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 aren't the weights of the beads considered in this equation?

I was solving this problem: A ring of mass $M$ hangs from a thread and two beads of mass $m$ slide on it without friction.The beads are released simultaneously from the top of the ring and slides ...
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2answers
54 views

Generalised velocities enough to be deterministic in Lagrangian mechanics?

In classical determinism we need to know $2n$ quantities of our system and the equation of motion to predict it's future. In Lagrangian mechanics this is equivalent to knowing $q$ and $\dot q$, the ...
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26 views

Beyond the third time derivative [duplicate]

Why do texts on classical mechanics never mention any derivative of position beyond the jerk, while at the same time being general in the sense of using of generalized coordinates?
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0answers
22 views

Book about fundamentals and concepts of classical mechanics [duplicate]

I want a book about fundamentals and CONCEPTS of classical mechanics. I have several books about classical mechanics, but all of them go directly to equations and applications. I don't know Really ...
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2answers
209 views

With a machete, why is a diagonal cut more effective than a right angle one?

When cutting back some thick growth in the garden a question that always nagged me. Why is cutting diagonally seemingly more effective than cutting at right angles? Part of the answer is obviously to ...
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1answer
1k views

What is an effective potential in classical mechanics?

What is an effective potential in classical mechanics? I have read the wikipedia article and David Tong's lectures notes, but I didn't understand how an effective potential simplifies a situation or ...
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4answers
699 views

Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)

It seems to me that Hamiltonian formalism does not suit well for problems involving instantaneous change of momentum, like particle collisions with hard wall or hard sphere gas model. At least I could ...
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236 views

Free energy of coupled classical harmonic oscillators

I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below: (image taken from ...
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115 views

Kater's pendulum graph

I was told that the graph of position vs period must be a straight line in Kater's pendulum, but my findings are more curved, also after searching in google graphs are like parabolas, my question is ...
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2answers
667 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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6answers
5k views

Why is superdeterminism generally regarded as a joke? [closed]

Before anything, I'm sorry for being an outsider coming to opine about your field. This is almost always a stupid decision, but I do have a good justification for this case. I've been reading about ...
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119 views

Variable tension in rope connected to mass

Problem 3.9 from Kleppner and Kolenkow's text An Introduction to Mechanics involves a uniform rope of length $L$ and mass $m$ that is connected at one end (its "bottom" end) to a block of mass $M$ and ...
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2answers
374 views

Are there any fully analytically solvable nonlinear oscillators?

I'm trying to find a simple one-dimensional problem, in which a particle would oscillate with some energy, and the period of oscillation would depend on particle energy (unlike in harmonic ...
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4answers
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How long it will take for a upright rigid body to fall on a ground

Let's suppose there is a straight rigid bar with height $h$ and center of mass at the middle of height $h/2$. Now if the bar is vertically upright from ground, how long will it take to fall on the ...
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2answers
104 views

Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ ...
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2answers
202 views

Is the Legendre transformation a unique choice in analytical mechanics?

Consider a Lagrangian $L(q_i, \dot{q_i}, t) = T - V$, for kinetic energy $T$ and generalized potential $V$, on a set of $n$ independent generalized coordinates $\{q_i\}$. Assuming the system is ...
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2answers
510 views

Why does a wind turbine have only three blades? [duplicate]

Why not four or five or even more? Intuitively, the more leaves the more power. So, what is the reason?
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2answers
96 views

Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
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2answers
268 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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What is the difference between configuration space and phase space?

What is the difference between configuration space and phase space? In particular, I notices that Lagrangians are defined over configuration space and Hamiltonians over phase space. Liouville's ...
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50 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
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0answers
98 views

What is the optimal slope for Archimedes screw?

The Wikipedia article has nice image showing how the Archimedes screw work: As I understand, the red balls do not fall down because they are in minima caused by the screw. Because of material ...
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37 views

Local conservation law involving Hilbert Transform in a classical field theory

Consider a nonlinear PDE of the form $$A_t +iA\mathcal{H}(|A|^2_x) +N(A) =0,$$ where the Hilbert transform $\mathcal{H}$ is defined as $$\mathcal{H}(|A|^2_x) \equiv P.V. \int_{-\infty}^{\infty} ...
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1answer
63 views

Tension along a curved surface [closed]

I'm curious what the tension in a rope will be when its exposed to a uniform load. Assuming a similar setup to this question what will the tension along the rope/tube be?
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21 views

Fun physics book for high school student [duplicate]

can anyone recommend me a physics book for a highschool student (not these typical school books) a book that will let you think mostly interested in theoretical /quantum physics done with the ...
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40 views

Bertrand's Theorem: Perturbative Methods Leading to $1/r^3$ Solution

My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While ...
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1answer
137 views

