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 Scattering of Slow Neutrons by a Diatomic Molecule [on hold]

Consider an experiment in which slow neutrons of momentum $\hbar k$ are scattered by a diatomic molecule; suppose that the molecule is aligned along the $y$ axis with one atom at $y=-b$ and the ...
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1answer
20 views

Two-Body with external force - energy confusion

Setup Imagine a two-body system of masses under a classical mechanics model. The separation and mass-ratio doesn't matter for this example. Presume they are initially stationary. Now suppose that we ...
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1answer
18 views

How to reconcile angular momentum measurements?

Imagine a particle tracing a counter-clockwise circular path on a flat table with a certain speed. The particle is tied with a massless string of length $R$ to a point $P$ at the center of the ...
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27 views

Some question about symplectic transformation

I read Arnold's book Mathematical Methods of Classical Mechanics and come across with three problems in page 229. 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues of a ...
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30 views

1. The problem statement, all variables and given/known data [on hold]

The problem statement, all variables and given/known data Consider a thin ring of radius a and mass M. A mass m is placed in the plane of the ring (not in the center!). Determine the gravitational ...
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1answer
39 views

Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and ...
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1answer
70 views

Universal gravity at small distance

Could it be that there is simply a maximum gravitational force that two bodies of finite mass can exert on one another? This would occur at $r=0$, so maybe there is some really really really small $a$ ...
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2answers
51 views

Find pressure of liquids without making contact with it

Is there any way to find the pressure of a liquid inside a closed container without making contact with it? You can make any assumptions, like transparent container or anything, only rule, the ...
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1answer
45 views

Center of mass of a cylinder from which liquid is flowing out

A cylindrical container is of mass M, radius R and height H. The cylinder is filled with a liquid of density D. The base of the cylinder has an outlet tap of radius r through which the liquid can flow ...
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2answers
39 views

Can a force applied to a wheel find the fastest way of getting to the other side?

I haven't studied much about this, so if I am mistaken about something please correct me. From what I have seen around the Internet, a force applied to a object takes time to propagate through the ...
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2answers
57 views

Inertia matrix of a rod rotating about an axis [on hold]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
3
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1answer
66 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
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2answers
34 views

How come a whistling kettle starts whistling only when water boils, and not long before - due to hot air escaping under pressure?

A whistling kettle will start to whistle when the water boils and turns into a jet of steam which then exits the small aperture in the spout. But why doesn't this happen much earlier - when the air ...
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1answer
54 views

Confusion about units of angular momentum

According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec I am confused about the derivation for this. Here is what I have done: $$L = I \cdot \omega \\ = m \cdot r^2 ...
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3answers
121 views

Newton's principle of determinacy

I am a mathematician. I have a (somewhat long term) goal of understanding some of the physical insights that have influenced my area of research. To this end I read Arnold's Mathematical methods in ...
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2answers
170 views

From Quantum Mechanics to Classical Mechanics [duplicate]

Is it possible, and has it been attempted, to use quantum mechanics to deduce Newtonian, macroscopic level mechanics laws as was the case of statistical mechanics deriving thermodynamic relations?
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25 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
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32 views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
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2answers
45 views

Types of circular acceleration?

To my knowledge there are three types of acceleration when a body (e.g. a rod) is moving in a circle about an axis. These are: Angular acceleration : this is the rate of change of angular velocity. ...
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1answer
35 views

A pearl that moves in a smooth vertical hoop

I wanted to ask about the situation of a pearl that moves in a smooth vertical hoop in circular motion as described in the following sketch. According to a simulation found in the internet , a ...
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1answer
34 views

A pearl that moves in a smooth vertical hoop (Circular motion) [closed]

I couldn't understand something about the situation of a pearl that moves in a smooth vertical hoop in circular motion. When the normal force equals 0 , the pearl didn't disconnect from the smooth ...
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1answer
28 views

Resonance and the driving frequency?

Why does resonance occur in a mass-spring system when the natural frequency = the driving frequency. I think it is because the driving force is always contributing to the kinetic energy of the system ...
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4answers
51 views

Acceleration and Circular Motion

Lets assume that there is a force that makes our body moves in circular motion. We know that the acceleration of a body that moves in circular motion is Velocity ^ 2 / Radius . How is it ...
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0answers
67 views

Why does Principle for least action hold for classical fields [duplicate]

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...
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1answer
89 views

What's the proper interpretation of canceling infinitesimals? [duplicate]

In most textbooks of physics I've found this demonstration of work-kinetic energy theorem: $$\begin{align} W &= \int_{x_{1}}^{x_{2}} F(x)\ dx \tag{1}\\ &= \int_{x_{1}}^{x_{2}} m\cdot a\ dx ...
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1answer
109 views

Kicking a soccer ball

I wonder which type of kicking may cause the ball to go a larger distance? One way is kicking the ball when it is at rest and another is kicking a moving ball in the opposite direction. If the ball ...
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1answer
82 views

A question about canonical transformation

I have posted this question in math.stackexchange before with no answer till now. It may be more suitable to post here. There is a problem in Arnold's Mathematical Methods of Classical Mechanics ...
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4answers
107 views

Gravity and acceleration

I've imagined this little scenario to help me conceptualize things. Let's say we have a doughnut-shaped object with a hole whose diameter is greater than that of a sphere. Let's say that the sphere ...
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3answers
124 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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1answer
35 views

Relationship between tangential & centripetal forces when angular speed constant but radius varies

The model of a circular motion in basic Physics textbooks and online resources (e.g., Wikipedia on circular motion) assumes that the motion is a circle with constant radius to derive relationships ...
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1answer
48 views

velocity in inertial and nontial frames

I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They ...
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2answers
43 views

Internal potential energy and relative distance of the particle

Today, I read a line in Goldstein Classical mechanics and got confused about one line. To satisfy the strong law of action and reaction, $V_{ij}$ can be a function only of the distance between ...
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0answers
44 views

Can all the systems have a Hamiltonian description? [duplicate]

I have heard of mechanical systems that might not have a Hamiltonian dynamics, but I cannot figure out an example that supports it. Please help.
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2answers
88 views

Derivation of Lagrangian?

I know that the Lagrangian $L$ is defined to be $T-V$, i.e. the difference between kinetic energy and potential energy. Also the Action $S$ is defined to be $\int Ldx$ and from this we can derive ...
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6answers
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Why is superdeterminism generally regarded as a joke? [closed]

Before anything, I'm sorry for being an outsider coming to opine about your field. This is almost always a stupid decision, but I do have a good justification for this case. I've been reading about ...
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Suggestions about these books [duplicate]

Which are the best books for the following( introductory level)? quantum mechanics classical mechanics statistical physics particle physics
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2answers
41 views

Query into the cumulative velocity of mounted platforms

Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine ...
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2answers
514 views

The other side of the lever

If I have a lever, but I can see only up to the hinge and not the other half, can I know whether the other half is 1 m long with a weight of 3 kg on it, or 3 m long with a weight of 1 kg on it?
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5answers
160 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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3answers
124 views

Does mass affect velocity when travelling through frictionless medium?

I found the following question on an standardized test, and was debating with some friends what the answer would be: A car of mass M is travelling with a constant velocity through a plane in which ...
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2answers
77 views

State of constant motion

Why does an object remains in its state of constant motion if there are no forces acting on that object? My understanding is that all the energy of the motion will be kept inside and a change in the ...
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0answers
34 views

How does a simple weighing balance actually work? [duplicate]

I have made a simple sketch of how I think the system looks like. My problem is: I always thought that the angle the balance makes is a function of the difference between the two masses (or the ...
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0answers
17 views

Am I understanding power correctly? [duplicate]

4 men weighing 380kg, carrying a 380kg piano up 5 meters will generate 31 watt if the load takes 20 minutes. Now this is very hard to do and saps the strength out of any human being. However, that ...
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1answer
18 views

Do I need the exact velocity when experimenting with sliding coins?

I'm doing a home experiment but it's not going very well. I'm pushing coins on a table. I'm taking the time for how long it takes coin A to hit coin B and then I divide it by the time between them ...
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1answer
52 views

Speed of liquid being blocked at end of pipe

How fast would water go if at the end of of a 1 inch diameter pipe was closed by a valve? The system is as follows: 5 meter high source of water that feeds a 1 in pipe. The pipe goes straight down ...
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0answers
32 views

Active and passive transformations and the change in potential energy

Under active transformation, the particle moves. On the other hand, for a passive one, the coordinate is just relabel. I've read that the passive one will not affect the potential energy and the ...
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1answer
96 views

Is there a systematic way to derive constraint equations?

There's this problem in Goldstein's (Classical Mechanics) derivations section: 5. Two wheels of radius $a$ are mounted on the ends of a common axle of length $b$ such that the wheels rotate ...
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1answer
41 views

Lorentz force in rotating frame of reference?

This is the common problem of a charged particle moving in a static electric and magnetic field. Say $\textbf{E}=(E_x,0,0)$ and $\textbf{B}=(0,0,B_z)$. In the inertial frame of reference, the ...
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1answer
26 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
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I need a micro-sized clutch for a project, what are my options?

Also, what's the proper stack exchange site to ask this on? mechanics.stackexchange seems to be for motorvehicles. I'm designing an automatic guitar tuner that clamps onto my acoustic guitar. The ...