Questions tagged [classical-mechanics]
Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].
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Constraint equation for an elastic pendulum
I would like to know if you can help me determine the restraining force for an elastic pendulum. The problem is the following
A particle of mass $m$ is suspended by a massless spring of length $L$. ...
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"Natural frequency" seems to be a poorly defined concept [closed]
Per wikipedia: natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force.
Let's take a wine glass as an example.
The ...
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Solution as the real part of complex exponential for simple harmonic motion
Reading through the "Solution as the real part of complex exponential" section of the John Taylor textbook on classical mechanics, I noticed the following :
$x(t) = C_{1}e^{i\omega t} + C_{1}...
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Finding the tipping force for a cantilever table [closed]
How would I find the force it takes to the table to tip over if you were sit on top the cantilever end?
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The dreaded incline plane [closed]
Source: Principles of physics 11th edition halliday Chapter 6 Q11.
Yes, this is a homework question and I am questioning my misconceptions. Answer at back says 3.9m/s^2 downwards.
Standard inclined ...
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Proof that two vectors [closed]
Calculate the result of this three vectors:a(vector no.1)=5u,b(vector no.2)= 7u,c(vector no.3)=4u.Calculate the resultant of the three if the angles between axis Ox and vector a is 30 degrees,the ...
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Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
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How do 4-vectors change under an "accelerated" Lorentz transformation?
I assume that an observer moving with velocity $\mathbf{v} = v\mathbf{n} = \mathbf{v}(t)$ (with respect to another observer) has coordinates
where $x^{\mu}$ are the coordinates for the observer who ...
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A question about space inversion symmetry of parity in a rotated disk
In a rotated disk (say, Faraday disk), is the space inversion symmetry of parity still preserved?
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Reading on weighing scales at the equator of a moon in a tidally locked two-body system
I'm trying a made-up extension of this problem. Consider the planet Mars and its moon Deimos, which can be approximated as meeting the following simplifying conditions:
Both objects are perfect ...
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Help in understanding this derivation of Lagrange Equations in Non-Holonomic case
Whittaker, Analytical dynamics pg 215
I don't understand how we get the final equations relating $Q_r$ with $\lambda$ given the conditions above?
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Solving forced harmonic oscillator differential equation using fourier transform
I am trying to solve the equation of a forced harmonic oscillator using Fourier Transform. I know that if a function $f(t)$ is such that $\lim_{x->\pm \infty} f(t) = 0$, then
$$\frac{1}{\sqrt{2\pi}}...
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Find collision time from velocity [closed]
A rock falls toward a static planet with velocity v(x) = 1/(2x) m/s where x is their separation. If initially the rock was at x = 0 and the planet at x = 1000m, when does the rock hit the planet? Hint:...
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Independence of generalized coordinates in the derivation of Lagrange equations from d'Alembert's Principle
I am confused by this remark in the derivation of Lagrange equations from d'Alembert's principle in Goldstein:
I am not comfortable that I understand why, at this late stage of the derivation, they ...
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Kinematics - confusion about signs of angular velocity and acceleration (general rule ?) [closed]
I have often found it challenging to determine the direction of angular velocity and acceleration in exercises involving rotational motion, much like the one depicted in the picture below. While ...
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Getting different answers by different methods for angle made by a pendulum moving with constant acceleration
A point mass $m$ is hanging by a string of length $l$ in a car moving with a constant acceleration $a$. Using car frame and pseudo force, we easily get that the angle made by string with vertical is :
...
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Why does $\vec{r}\cdot\dot{\vec{r}}=r\dot{r}$?
Why is $$\vec{r}\cdot\dot{\vec{r}}=r\dot {r}$$ true? Before saying anything, I have seen the proofs using spherical coordinates for $$\dot{\vec {r}}= \dot{r}\vec{u_r}+r\dot{\theta}\vec{u_\theta}+r\sin\...
