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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Approximating energy loss caused by drag force

We know the usual aerodynamic drag equation is given by: $$F_d = -bv^2$$ Where $b$ here is just some constants combination related to the property of the fluid and the material passing through. My ...
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1answer
21 views

Which of the Physics textbooks would you recommend I read this quarter (Analytical Mechanics)? [duplicate]

My Analytical Mechanics class this quarter has one required textbook: "Classical Dynamics of Particles and Systems" by Thornton & Marion and three recommended readings: "Mechanics" by Landau ...
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1answer
82 views

Momentum is a cotangent vector?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...
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1answer
40 views

Determine the equation of motion

The problem is the following. A ring of mass $m=1$ is moving along a circle of radius $R$ without friction. It's tied to a spring (coefficient $k$) of natural length $0$. The other end of the spring ...
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9answers
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+200

Can a car get better mileage driving over hills?

Two towns are at the same elevation and are connected by two roads of the same length. One road is flat, the other road goes up and down some hills. Will an automobile always get the best mileage ...
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3answers
232 views

Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice) I understand it being related to the resistance caused by fluid in the ...
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1answer
31 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
2
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1answer
147 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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1answer
41 views

Definition of kinetic energy without the second Law of Newton

As I see it, the definition of kinetic energy $$T= {1\over2} m u^2 \text { where $u<<c$}$$ comes by using the definition of work $$W= {\int F\cdot\ dx }$$ and we use for the meaning of ...
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2answers
55 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
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0answers
45 views

The position vector of particle in horizontal wire [on hold]

A particle of mass $14~\text{kg}$, slides along a straight wire in a horizontal plane. The coefficient of dynamic friction $\mu_k = 0.6$ The equation of the line of the wire is $y = \sqrt{3}x$ so ...
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2answers
55 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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133 views

Is it possible to write explicitly the exact solution for forced damped harmonic oscillator?

Preamble Consider a damped harmonic oscillator, with his well know differential equation \begin{equation*} m \ddot{x} + c \dot{x} + kx=0 \end{equation*} and let's find the solution that satisfies ...
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0answers
30 views

Calculus in Problems in General Physics by I.E.Irodov [on hold]

My teacher recommended me about Problems in General Physics. I am 11 grader and master school level calculus. So far I solved dozens of problems in the mechanics section. I also encountered problems ...
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1answer
25 views

What is a “Reversed Effective Force”?

I have some confusion about the "Reversed effective force" as it appears in the derivation of D'Alembert's principle. First I have sources that seem to be contradictory. ...
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2answers
65 views

What is the significance of angular frequency $\omega$ with regards to wave functions?

What is the physical significance of $\omega$ in a function like $$ f(x) = Asin(kx + \omega t) $$ The only place that I am familiar with angular frequency is when dealing with circular motion, but ...
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0answers
21 views

Fluid flow: Force acting on the fluid and the Navier-Stokes equation

Consider a one dimensional fluid flow in a rectangular tube. Typical streams are the poiseuille streams. Consider the case in wich we apply a force on the fluid. The Navier-Stokes equation is ...
8
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1answer
98 views

What is the physical interpretation of the Poisson bracket [duplicate]

Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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0answers
22 views

Ratio between power of chaotic and regular airflow

Turbulent field is created as a result of an impact of an airjet on an edge (the flow velocity is high enough). The field of velocities have a regular and a chaotic component. What I need is to ...
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2answers
167 views

Can we describe the classical laws of physics in a frame-of-reference-independent way?

First of all, I am not a physicist, so I cannot guarantee things I say will make sense. I will try my best, though. In classical mechanics we have the notion of inertial frame of reference. If my ...
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1answer
345 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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4answers
393 views

Is this solveable? Simultaneous elastic collision of 4 objects in XY plane

I'm writing a computer program/game and can't figure something out; I want to be able to calculate the resulting velocities of 4 particles (hexagons, specifically) after they simultaneously ...
2
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2answers
64 views

Does the second law of thermodynamics take into consideration interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...
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1answer
63 views

Relative kinematics and laws of Newton

I am an engineering student and currently taking a class on kinematics and dynamics. I study at a German university so it may be that I don't translate everything correctly. In the first module of ...
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2answers
224 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
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2answers
91 views

Maximum Extension of a Spring [closed]

In the given figure: m= 5kg, F = 30N, K = 700N/m In the figure shown above. the surfaces are friction-less. The blocks are initially at rest and the spring is initially in its natural length. What ...
3
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1answer
378 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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2answers
66 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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2answers
81 views

Explain how waves have momentum?

