frequency

Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ...