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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power of aircraft engine [on hold]

An aircraft flies with velocity of 180 m/s and its engine takes in air by a rate of 70 kg/s so that it could burn fuel by rate of 2.9 kg/s and thrust it backward with relative velocity of 490 m/s with ...
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0answers
22 views

Criteria for stable equilibrium [on hold]

A homogeneous wooden bar of length 10 cm, thickness 4 cm and weight 1 Kg is balanced on the top of a semicircular cylinder of radius R as shown below. What is the minimum radius of the semicircular ...
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1answer
40 views

Classical static equilibrium in atomic physics

Consider a collection of $n+1$ mass weighted points in $\mathbb{R}^3$. Suppose we have one mass located at the point (0,0,0) with mass $m\in\mathbb{N}$ and further suppose we have $n$ masses arranged ...
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0answers
14 views

Momentum of a divided sphere [on hold]

I have a problem with a exercise, please, anyone knows where I wrong? I can not find the error in my solution... Basically I consider that the equation of the horizontal momentum is equal the initial ...
3
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1answer
92 views

Hamilton-Jacobi equation with time dependent Hamiltonian

I was struggling with this exercise about Hamilton-Jacobi equation. I have to solve by menas of Hamilton's principal function the system with Hamiltonian: $$ H=\frac{p^2}{2m}-mAtx $$ with $A$ constant ...
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31 views

Coupled Oscillation Simulation

I'm looking for an online coupled oscillation simulation. The best I have got so far is this --- https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html But I'm looking for something which ...
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1answer
26 views

What would be the change in gravitational potential energy? [on hold]

QUESTION ------------ A rope of length L and mass M is connected to a chain of length L and mass 2M and hung vertically from a point. What is the change in potential energy if the system is INVERTED ...
2
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1answer
125 views

Sum of torque from a sphere

A sphere (grey color) turn in rotation at $\omega$ rd/s. There are 2 walls that prevent sphere to escape. Walls can only turn around center of rotation. The sphere turn only at $\omega$ rd/s too. The ...
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0answers
18 views

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 ...
1
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1answer
22 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 ...
0
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1answer
19 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 ...
4
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1answer
52 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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31 views

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

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 ...
3
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1answer
44 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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2answers
93 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
54 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 ...
1
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1answer
48 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 ...
2
votes
2answers
41 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 ...
0
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2answers
65 views

Inertia matrix of a rod rotating about an axis [closed]

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
votes
1answer
76 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 ...
0
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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 ...
4
votes
3answers
124 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 ...
2
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2answers
172 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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0answers
27 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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0answers
34 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 ...
0
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1answer
35 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 ...
0
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1answer
31 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 ...
2
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4answers
53 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 ...
1
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0answers
68 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 ...
4
votes
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
111 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 ...
3
votes
1answer
84 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 ...
1
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3answers
125 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. ...
0
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1answer
39 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 ...
0
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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 ...
3
votes
2answers
45 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 ...
0
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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.
0
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2answers
91 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 ...
19
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6answers
2k views

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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0answers
20 views

Suggestions about these books [duplicate]

Which are the best books for the following( introductory level)? quantum mechanics classical mechanics statistical physics particle physics
0
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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 ...
6
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2answers
516 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
161 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 ...
2
votes
3answers
133 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 ...
1
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2answers
78 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 ...
1
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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 ...