Tagged Questions

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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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 ...
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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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Why is the Hamilton-Jacobi equation important? [closed]

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 ...
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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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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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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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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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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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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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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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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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Why is it easier for the ocean to push someone over by exerting force on their front side than by exerting force on their left or right side?

If I put two clones of normal weight on a beach in the ocean, with one standing perpendicular to the waves, and the other standing parallel to them, the one standing perpendicular to the waves will be ...
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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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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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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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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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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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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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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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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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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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Can a nozzle increase the thrust of a water rocket?

First of all, what is the correct equation to determine the thrust produced by a water rocket? $$F_T = \dot{m} V_e \tag{1}$$ $$F_T = \dot{m} V_e + (p_e - p_0)A_e \tag{2}$$ Using the first ...
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Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
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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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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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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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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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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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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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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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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 ...
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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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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 ...
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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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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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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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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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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 ...
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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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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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How to work out the gravitational potential energy of rotating rod

I know that the kinetic energy of a rotating rod is $$KE_{rot}=\frac12I\omega^2$$ where $I$ is the moment of inertia. But is there some way to calculate gravitational potential energy using just ...
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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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Time-independence of Hamiltonian of atomic chain

In the first chapter of Atland and Simons book he gives the Hamiltonian of the atomic chain $$H[\pi,\phi] = \int dx \Bigg(\frac{\pi^2}{2m} + \frac{k_sa^2}{2}(\partial_x\phi)^2\Bigg)$$ After ...
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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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rotational springs

With a normal spring, you compress it using a linear force to store energy and then it decompresses and releases the energy, again in a form of linear force. Is there a mechanical mechanism that ...
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canonical ensemble that is quantum mechanical and continuous?

I do not understand what the following statements from Wikipedia mean For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as  Z = \...
Example where Hamiltonian $H \neq T+V=E$, but $E=T+V$ is conserved
I'm looking for an example of a Hamiltonian $H$, where $H\neq T+V$, but the total energy in the system, $E=T+V$, is still conserved. While I'm at it, I might as well add that I'd be most interested ...