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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Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything? [duplicate]

Assuming that I learn Quantum Mechanics first, and then I approach Classical Mechanics as a special case of Quantum Mechanics, I will definitely find the relationship between Quantum Mechanics and ...
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234 views

Equation of a flying kite

My question is the following: What is the shape of the rope which holds a kite flying? (Steady state.) I am not a physicist (I am a mathematician), so I can not work the physics part of the question....
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Correct way to include constant external force in virial and pressure calculation

Halo, given a simulation cell with N particles where particles interact only with bond and pair potentials and periodic boundary conditions (minimum image convention) are used. On a subgroup of ...
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1answer
102 views

Two masses collide on a ramp [closed]

M1 slides down a frictionless ramp and collides with M2 They both compress the spring. How far is the spring compressed? What is the final velocity of M1 on the rebound up the ramp? I was thinking if ...
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3answers
11k views

How to calculate the moment of inertia of a solid cube

How do I calculate the moment of inertia of a uniform solid cube about an axis passing through its center of mass? I also wanted to know if the moment of inertia ...
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214 views

Angle rotated by a rod when it's hit by a pendulum

Consider a pendulum of length $h$ with a bob of mass $m$ it is held horizontally at and angle of $90^{\circ}$ with the vertical. A rod of mass $M$ and length $h$ is pivoted at its upper end and this ...
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110 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
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1answer
942 views

Modeling a 2-dimensional mass spring system

First of all, I am unfortunately not an expert in physics, so please be indulge with me. I am trying to model a $2$-dimensional mass-spring system with $1$ mass and $3$ springs to solve a dynamics ...
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1answer
92 views

$\cos^{2}(\phi)$ in the kinetic energy term of the Lagrangian is one?

I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing. The kinetic energy I'm using ...
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1answer
232 views

From Lagrangian to equations of motion [closed]

I have a given Lagrangian: $$L= e^{st}\cdot\frac12\cdot(mv_y^2-ky^2)$$ And are asked to identify the equations of motions, the constants of motions and physical system. Without the exp-time-term, ...
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3answers
404 views

A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]

I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was ...
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1answer
989 views

Pendulum with a rotating point of support from Landau-Lifschitz

I found this problem in Landau-Lifschitz vol.1 (Mechanics) A simple pendulum of mass $m$, length $l$ whose point of support moves uniformly on a vertical circle with constant frequency $\gamma$. $$...
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328 views

Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
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121 views

Impulse & Momentum

please could someone check this MIT video (http://www.youtube.com/watch?v=Lkuo6nZ6nZM) at 26mins 31secs. He says that if you threw a tomato on a bathroom scale then you would get a certain force ...
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154 views

Lagrangian formalism and Contact Bundles

In his Applied Differential Geometry book, William Burke says the following after telling that the action should be the integral of a function $L$: A line integral makes geometric sense only if it'...
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61 views

Good Source to Understand Angular Momentum [duplicate]

I am looking for a good source to understand angular momentum. I know the basics but I am looking for a sound in-depth knowledge like directions of angular momentum, when it is not parallel to angular ...
0
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1answer
82 views

Power and speed [closed]

I'm asked to calculate how much POWER a 1210kg car needs to drive with a 85 km/s speed up a 655 meter long slope of 4.5°. I can find how much energy and work is required to do this, but isn't POWER=...
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88 views

Bullet energy loss in solid materials [closed]

Does someone know simple model of energy loss in solid materials for a solid bullet? For example: I want to estimate momentum transferred to a thin plastic plate given by a small bullet. No matter ...
0
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1answer
162 views

Classical disintegration of particles, Landau-Lifshitz series on Physics

i read Landau's book recently. In this book p.43 Landau says from (16.1) (16.2) can be write down $T_10$= $p_0^2$/2$m_1$=($M-m_1$)($E_i-E_1i-E_i'$)/$M$ For me, it is hard to understand the factor ($...
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1answer
269 views

Moment of inertia of a system in different cases

A rod of mass $m$ and length $l$ is pivoted at one end to ceiling and free to rotate in the vertical plane. A disc of radius $R$, which is less than $l$, can be fixed at its other end in 2 ways : ...
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1answer
509 views

Why does a car bonnet (hood) rise when you connect the clutch with a brake on?

Is the rotational force to overcome the brakes moved to the opposite effect of moving the car chassis, until the brake is released?
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Do we need inertial frames in Lagrangian mechanics?

Do Euler-Lagrange equations hold only for inertial systems? If yes, where is the point in the variational derivation from Hamilton's principle where we made that restriction? My question arose ...
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678 views

Why is classical mechanics determinism based on position and momentum only and not forces and scattering rules?

Consider a closed system (say a box) of $n$ particles. There is a well-known idiom/meme/law in classical mechanics that says that the position and momentum of those $n$ particles is all that is needed ...
6
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1answer
233 views

Why isn't $F = \frac{\partial \mathcal{L}}{\partial q}$?

If momentum is, $$p = \frac{\partial \mathcal{L}}{\partial \dot{q}}$$ and force is, $$ F = \frac{dp}{dt}$$ and by Euler-Langrange equations, $$ \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial \dot{...
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194 views

Conceptual question on superposition of forces holding a specific mass in equilibrium

Consider a point mass $x$ (like for example the earth in space) and let $A$ and $B$ be two sets of point masses which each hold the point mass $x$ in equilibrium, meaning the acceleration induced by $...
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91 views

The superposition of force (or acceleration) configurations

My question is quite specific as it refers to this article but I hope that someone here could help me. I cite the relevant part of the article: ... The second example consists of gravitational ...
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1answer
907 views

Why don't clouds fall? [duplicate]

Well I do know that they sometimes fall as rain, but my question is why don't the droplets fall as soon as they condense from steam to cloud. Clouds are white by the process of Mie scattering so the ...
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3answers
2k views

Where is the energy lost in a spring?

