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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BiCopter simulation problem [on hold]

I derived bicopter dynamical model with two servos and two BLDC motors. And now am trying to simulate it using Matlab. As base for simulation I used this paper and this code: ...
-2
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1answer
21 views

Problem: When does a constant velocity catch up to a certain acceleration? What is the maximum acceleration? [on hold]

Physics noob here. Romeo is at x = 0 at t = 0 when he sees Juliet at x = 6m. (a) He begins to run towards her at v = 5m/s. She in turn begins to accelerate towards him at a = −2m/s2 . When and where ...
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5answers
94 views

How can we explain the difference in change of kinetic energy, due to different frames of reference?

Imagine a ball ($m= 1\,{\rm kg}$) moving at a velocity $2\,{\rm m}/{\rm s}$ towards a wall. When it hits the wall, it suddenly stops, thereby liberating all its ${\rm KE}$ as heat. Here, the initial ...
2
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0answers
64 views

Poisson brackets and magnetic field [on hold]

I'm a maths student trying to teach myself some physics so sorry if I'm missing something simple here. I think the main problem is lack of experience with the Levi-Cevita symbol. We have a particle ...
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3answers
62 views

What was the motivation behind the work formula?

Surely there must be a reason we decided to use this as a metric for mechanical energy.How was it developed and what made it more acceptable than other work formula candidates (Like force over time, ...
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1answer
76 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
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2answers
31 views

Is configuration space in any similar to vector spaces?

The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else. I have just learned about vector spaces and their properties and on the other hand have also ...
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1answer
35 views

How much does a light heat the air around it?

My dad told me to turn off the lights when I'm not using them because it will keep the house cooler. I don't think he is correct that a light can heat up the room. How much of a difference in the ...
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0answers
16 views

What axial forces does the vertical load induce? [on hold]

What axial forces does the vertical load P induce in the members of the system down in the figure? Neglect there weights of the members themselves and assume an ideal hinge at A and a perfectly ...
-3
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0answers
30 views

what is the equivalent resistance of the circuit?.using R1,R2,R3 calculate theoretical values of equivalent resistance [on hold]

Aim:set up a series parallel network with known resistor.determine the equivalent resistance using an ammeter and voltmeter and compare with their theoretical values Apparatus:4 cells 1,5v.cell ...
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1answer
50 views

Why is centre of mass taken as integral of x.dm and not m.dx?

Forgive me if I'm being naive, but, I don't understand why the X-coordinate of the Centre of mass is taken as an integral of x.dm and not m.dx. I understand the summation part, but how do we convert ...
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2answers
54 views

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
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0answers
42 views

Hausdorff spaces and finite elements

Must the shape functions and the interpolation functions (which are the same in an isoparametric element) in a finite element model be elements of a Hausdorff space? If so, is this necessary to ...
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0answers
26 views

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
4
votes
1answer
44 views

Without using rotational mechanics, why does a gyroscope precess the direction it does?

When a top is spun, it will precess in some direction, either clockwise or counterclockwise. It's possible to find out which way using $\boldsymbol{\tau} = d\mathbf{L}/dt$ and $\boldsymbol{\tau} = ...
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0answers
21 views

need reference on the minimum moment of inertia [duplicate]

I would like to know if there is a book on clasiscal mechanics about the following Moment Of Inertia About Centre of Mass
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0answers
42 views

why do things stick to surfaces when left for a really long time?

I tried to move a cardboard box off the top of a cabinet, which left it on for probably years, and it was insanely difficult to remove. I don't know why this happens, but it also seems that my feet ...
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1answer
34 views

The Real Rocket

Suppose we have a Rocket with initial mass $M_o$ and we want to sent it into space. The equation of motion is (i think... please tell me if there is something i forgot) $$\frac ...
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1answer
27 views

How does height of a parachute affect air resistance compared to circumference or diameter?

I'm trying to find out how much a double in height (making it more ovular or oblong in shape) of the parachute affects air resistance compared to a double in circumference or diameter. Can someone ...
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0answers
42 views

electric circuit experiment [closed]

I did the first part but a bit confused when it comes to drawing the graph for it with the table values and the conclusion to the experiment Aim:set up a series parallel network with known ...
2
votes
0answers
37 views

Classical Statistical thermodynamics phase space and residue $h$

In classical statistical mechanics we have to divide the partition function by a factor of $1/h^n$. In almost every calculation of a real quantity this cancels out and is thought to be a remnant of ...
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2answers
40 views

Independent Variables of a Lagrangian

Let us consider a particle in one spatial dimension $x$ and one temporal dimension $t$. Its Lagrangian $L$ is given by \begin{eqnarray*} L &=& T- V \\ &=& \frac{1}{2} m\dot{x}^2 - ...
2
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3answers
166 views

Is there an intuitive explanation of the work formula?

Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
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0answers
25 views

Magnitude of acceleration uniform circular motion

A particle moves in a plane with uniform velocity $ r' = 4 m/s$. The angular velocity is constant and has magnitude $θ' = 2 rad/s$. When the particle is $3 m$ from the origin, find the magnitude of : ...
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0answers
43 views

Two Particles in a Harmonic Oscillator with repulsive short-range potential

Do bear with me, I am attempting to learn to write some simulations on the computer and learn some simple MD, so I defined sort of a toy problem. I have two particles confined in a Harmonic Potential ...
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1answer
48 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
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1answer
54 views

Why is it effectively impossible to balance this rectangle block on a triangle block? (See photo)

I've always wondered why it's basically impossible to balance a rectangle block on top of a triangle one like this. This is my nine-year-old giving it a try. I have never in my life gotten it to ...
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2answers
51 views

The pressure in a container of water is based on depth. So what happens if I remove the bottom of the container?