A question on a practice test I'm taking is as follows: By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries: A. mass B. energy C. momentum D. ...
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2answers
427 views

Heisenberg picture of QM as a result of Hamilton formalism

Consider the formula for the total time-derivative of a physical value in Poisson's formalism: $$\tag{1} \frac{dA}{dt} = -\{H, A\}_{P.B.} + \frac{\partial A}{\partial t}, $$ where $\{A, B\}_{P.B.}$ is ...
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2answers
79 views

Phase space Lagrangian?

Reading out of this lecture series we define a phase space Lagrangian $\mathcal L$ to be a function of $4n+1$ variables namely $q,\dot q,p,\dot p,t$. My question is, what space is this function ...
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4answers
2k views

How far does a trampoline vertically deform based on the mass of the object?

If a baseball is dropped on a trampoline, the point under the object will move a certain distance downward before starting to travel upward again. If a bowling ball is dropped, it will deform further ...
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1answer
66 views

Can we disconnect an object from the pull of gravity using some material? [duplicate]

I have once come across a material/ substance/ compound, or something, that cuts off objects from Earth's gravitational pull. In other words, it would keep the object suspended in the air and will ...
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1answer
32 views

Mechanics Question Help? [closed]

I have this question that has been puzzling me for a while, I can find the net force acting or at least express it at $6.5974-{F\over m}=a$ but can't find any way to calculate or use this to find a? ...
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0answers
31 views

How to find the velocity ratio of a pulley system? [closed]

How would you draw a labelled diagram of a pulley system with a velocity ratio of 5? How would you relate a pulley system to its velocity ratio? How would that diagram even look All I know is that ...
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0answers
30 views

Rotating rod assembly, finding the force reactions at the bearings [closed]

I need help with this problem. The solution given in my text book is very bare bones and I don't understand it. I'm have trouble with finding the moment of inertia and products of inertia. Any ...
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0answers
48 views

Lagrangian of constrained point mass [closed]

I'm trying to learn calculus of variations independently and I'm trying to solve this interesting looking problem 18.5.13 from Weber Essentials of Math Methods for Physicists (google preview here) but ...
7
votes
3answers
3k views

Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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1answer
89 views

Coupled wheel and rod (analytical mechanics)

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
2
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1answer
56 views

When can an autonomous system be written using a Hamiltonian?

If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all ...
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1answer
45 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
5
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2answers
477 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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1answer
59 views

How to find equations of motion when potential is given by inverse-square? [closed]

When potential is $U=-\dfrac{a}{r^2}$ ($a>0$), how can I find $r=r(\phi)$? I'm trying to solve this problem during several hours. From $E=T+U$, and constant angular momentum $L$, I can get the ...
8
votes
1answer
299 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
2
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0answers
74 views

Expansion of gauge potential on infinite dimensional manifold

I'm studying geometrical approaches to locomotion at low Reynolds number by reading the article Geometry of self-propulsion at low Reynolds number by Alfred Shapere and Frank Wilczek and found a ...
2
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1answer
97 views

Physics of a cold and hot top

Imagine two tops made up of exactly one thousand atoms. One is kept at 4 degrees Kelvin, the other at room temperature. 1. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
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6answers
10k views

Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin ...
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0answers
43 views

Higher order principle of isotropy

Let us work with classical mechanics in the substantivalist metaphysics, that is, space and time are seen as absolute. Call $n$-th order of motion any observer such that $n$ is the biggest order of ...
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70 views

When to use Hamiltonian vs Lagrangian?

I currently studying the Lagrangian and Hamiltonian formalisms in classical mechanics, but something I'm not seeing is how do I know which one to use in a given problem? After I find the Lagrangian, ...
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2answers
142 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...