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Question about velocities in different reference frames
Suppose $\hat{x^{'}}, \hat{y^{'}}, \hat{z^{'}} $ are the unit vectors of an inertial frame and $\hat{x}, \hat{y}, \hat{z} $ are the unit vectors of a frame which maybe accelerating, rotating, whatever....
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Doubt in fictitious forces chapter in Morin
The question is this -
I know 2 is what the non-inertial frame measures, but isn't $\frac{d\mathbf{A}}{dt}$ the real thing, the physical thing? And you can write that too in terms of the unit vectors ...
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Weird sign in EOM: Centripetal vs. centrifugal term [duplicate]
Something goes wrong when I was deriving the equation of motion in Kepler's probelm, as below,
Angular momentum conservation $L = Mr^2\dot{\theta}^2$.
And Lagrangian is $L = \frac{1}{2}M(\dot{r}^2 + ...
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Confusion about torque [duplicate]
Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in ...
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Lagrangian mechanics and generalized coordinates
In Lagrangian mechanics, we use what is called the generalized coordinates (gc's) as the variable of the machanics problem in hand. These gc's represent the degrees of freedom that the studied system ...
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Should you study all the chapters in griffith electrodynamics and taylor classical mechanics? [closed]
I'm an undergrad student (just started 4th year) from Iraq, we don't really have that good of a physics edu.
so I'm self-teaching myself most if not all of the subjects.
in classical mechanics, we ...
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Derivative of a curve on a manifold in time-dependent (rotating, comoving) coordinates
This should maybe go in the math SE but the example is more relevant to physics and the way physicists think so I'm posting here.
what I understand: Let $\mathcal{Q}$ be a smooth $n$-dim manifold and $...
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According to inertial frame, how can a bead move in a groove made on a rotating table? [duplicate]
Context:
Consider a smooth circular table rotating uniformly. Along it's radius , a groove is made. While it's rotating , a bead is placed on the groove gently at some distance (say $x$) from centre. ...
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Lagrange multipliers method for a bead on a parabola-shaped wire [closed]
I have this simulation problem that looks very easy at first look (and maybe it is, especially using Lagrange equations of the 2nd. kind). I am using the Lagrange multipliers and I am kinda not sure ...
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Virtual work of constraints in Hamilton‘s principle
Goldstein 2ed pg 36
So in the case of holonomic constraints we can move back and forth between Hamilton's principle and Lagrange equations given as $$\frac{d}{d t}\left(\frac{\partial L}{\partial \...
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Independence of variables in Lagrangain and Hamiltonian mechanics - Rigorous Mathematical approach
I am trying to self-learn the Hamiltonian and Lagrangian mechanics and I came across thoughts to which I could not find an answer therefore I would like to try and ask them here.
My questions are as ...
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Can you prove the possibility to rewrite any lorentz invariant equation as the component of a 4-tensor?
When studying special relativity, there is usually a point where 4-tensors get introduced. Since all of physics equations are supposed to be lorentz-invariant, it is assumed that these equations are ...
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Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so which one is right? [closed]
Some books write $V(\vec{r})$ instead of $V(r)$ as a notation for the electric potential, so can the electric potential depends also on the direction?
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Confusion of variable vs path in Euler-Lagrange equation, Hamiltonian mechanics, and Lagrangian mechanics
In Lagrangian mechanics we have the Euler-Lagrange equations, which are defined as
$$\frac{d}{dt}\Bigg(\frac{\partial L}{\partial \dot{q}_j}\Bigg) - \frac{\partial L}{\partial q_j} = 0,\quad j = 1, \...
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Does work depend on a point of reference? [duplicate]
Imagine there is me, Earth and some other guy. Me and a guy move parallel to each other at the speed of 1000m/s relative to Earth.
I am so fit that my mass is 0.5kg, so when a force of 1N in the ...
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If we use a small angle approximation on a compound pendulum, is it accurate to say it exhibits simple harmonic motion?