So I understand that if we have a system that involves a container of water the pressure will equal atmospheric pressure at the top and as we go further down the container the pressure will increase ...
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0answers
29 views

How is the Routhian of classical mechanics defined?

The Hamiltonian is a function on the cotangent bundle to a configuration manifold $H:T^*M\rightarrow \mathbb R$. The Lagrangian is a function on the tangent bundle to the configuration manifold ...
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0answers
24 views

What distance does a particle move? [closed]

I'm trying to figure out the distance that a particle moves along $x=3t^2-2t^3$ from $t=0$ to $t=4$. What method can I use to go about figuring this out?
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2answers
48 views

How does friction act on a body, if only 2 regions on it are rough? [on hold]

While tackling an Olympiad question, it came to my mind that friction need not act in the same direction at all points on a body. I thought of using integration to evaluate the net frictional force, ...
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votes
1answer
45 views

Why do systems with a fixed gear-ratio still use gears?

From my understanding, there are two uses of a gearing system: to change the speed of output rotation (trading it with torque), and to change the axis of rotation. Now, in a car, for example, it is ...
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2answers
72 views

Why is sometimes more difficult to lift a baby?

I have a small cousin and she enjoys when I pick her up, which I can do pretty easily. Sometimes though she decides she wants to make my life difficult, and when she decides so, she tells me she is ...
1
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1answer
61 views

Why closed in the definition of a symplectic structure?

Why do we want the 2-form $\omega $ to be closed? What if it is not?
4
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1answer
77 views

Chaos and integrability in classical mechanics

An Liouville integrable system admits a set of action-angle variables and is by definition non-chaotic. Is the converse true however, are non-integrable systems automatically chaotic? Are there any ...
1
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1answer
22 views

Extension spring and permanent damage

Is there a way to calculate how far an extension spring can be extended before it suffers permanent damage? There are some online calculators, but how are they done? This calculator is the most ...
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0answers
53 views

How fast must a penny roll to remain upright?

I solved this question, however my professor's answer is different from mine. I modelled the penny as circular disc of radius $a$ so its moment of inertia is: $$I_s = \frac{ma^2}{2}$$ so $$I = ...
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1answer
33 views

Harmonic oscillator :Two masses are attached to one unfixed spring from both sides (vertically) [closed]

while ($t<0$) the system is still ($\Sigma$ F=0). Mass $m_2$ is held while $t<0$. Mass $m_1$ is located $h_0$ meters above the ground and the spring is currently stretched $L$ meters. The ...
3
votes
1answer
54 views

Why was the Stark effect discovered much later than the Zeeman effect?

This is strange. The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical ...
3
votes
3answers
96 views

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...
3
votes
1answer
26 views

What is the Optimal Separation Length for the Tines of a Tuning Fork?

I'm building tuning forks (for fun... why not?), and among one of the design decisions is how far apart should I place the tines (the two long prongs) from each other. I'm not entirely certain whether ...
2
votes
1answer
60 views

Every central-force field is integrable, right?

In 3d, there are four independent first integrals, namely, the three components of the angular momentum, and the total energy. So by the Liouville theorem, it is integrable, right?
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2answers
98 views

Why is the Hamilton-Jacobi equation important? [on hold]

Someone may say it is related to the Schrodinger equation. Okay, let us forget about quantum mechanics. So, if we confine ourself to classical mechanics, why is the Hamilton-Jacobi equation important ...
-7
votes
1answer
44 views

Limits of integration [closed]

In the following video can someone explain why did he take the limits of integration to be from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ ? ...
0
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0answers
53 views

Mechanics question I don't understand solution

A simple top consists of a heavy circular disc of mass m and radius a mounted at the center of a thin rod of mass $\frac{m}{2}$ and length a. If the top is set spinning at given rate S, and with the ...
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0answers
16 views

spin-orbit coupling for a rigid body

Consider the motion of a coffee cup in the gravitation field of earth. The force acting on the cup apparently depends on the orientation of the cup. Therefore, the internal rotation (with respect to ...
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0answers
29 views

Is there a Lagrangian that can lead to the Rayleigh-Jeans law?

Is there a way to derive the Rayleigh-Jean's law using classical statistical mechanics only? On the internet there is a common way to arrive at the equation by using concepts in electrodynamics. This ...
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0answers
6 views

Winch bridle force calculation for performer flying

Hi this is my first post o this site so please forgive me if I have got anything wrong in the process. I am trying to do some calculations on the forces some performer flying winches are seeing. ...
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0answers
38 views

Configurations and configuration manifold in Lagrangian Optics

In Classical Mechanics, given a certain system of particles it is possible to consider the configuration manifold $Q$ which is a differentiable manifold whose points are possible configurations of the ...
2
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1answer
35 views

Do time-invariant Hamiltonians define closed systems?

In classical mechanics, every time-invariant Hamiltonian represents a closed dynamical system? Can every closed dynamical system be represented as a time-invariant Hamiltonian? Or are there closed ...