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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momentum and energy of the rods

I have two electromagnets and I attach them to two rods(same mass) such that, first one will be attached to centre of first rod and the second one will be to the end of second rod. Now I bring them ...
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111 views

Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$ EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1 $$ Where, $E$ is modulus, $I$ is second moment of ...
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106 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
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95 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
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73 views

Equilibrium in Stat Mech and Phase space density

I was wondering if there is any relationship between equilibrium in Stat Mechanics and the phase space density of a system? This does not seem to be completely independent, as Entropy is maximized in ...
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119 views

Euler-Lagrange equations of a current-loop pendulum in a magnetic field

I am reading "Nonlinear Electromechanics", by Dmitry Skubov and Kamil S. Khodzhaev, Springer 2008. Here is the relevant and freely available chapter. Essentially, a loop of area $S$, mass $m$, moment ...
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I need help figuring out what is wrong in this aspiring perpetuum mobile

Credits: My question is motivated from a question from another user (One disk/ring in double rotation and sum of energy), I just reformulated what I think he tried to ask into, what seem to me, ...
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129 views

Langevin equations in translational and rotational direction

I want to describe the following system. A bead is connected with a tether. There is a force $\vec{F}_{up}=F_{up}\hat{y}$ that acts on the bead. The tether acts with a force on the bead, this force ...
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424 views

Understanding Poisson brackets

In quantum mechanics, when two observables commute, it implies that the two can be measured simultaneously without perturbing each other's measurement results. Or in other words, the uncertainty in ...
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37 views

Trying to model the acceleration of a system due to an impulse forcing function

My team and I are working on a design project to design/modify a device that can go on hikes for paraplegic/quadriplegic people. Here is the current design (not designed by us): We are thinking ...
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62 views

Power dissipation in High Voltage Cables

I was doing the following physics problem in physics class: You have two dimensionally identical pieces of metal, one made from aluminium the other made from iron. It is given to us that ...
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179 views

Finding the maximum extension of a Spring

I have solved that after the body m1 hits m2, the velocity of m2 is going to be (3/4)*v0. I did this by using the law of conservation of momentum and using the coefficient of restitution (relative ...
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67 views

Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
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2answers
187 views

modelling elastic collisions and reflection from wall in 1-d box of two particles

I have a very simple system of two particles. Particle $A$ and particle $B$. Particle $A$ is acted by constant potential along wall $C$ while no potential is acted on particle $B$. If they both ...
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3answers
236 views

Steering a motorcycle

From my experience riding, at low speeds (between 0 and 10 mph) you mostly steer the bike with the handlebars. What I mean by this is if you want to turn left you rotate the handlebars ...
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3answers
87 views

Point, bar and a mass

This question is a simplified down version of my first question to understand the core essentials of my question. The question now stands with the simplified diagram: There are three things in the ...
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4answers
421 views

Is there a fundamental reason not to define the work vice-versa

My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as: $$W=\int_\Omega ...
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2answers
86 views

A question regarding 3 bodies connected as a system

Let us consider three bodies of equal mass connected to each other with 2 ideal strings of length l. The three bodies are placed in a straight line In this arrangement there is 1 body connected to 2 ...
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137 views

Importance of periodic orbits

In the study of dynamical systems, one often talks about solutions that repeat themselves after a certain time, hence their name of "periodic orbits". Then one moves to the distinction of "stable" ...
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98 views

Rigorous version of field Lagrangian

In Classical Mechanics the configuration of a system can be characterized by some point $s\in \mathbb{R}^n$ for some $n$. In particular, if it's a system of $k$ particles then $n = 3k$ and if there ...
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69 views

Superfluid rotating frame of reference

I'm currently studying a text about Bose-Einstein condensates (BECs) and vortices. When they want to study whether a vortex will be formed, they look at the fact wether it's enegetically favorable. ...
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88 views

Why doesn't a Brownian ratchet provide free energy?

A Brownian ratchet is described here at Wikipedia. The "why it fails" section reads: Feynman demonstrated that if the entire device is at the same temperature, the ratchet will not rotate ...
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1answer
66 views

Why does a gear rotating around another gear rotate twice as fast around its own center?

Take two gears: One is fixed, the other rotates around it. If the gears are the same size the rotating gear has to rotate around its center twice as fast as it rotates around the other gear. I'm ...
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Precession of relativistic orbit in pure inverse-square force [closed]

PROBLEM: Show that Special Relativity predicts a precession of $\pi (GMm/cl)^2$ radians per orbit for any elliptic orbit under a pure inverse-square force. Where $G$ is gravitational ...
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68 views

why ostriches cannot fly? physics explanation

I'm looking for a physics explanation concerning to the fact "The ostriches cannot fly". My statments: During the time interval $\Delta$t of the upward wingbeat, the ostrich drops a distance h ...
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1answer
45 views

Can this type of graph be analysed to produce any meaningful data?

