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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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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25 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
95 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
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260 views

Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
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48 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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74 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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70 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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120 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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28 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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1answer
146 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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40 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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26 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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84 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, $r$. ...
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59 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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36 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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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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2answers
3k 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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39 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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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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174 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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113 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
81 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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1answer
82 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 ...
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3answers
223 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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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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83 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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196 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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97 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
2k 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 ...
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2answers
446 views

Pendulum Wave Period

Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$. I am trying to work out the relationship ...
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1answer
93 views

buckling of tube - shell thickness vs. momentum of inertia optimum

is there any simple formula (perhabs semi emperical, or aproximatively derived model) for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly ...
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5answers
599 views

Is an “infinitely sharp blade” possible?

A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to ...
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159 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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30 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 ...
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2answers
95 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
55 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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1answer
42 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 ...
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49 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 ...
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5answers
219 views

Why is a beam reach the fastest point of sail on modern sailboats?

I've heard that a beam reach (perpendicular to the wind) is the fastest point of sail on modern sailboats, but I haven't heard a satisfying explanation of the physics behind the claim. Triangular ...
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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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51 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 ...
5
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1answer
229 views

Symplectic leaves, tori and Poisson manifolds

For classical systems we can define a configuration manifold, whose cotangent bundle is a momentum phase space equipped with a closed, non-degenerate 2-form. Upon the commutative algebra of smooth ...
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27 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 ...
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1answer
49 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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2answers
64 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
74 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
149 views

Do waves accelerate?

Typically we think of acceleration as a particulate property but a previous question on this forum got me thinking. If we think of a wave increasing its velocity by increasing its energy/frequency ...
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3answers
6k views

Finding Lagrangian of a Spring Pendulum

I'm trying to understand Morin's example of a spring pendulum. What I don't get is his expression for $T$. I can understand the $\dot x^2$ term in the brackets. But I don't understand the $(l + ...
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29 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 ...