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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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 $\frac{\pi}{2}$ ? https://www.youtube.com/watch?v=bJWFgJTxIFk&index=9&list=...
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11k views

Calculation of the maximum load to the bar

Looking for a way of calculating the maximum weight (W) to the rod with the given length (L) where the rod did not break and that only bend for (b) mm. Need only approximative solution (read: ...
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95 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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22 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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2k views

Definition of generalised coordinates?

I think the definition of generalised coordinates is something along the following lines: A set of parameters that discribe the configuration of a system with respect to some refrence ...
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50 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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1answer
115 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 ...
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61 views

Foliation of the phase space

Consider an arbitrary classical Hamiltonian system. Given an initial state $(p_0, q_0)$, we can get a solution of the equation of motion, a curve in the phase space. Now the problem is, for a generic ...
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281 views

Examples of singularities in classical physics [closed]

I am a math teacher and I have to teach a topic called "Bruchterme" and "Bruchgleichungen" in german (I don't know the english word for it). For example $$ \frac{x^2 - 3}{(x - 2)x^2} + \frac{4}{x} + ...
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329 views

Tidal Forces Misunderstanding [duplicate]

I'm sure there are several misconceptions here and I'd greatly appreciate it if someone could help me identify and correct them. When calculating tidal forces across an object, the earth for example, ...
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1answer
78 views

In geometric optics we treat light as a collection of particles?

I've been reading the book "Geometric Mechancis" by Darryl Holm and the in the first chapter he treats geometric optics. There the author talks about light rays and those light rays looks like ...
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153 views

Lagrangian formalism and Contact Bundles

In his Applied Differential Geometry book, William Burke says the following after telling that the action should be the integral of a function $L$: A line integral makes geometric sense only if it'...
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117 views

Shape of water jet

Suppose you are shooting a water jet in a vacuum vertically onto a flat plate in a gravity-less room. The jet makes a right angle to the plate and water is assumed to be incompressible. The mass ...
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435 views

Classical Mechanics - Equation of motion, Lagrangian, Newtons 2nd Law [closed]

I really don't even know where to start with this question. A particle with charge $q$ moving in an electromagnetic field is described by the Lagrangian $$L=\frac{m\mathrm v^2}2+\frac qc\mathrm v\...
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71 views

Finding the configuration space and degrees of freedom of spherical pendulum

Suppose we have a spherical pendulum tethered to the origin in $\mathbb{R}^3$ where the length of the rod is a time varying function $l(t)$. What is the configuration space of this system, and how ...
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3answers
1k views

Should I use Coulombs law when magnets attract/repel?

When magnets attract to each other or repel. Should I use Coulombs law? If not, why not? Some would say that I shouldn't because: "Coulomb's law deals with static charges and force due to them. ...
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36 views

forces between two dipoles, one of them oscillating

so, imagine we have two dipoles A and B, A is fixed at the origin and B is free to move on the X axis. Suppose we make the dipole A oscillate, say reversing it's direction every one second, then B ...
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1answer
338 views

Independence of position and velocity in Lagrangian from the point of view of physics? [duplicate]

I would like to continue discussion from my previous post on time dependence of lagrangian Time dependence of the Lagrangian of a free particle?. I have also read this old post Why does calculus of ...
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2answers
598 views

Movement of a rotating coin

Why is it that whenever a coin, like a quarter, is rotated that it always begins to circle around a point some distance from itself; it begins to almost revolve around nothing?
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74 views

Rod partially handing off edge of table

A uniform rigid rod of length $L$ lies at the edge of a frictionless table so length $x$ of the rod rests on the table and the rest is beyond its edge. Intuition suggests that the rod will stay like ...
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77 views

How is electric dipole moment analogous to mechanical moment?

Diplole moment is q*2l. I don't understand the similarity between dipole moment and ordinary mecanical moment.
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1answer
60 views

What are the proper unit types for the calculation of the frequency of a tuning fork? [closed]

Wikipedia Article on the subject The formula states that the calculation of the frequency with cylindrical tines should be $$1.875^2/(2\pi L^2)\times(Er^2 /(4P))^{1/2}$$ where the variables are ...
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1answer
99 views

For infinitesimal Canonical Transformations, what functions are allowed for this to be a canonical transformation?

Consider two infinitesimal transformation: $$q_{i} \rightarrow Q_{i} =q_{i} + \alpha F_{i}(q,p) $$ $$p_{i} \rightarrow P_{i} = p_{i} + \alpha E_{i}(q,p) $$ where $α$ is considered to be ...
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1answer
131 views

Newtonian motion of a particle confined to a smooth surface

Recently, I've been considering a model wherein a lone particle with constant mass m is confined to a surface $F$: $\mathbb{R}^m \to \mathbb{R}^n$ , where $m < n$. I declare this surface to be ...
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5answers
3k views

Why is it easier to go uphill on a lower gear?