Thinking about springs, and their extensions, I recently came to a confusion which I hope this wonderful community can help me solve. The question is this. When the block is initially attached to ...
5
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1answer
253 views

Stress calculations in a perforated paper

You have a sheet of paper (torn out of a good quality foolscap notebook) as shown above, and you start pulling it apart with both your hands (forces indicating by the blue arrows). Its difficult to ...
2
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1answer
383 views

Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
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1answer
106 views

Kinetic energy and temperature

I've randomly been thinking about smoothies and internal energy all weekend. If we have an assortment of fruit in the solid phase and then proceed to blend it all so that it ends up being in the ...
5
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1answer
250 views

How Hamilton's Principle was found?

Hamilton's principle states that the actual path a particle follows from points $p_1$ and $p_2$ in the configuration space between times $t_1$ and $t_2$ is such that the integral $$S = \int_{t_1}^{...
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1answer
193 views

What is the neatest way to describe a “non-autonomous” (lagrangian) system?

The configuration space of a system of particles $(m_i,x_i)$, $i=1,\dots,n$, subject to constraints $$\Phi (x)=0,\qquad \Phi\colon \mathbb R^{3n}\to \mathbb R ^{3n-k},\qquad x=(x_1,...,x_n),$$ if the ...
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288 views

Is rotational motion conditioned to a central force?

We know rotational motion as a combination (a resultant) of two effects the tangential velocity and a centripetal force. Does rotational motion turn into linear motion at the same instance this ...
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13k views

Why does the tension on the pulley in an Atwood machine not equal $(m_1 + m_2)g$?

Consider the following simple Atwood machine with an ideal pulley and an ideal string According to my textbook, the tension on the clamp that holds the machine to the wall equals $2T$. I don't ...
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2answers
129 views

How to derive energy expressions thinking of it as a conserved quantity only?

By now I understand that "energy is a conserved quantity" and that's all we need to know. Then, the idea of work comes as the change in kinectic energy of a system and we realise that having energy is ...
0
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1answer
399 views

Calculate integral of motion condition with Poisson brackets

Problem statement: The Hamiltonian of a system is given by the formula: \begin{equation*} H = \frac{p_r^2}{2m} + \frac{p_\theta^2}{2mr^2} + V(r,\theta). \end{equation*} Under what condition is $f=p_\...
5
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1answer
386 views

Why must allowable physical laws have reversibility?

I'm watching Susskind's video lectures and he says in the first lecture on classical mechanics that for a physical law to be allowable in classical mechanics it must be reversible, in the sense that ...
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160 views

Idea of integrable systems

I do not quite understand the idea an integrable dynamical system. Does it mean that the EOMs are analytically and exactly solvable? What are the necessary and sufficient conditions such that a system ...
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1answer
259 views

Rope on an inclined plane problem

My book says the answer is (a)zero but i don't understand how it came zero. What will the acceleration if horizontal level of the two ends of the rope are different?
2
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1answer
647 views

Is there a better choice of coordinates for a bead on a rotating helical wire?

A bead of mass $m$ is threaded around a smooth spiral wire and slides downwards without friction due to gravity. The $z$-axis points upwards vertically. Suppose the spiral wire is rotated about the $z$...
3
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2answers
3k views

Euler-Lagrange equations and friction forces

We can derive Lagrange equations supposing that the virtual work of a system is zero. $$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\...
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1answer
102 views

Power of viscous friction on a falling sphere

I have derived a simple model of a rotameter using an homogeneous solid ball in a rigid cone where a fluid flows. I consider 4 forces: Weight, Buyancy, Viscous Friction and Drag. I have written my ...
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1answer
129 views

Canonical partner of time in QFT and string theory

In analytical mechanics, the Hamiltonian or total energy becomes the conjugate momentum of the time in the symmetric form of the equations. This seems very strange and interesting to me. Does it have ...
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2answers
348 views

Electrical analogy for stress and strain

It feels like the relation between stress and strain (and other mechanical properties) is analogous to that of some electrical properties (voltage and current?). I'm comfortable with electrical ...
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1answer
523 views

The most stable way of standing in a bus

Here's what's bugging me for quite a long time. Imagine the every day situation, that you are standing in a bus with your back on wall having only limited space on the floor and no handle to hold. You ...
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198 views

Virtual-work problem [closed]

I have a very specific doubt about the next exercise: I have the crane of the picture: With a force $F_a=-K\varphi$ Applied on the point B, perpendicular witch AB, and another force $F_b=-K\psi$ ...
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1answer
166 views

Is there a Lagrangian whose Euler-Lagrange equation is the gradient?

I am trying to recast a problem I am working on in terms of Lagrangian mechanics. I am in the following situation. Suppose I have a function $f:X \rightarrow \mathbb{R}$ (a field). In the its ...
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1answer
169 views

Canonical transformations in Hamiltonian mechanics

How to prove that in the new Hamiltonian, which is formed by any of the generator function will not contain $Q$ (transformed from $q$)? I.e. new Hamiltonian will only be a function of $P$ (transformed ...
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33 views

Could each non-dependent physical contant represent dimentions, and our universe be a point on this n-dimentional structure?

For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity. Our Universe would be at a point on this range (equal to our G value) where ...