Preventing Heat Escape

Is is possible to completely prevent heat from escaping from a closed container? Here is a diagram of vacuum flask, which tries to implement the design - Vacuum Flask prevents heat from escaping ...
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85 views

Classical Mechanics — Sign of work done

It seems that work has two possible ways to decide it's sign: Whether you take the perspective of the system or the surrounding (whether you consider work done on the system as positive, or work done ...
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1answer
34 views

Comparison of the effects of collisions from an NFL Nose Tackle and a Car with roughly the same momenta

If you get hit an NFL Defensive Tackle who runs at roughly 17mph (7.6m/s) it'd hurt a lot, but if you got hit by a normal car at 1.3mph (about 0.6m/s) it hardly hurts at all, and a collision from an ...
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69 views

What is the meaning of this definition of potential energy?

The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
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2answers
92 views

Classical trajectories that are not a minimum of the action [duplicate]

Are there physically realizable dynamical systems where the true trajectory is not a minumum action trajectory? Formally, Lagrangian mechanics only requires that the trajectory be an extremum (or ...
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1answer
155 views

A course in Lagrangian Mechanics [duplicate]

I would like to know: what are some of the best introductory books to Lagrangian Mechanics?
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31 views

Why does not the optical fiber break? [duplicate]

Glass is a very fragile object. So why does not the optical fiber break? Everytime I take them, I am worried about this problem.
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0answers
54 views

Time evolution of a classical system [closed]

For a harmonic oscillator the Liouville operator is given by $$L = p \partial_q- q \partial_p.$$ Now I have a phase space distribution $f(t,q,p)$ for which it holds (in general) $$f(t+\tau,q,p)= ...
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132 views

Equations of motions uneven see-saw

How do I set up equations of motions for a see-saw where the distance between the masses $m_1,m_2$ to the pivot are given by $\ell_1, \ell_2$, respectively? My idea was to first set one of the masses ...
2
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1answer
100 views

Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
0
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2answers
241 views

Proof of vertical and horizontal velocity component in projectile motion

Why is it that $v\cdot sin(x)$ gives the vertical component and $v \cdot cos(x)$ gives the horizontal component, where $v$ is the speed? What logic is there behind it, or even better is there a proof ...
0
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1answer
50 views

Vector representation of angular quantities?

In the world of pure rotation, a vector defines an axis of rotation, not a direction in which something moves. Does it means that angular quantities like angular momentum, angular speed, torque etc ...
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0answers
18 views

Determining the range of values for separation angle (Landau problem)

I encountered a problem while reading the following exercise from the second Landau & Lifshitz volume: Determine the range value in the $L$-system for the angle between the two decay particles ...
2
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2answers
5k views

Rolling resistance and static friction

I am a bit confused about the relation between rolling resistance and static friction. I have often heard that it is the static friction that lets the wheel roll. Consider the following two cases: ...
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0answers
16 views

Effective length factor of a polymer in solution

If one wants to calculate the force needed to buckle a polymer in solution with Euler buckling, what would the effective length factor be? The polymer is free to move and rotate in solution as it sees ...
5
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1answer
126 views

Do vortex tubes work with a reversed end plug?

Would a vortex tube still work if instead of a cone plugged into the 'hot' end you had a smaller hole on the 'cold' end? As I understand it, the point of the cone on the hot end is to only allow the ...
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3answers
234 views

Having trouble understanding spectral lines

In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know ...
3
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1answer
119 views

Confusion about imposing constraint in the action

I'm totally confused by one thing. I know that I probably shouldn't be confused about that, but at the moment I don't quite know what fails in the following: Suppose we have a particle of unit mass ...
4
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3answers
379 views

Constructing Lagrangian from the Hamiltonian

Given the Lagrangian $L$ for a system, we can construct the hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
3
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1answer
69 views

Can a “flat function” be a particle trajectory? [duplicate]

Recently I came across the concept of a flat function, which is a smooth function $f:\mathbb{R}\to\mathbb{R}$ all of whose derivatives vanish at a given point $x_0\in\mathbb{R}$, the canonical example ...
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2answers
139 views

Definition for potential energy

I came across this definition for potential energy: If we let $T$ be the Kinetic energy, we have that: $$T = \frac{1}{2}mv^2 \implies T = \frac{1}{2}m{x'}^2$$ $$T'= mx'x'' = F(x)x' \implies \\T = ...
4
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3answers
282 views

Two different time periods for a movement with constant acceleration?

I'm studying for my physics exam and I keep running into the same problem. It's so specific I have no idea how to phrase it in a Google or stack exchange search, and I've already wasted 2 hours on it. ...
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2answers
180 views

Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
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4answers
6k views

Physics of the inverted bottle dispenser

When you invert a water-bottle in a container, the water rises and then stops at a particular level --- as soon as it touches the hole of the inverted bottle. This will happen no matter how long ...