I have an experiment where I have to find the damping coefficient of a compound pendulum situated in a clock. It swings at a very low amplitude, so I think I can make a small angle approximation. ...
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Landau/Lifshitz Particle Disintegration
In Landau/Lifshitz "Mechanics", 3e., there is a problem which asks the reader to find the relation between the angles $\theta_1,\theta_2$ in the lab frame when a particle disintegrates into ...
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How to determine which coordinates to use for calculating the Hamiltonian? [closed]
In my classical mechanics course, I was tasked with finding the Hamiltonian of a pendulum of variable length $l$, where $\frac{dl}{dt} = -\alpha$ ($\alpha$ is a constant, so $l = c - \alpha t$.).
I ...
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How do we know what physics or science textbook said is correct? [closed]
I have a question. I have a problem that when I learn science, I like to think 'how do they know this is right?'.
When we learn physics or science from a textbook, we read and understand it, and then ...
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Does Group Velocity violate Uncertainty Principle?
I've recently begun studying Quantum Mechanics and went through the descriptions of phase and group velocities and the fact the group velocity or the velocity of the resulting wave envelope represents ...
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Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]
John Taylor's Classical Mechanics says this...
I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
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WKB method as a Semiclassical Approach
A naive question about WKB approach. It is dubbed to be a "semiclassical" method. What is precisely mean in quantum mechanical context to be "semiclassical"? Wikipedia states that ...
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Why does a higher frequency mechanical wave have more energy?
(that question may sound like my last question What makes a higher frequency sound wave more energetic? but I wouldn't consider it a duplicate, the focus is very different.)
Comparing two mechanical ...
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What makes a higher frequency sound wave more energetic?
The energy of a mechanical wave (in this case, the sound wave, which stimulates periodic movements of a gas) is proportional to both amplitude and frequency. Often, I read that it is written that ...
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Derive $L = T - U$, in newtonian mechanics, assuming the principle of least action [duplicate]
I am trying to get a better understanding of the Lagrangian. From what I know, we say that each trajectory in physics must be a path that is at a minimum, which means that is satisfies the Euler-...
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Scattering Differential Cross Section Laboratory Frame
Let the differential cross section of a scattering experiment given by $\frac{\text{d}\sigma_{c}}{\text{d}\Omega_{c}}(\vartheta_{c})$, where $\vartheta_{c}$ describes the scattering angle in the ...
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Why is the conserved Lagrangian energy $E$ equal to the total energy in this example but not in a similar example? [duplicate]
I am aware that there exists duplicates to the title and have gone through the answers but it still doesn't answer my issue with a statement in the last image.
These two similar situations with slight ...
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Isotropy of space doubts
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we ...
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Pressure in a hydraulic cylinder with piston in free fall?
I have a double-acting asymmetric hydraulic cylinder with chambers A and B (A has a larger area). The piston has a heavy weight mounted on it, and both chambers are connected to supply and return ...
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Separating boundaries of Classical mechanics and Quantum mechanics
I had my very first class of Quantum Mechanics a few months back. The discussion was on what is the limit after which an object starts showing quantum behavior. My professor said that when an object's ...
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Where does the $\pm$ in Einstein's energy-mass equivalence come from?
Our professor taught us the equation $E= mc^2$ today, but he mentioned that this is only a part of a solution. He never taught us where it came from, but he did mention that this is only a partial ...
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What is the most general transformation between Lagrangians which give the same equation of motion?
This question is made up from 5 (including the main titular question) very closely related questions, so I didn't bother to ask them as different/followup questions one after another. On trying to ...
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Obtaining the critical solution for a functional
So, I was trying to calculate the critical solution $y = y(x)$ for the following functional:
$$J[y] = \int_{0}^{1} (y'^{\: 2} + y^2 + 2ye^x)dx$$
and a professor of mine said I should use conservation ...