The above is a graph of pendulum length on the x-axis measured in metres, and pendulum period on the y axis measured in seconds. The pendulum period is not squared. I know that if I square the ...
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91 views

Finding potential energy of a solid hemisphere on top of another solid hemisphere [closed]

A solid hemisphere with radius $b$ has its flat surface glued to a horizontal table. Another solid hemisphere with radius $a$ rests on top of the hemisphere of radius $b$ so that the curved ...
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72 views

Finding the initial velocity of a vertical circular motion [closed]

A particle P is suspended from a fixed point O by a light inextensible string of length a. When hanging at rest under gravity at A it is given a horizontal velocity u. The particle moves freely ...
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62 views

Separating the potential energy of a system of particles.

Assuming all forces derive form a conservative source and that all forces observe the strong form of the third law, how do we arrive at the following equation? \begin{equation} V=\sum _i V_i+\frac ...
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259 views

Two carts connected by spring on frictionless track

I have the following homework problem: Consider two carts of equal mass m on a horizontal, frictionless track. The carts are connected by a single spring of force constant k, but are otherwise ...
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4answers
129 views

Mathematical Reasoning for Fluid Pressure as a Scalar

This question from a while ago and answers/comments to this question from earlier today both make heavy mention of the fact that fluid pressure is a scalar. Although this information was surprising ...
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54 views

Latent heat of solidification

What is the heat release mechanism involved in solidification from liquid phase? Is the energy transferred to nucleation centres?
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80 views

The classical hydrogen atom

Suppose we want to analyze a hydrogen atom using purely classical mechanics. This obviously is not exactly how things work - quantum mechanics plays a huge role and probability distributions are ...
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25 views

Strain-Displacement relationship symmetrization

In the context of infinitesimal elastic strain theory, one writes the relationship between displacement and strain as $$ \epsilon_{ij} = \frac{1}{2}( \frac{\partial u_i}{\partial x_j} + ...
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Action principles and covariant equations [duplicate]

Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a ...
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88 views

Landau Mechanics equation 16.9

I am having trouble deriving the equation 16.9 from Landau's Classical Mechanics book. This equation is the maximum kinetic energy of a particle if a massive particle with mass $M$ disintegrates into ...
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1answer
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Forces Create Angular Acceleration And “Straight” Acceleration - But How Much Of Each?

Let me set up the following problem for a rectangle floating in space: We know its dimensions. We know its mass. There's a force pushing it for a known amount of time - we know the angle & ...
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2answers
103 views

Conservative force as a potencial energy gradient

A conservative force $\vec{F}$ is apparently defined as the gradient of a potential energy $U$: $$\vec{F} = -\nabla\ U$$ I am curious if this definition was originally used to describe a ...
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641 views

Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is ...
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4answers
504 views

Non-linear systems in classical mechanics

In general, what is meant by non-linear system in classical mechanics? Does it always concern the differential equations one ends up with (any examples would be greatly appreciated)? If so, is it ...
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3answers
65 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
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1answer
153 views

Equation for Terminal Velocity on an inclined plane and the time it takes to reach it

Now I'm doing a research on the matter similar to this thread : Terminal Velocity of identical shape/size objects which is very self explanatory and very helpful. However in my case, the objects will ...
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2answers
267 views

What's wrong with my derivation for the spring constant? [duplicate]

An $8.00\ \mathrm{kg}$ stone at rest on a spring. The spring is compressed $10.0\ \mathrm{cm}$ by the stone. What is the spring constant? I used conservation of energy to solve this problem. The ...
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1answer
87 views

Pressure inside a plastic bottle filled with water and squeezed by X weight?

I'd like to know how it'd be possible to calculate the pressure inside a plastic bottle filled with water and squeezed by say 20 kg sitting on the bottle, which is lying on its side (so that ...
3
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1answer
74 views

Non-deterministic particle system

This question is in the spirit of Norton's dome, an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the Picard–Lindelöf theorem guarantees the ...
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2answers
146 views

Isolated and non-isolated systems: Momentum?

I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the ...
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2answers
102 views

Pulling on a weakened rope - where will it tear?

Let's say I have a rope of 10m length and it is weakened in 3 spots: at 2.5m, at 5m and at 7.5m. Weakened means that if enough tension is applied it will tear at these points (all points are equally ...
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1answer
147 views

Two masses on frictionless table with one string connecting both masses on ground and the other string [closed]

From Morin's Introduction to Classical Mechanics page 342: A solid cylinder of mass $m$ and radius $r$ lies flat on frictionless horizontal table, with a massless string running halfway around ...
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Robot speeds in body frame

I am building a robot with two wheels (and differential drive) and I am trying to make it have the same performances over very different loads (an order of magnitude between the ), so I decided to try ...
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Should the liquid come out of the tank if a hole is drilled in the vertical wall?

This is a tank filled with water kept on ground. The points $A$ and $B$ are at 'same horizontal level', hence, as per an interpretation of pascal's law, pressure at $A$ must be equal to the pressure ...