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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9 views

Shear flow in J section type beam

What does the distribution of shear flow look like in a J section type beam. I'm only interested in a qualitative picture of it. I'm not interested in the calculations themselves. It is the top of the ...
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1answer
38 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
20 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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1answer
32 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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0answers
11 views

Possible values of coefficient of friction on a banked turn [duplicate]

From wikipedia http://en.wikipedia.org/wiki/Banked_turn : What if coefficent of friction $$μ_s=cotθ$$ What would equation (1) mean then ? and What about the magnitude of frictional force ?
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78 views

Lagrangian perturbation theory

So I have been playing around with perturbing a known Lagrangian $ L_0(\boldsymbol {q_0},\boldsymbol{\dot q_0})$ with $L_1(\boldsymbol q,\boldsymbol{\dot q})$ but I am not really sure of some points ...
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2answers
45 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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16 views

Bead and Disc with a String [on hold]

I want to know about the path the bead follows, and whether tension increases , decreases or remains constant and work done by tension (along with analysis and reasoning).
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1answer
57 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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2answers
70 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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0answers
26 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
33 views

Time evolution of a classical system

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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1answer
19 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 ...
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2answers
49 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 ...
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37 views

EDIT: Intuition behind divergence theorem and gravitational field [closed]

If we have planet (sphere) made out of two materials-metal and wood. One half is made of wood and the other one made of metal. So why does not the metal part pull the object in the gravitational field ...
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14 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 ...
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0answers
6 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 ...
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1answer
31 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
36 views

question regarding work energy theorem [closed]

The question says A smooth track in the for of a quarter circle of radius 6 lies in the vertical plane. A ring of weight 4N moves from $P_1$ to $P_2$ under forces $F_1$,$F_2$ and $F_3$. $F_1$ is ...
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0answers
45 views

фкуDoppler Effect on Standing Waves [closed]

The Two oppousing harmonic waves are interfere with each other , producing a Standing wave. What are will be a Galileo Transformation for a Standing Wave , including it`s Phase Velocity and Group ...
3
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1answer
66 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 ...
3
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1answer
58 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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3answers
74 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 ...
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2answers
74 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 = ...
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3answers
208 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 ...
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3answers
187 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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1answer
132 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence ...
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2answers
89 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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2answers
28 views

Kinetic energy dissipation in braking a vehicle

Let's say a vehicle that weighs 20t is hauling along at 50m/s and we want to brake it down to a full stop. The kinetic energy we need to dissipate into heating up the brakes is ...
3
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2answers
84 views

Derivation of law of inertia from Lagrangian method (Landau)

I'm reading Landau's Book. He tries to conclude the law of inertia from the Lagrange equations. For that, he argues (by nice suppositions about space and time), that the lagrangian must depend only ...
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1answer
35 views

How does the masless pulley gets the force from rope?

I have seen whenever we solve for forces on pulley by rope we take the force on pulley exactly as the tensions in the rope around it. But , why do we do this ? Exactly how does the rope exerts forces ...
2
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2answers
99 views

Detailed conditions for symmetries of Lagrangian

Edit: To clarify the question, I am asking why we are justified in calling a continuous symmetry a symmetry of a system when it changes the Lagrangian by a total derivative of a function of $t, q(t)$ ...
1
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1answer
48 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction ? If so why ? Please try to give a different ...
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25 views

How is angular momentum conserved in this proton+water scenario?

Consider a universe consisting of only one water molecule and one proton. ...
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2answers
44 views

When considering the acceleration as constant? [closed]

I'm solving a simple dynamic exercise, exercise says: "What is the absolute value of the force necessary to speed up a 500kg mass subject to 1600km/h in 1,8s, with the object from rest?" Then I had ...
4
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0answers
153 views

What exactly is the relationship between the symplectic 2-form and the frequency of leaves of integrable systems in classical mechanics?

In classical mechanics we equip a differential manifold with a closed symplectic 2-form $\omega$. The symplectic leaves of integrable systems also have a unique frequency, in literature denoted ...
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3answers
2k views

Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?     ...
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1answer
49 views

By what factor would you have to slow down time for water to feel like glass?

I have been told that though glass seems like a solid, it is somehow, in theory, a liquid -- but is just somehow a liquid that is so thick that it appears to be solid. (Of course --- if this premise ...
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0answers
21 views

Bezier curve and deceleration

I have a question regarding calculation of a bezier curve. I'm programming an app where in there's continuous straight line motion of a vehicle at a constant speed. (Let's call it 'u'). When the user ...
0
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2answers
53 views

Converting Pendulum into Electricity? [closed]

I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and ...
2
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0answers
69 views

Is there any physics arguments behind NASA pen joke

I am just wondering are there any reasonable physics arguments behind difficulty making pen for no gravity conditions. My thoughts are that there are many ways to make it working as: Pressurized ...
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1answer
41 views

Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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0answers
23 views

Integral of absolute value of spin angular momentum of $N$-body system

There are $N$ particles moving freely in a plane. Let $J(t)$ be the spin angular momentum of the system of particles about its center of mass. (even center of mass keeps changing with time as ...
1
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0answers
35 views

Normal coordinates for harmonic approximation (classical lattice vibration)

I am reading Jenő Sólyom's "Fundamentals of the Physcs of Solids" vol. 1. and i am very much stuck at this point (chapter 11.3.2 in the book): In the harmonic approximation the potential energy of a ...
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0answers
31 views

Cylinder swinging in a halfpipe [closed]

I'm having a problem while solving this exercise: Consider a cylinder of radius 'a' swinging in a halfpipe whose radius = 10a. Find the equation of motion of the cylinder using the angle $\phi$ ...
0
votes
1answer
45 views

Potential for particle rolling down slope of arbitrary shape

I've been thinking about how to calculate the potential $V(x)$ of a particle rolling under the force of gravity down some curve, given by $f(x)$ (suppose nonincreasing). My idea was to simply ...
0
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1answer
30 views

Minimum distance between two bodies attached by a spring

Take two bodies of masses m and M attached by a spring of constant K on a smooth horizontal surface. The system is at rest. A constant force F acts on body M, horizontally. To study the motion of the ...
1
vote
1answer
24 views

Why is a bending rod assumed to be undergoing torsion?

If I take a rod and bend it at both ends as far as it will go, why is there an assumption that I am also exerting a torsion along with my bending? Referencee: ccording to the third edition of "Theory ...
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2answers
43 views

confused about the direction of friction force

I'm really confused about the direction of friction force. I think about collision of two balls and think that "friction force is opposite to the relative speed of the contact point of the two ...
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0answers
24 views

Conserved charge for boosts? [duplicate]

In (3+1) dimension Poincare group has three types of Symmetries : a) Four space-time translations b) Three spatial rotations and c) Three boosts Among them, (a) implies "conservation of ...