In cars as well as bicycles, when we are on a lower gear, the driving wheel (the one on the wheels) has a bigger radius compared to when on a higher gear. So on a lower gear the bike/car would move ...
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49 views

A metal block in a tub of frictionless ball bearings [closed]

If you place a metal block in a tub of small frictionless ball bearings of the same metal, would it stay on top or sink?..
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253 views

Can all the theorems of classical mechanics be deduced from Newton's laws?

As above, is the whole edifice of Newtonian mechanics built upon Newton's three laws of motion? Can I deduce all the theorems without referring to further assumptions?
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142 views

Why spinning a pen makes it easier to remove it from the stand?

I have a ballpoint pen stand on my desk. The pens are held inside their caps with the point down, like this one (but not as fancy): If I try to simply pull up one pen, the friction between cap and ...
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2answers
148 views

How does rotational energy transfer to linear energy?

So I have recently started looking into moments of inertia, and all that stuff. I have come to a question which has a plane inclined at some angle theta and a sphere at the peak. The G.P.E at the top ...
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2answers
316 views

Why can I put my hand through sand but not a table? [duplicate]

I've read in books that one can't put one's hand through a table because the table offers a "Normal Reaction" to the hand. And it is also stated that this force is electromagnetic in nature. But what ...
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3answers
123 views

Formulating the Lagrangian in terms of invariant quantities

Consider a closed system consisting of $N$ point particles, whose Lagrangian is given in the standard way, by the total kinetic energy minus the potential energy: $\mathcal{L}(\dot{q},q):= T(\dot{q}) -...
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156 views

Driven Pendulum

If the point of suspension of a pendulum is driven periodically in the vertical direction , we can derive the equation of motion for the suspended mass to be of the form, $\ddot{\theta}(t) + (a-b\cos{...
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68 views

Formula or relation for forcing spring movement over a certain time (as the image shows) [closed]

i have explained my objectives in the image the fact is i'm planning to use such motion in programming but i have some serious trouble over controling the time that this motion finishes! what i'm ...
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170 views

Composing integrals in physics?

OK... so this problem isn't really specific... it's more of a conceptual puzzle. I've recently started using integrals while solving problems in physics (specifically Newtonian Mechanics and other ...
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65 views

Terminology: Gauge stress?

When a material is loaded with a force, the stress at some location in the material is defined as the applied force per unit of cross-sectional area. If I have a material submerged in pressurized ...
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1answer
75 views

Alka Seltzer Model: formulas/models requested [closed]

This evening I became fascinated with how my Alka Seltzer tablet disintegrates over time within a small portion of Diet Lipton Citrus Ice Tea. I used a nearly frozen cup; tall, as one might request in ...
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4answers
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Method of calculating eddy currents of a conductor, is this correct?

I have a conductor with volume $V$, passing a magnetic field($B$) with velocity($v$): I'm trying to calculate the Eddy currents to figure out the magnitude of the drag force($F_d$) generated the ...
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9 views

Region of resonance and overlap

In planetary dynamics what does a region of resonance (mean motion) between two bodies mean and how to quantify the region? How does resonance overlap occur and what are its consequences? What is ...
4
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2answers
479 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = \...
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1answer
63 views

Earnshaw's theorm and Effective potential

Earnshaw's theorm says "no stable equilibrium for any $\frac{1}{r}$ potential field in charge-free space". Now I am confused in some aspects, and I would like some helping hands. 1.)General physics ...
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1answer
147 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?
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2answers
301 views

What would happen if we tried to run a motor in space when it is not attached to anything to provide support to it?

I know that a when a motor runs it generates torque and that torque can be used to do useful work. On the other hand, the motor needs strong support that absorbs the reaction torque. In our case let ...
2
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1answer
288 views

How does a tightrope walker return to equilibrium?

I do not understand how tightrope walkers return themselves to equilibrium. I am not concerned with the direction along the rope or wire where their base can be large, and they are able to move ...
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1answer
154 views

How to make a body rotate about a line that does not go through its center of mass by applying external torques

In space, is it possible to make a body rotate a point that does not go through its center of mass by applying external torques?
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How to sail downwind faster than the wind?

Recently a group set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a page talking about it, but it doesn't explain exactly how ...
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1answer
61 views

Is rigid body rotation an integrable problem?

Is there chaos? The configuration space is 3d. There are four constraints, namely, the energy, the three components of the angular momentum. So there are still two degrees of freedom.
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2answers
110 views

how is this kind of rolling motion possible?

I was solving this problem : Suppose you put a sphere in a rough ground with velocity of center of mass $v_{cm}= v_o$ in the positive $x$ axis and with anticlockwise angular momentum $\omega_o$ so ...
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54 views

Particle slides on incline where incline angle increases with rate $\omega$: why does kinetic energy have a term $(1/2)m(\omega^2 x^2)$?

A particle slides on a smooth inclined plane whose inclination is $\theta$ is increasing at a constant rate $w$. If $\theta = 0$, at time t = 0 at which time the particle start from rest, Find the ...
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2answers
97 views

What can be inferred about this particle from a Lagrangian?

If Lagrangian, $\mathscr L = \dot{q}^2 - q \dot{q}$. Then what can be inferred about the particle? Simply that it is a free particle or something else?
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41 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...