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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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43 views

Energy-momentum vs charge-current

Is there a simple intuitive way to explain why energy-momentum density requires a tensor, while charge-current density is a vector? $\partial_{\mu} J^{\mu} = 0$ is a statement, in effect, that the ...
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1answer
41 views

Relation between classical and quantum explanations [on hold]

It is said that the classical world emerges from the quantum world, but would it be more reasonable to say that the classical explanation is the limit of the quantum one, whilst the quantum ...
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2answers
33 views

Poisson's ratio in analytical beam deflection equations

After looking at some of the analytical expressions for analyzing beams, I noticed that none of the equations depend on the material's Poisson ratio. Some analytical expressions can be found in https:/...
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2answers
88 views

Which forces violate Newton's third law of motion? [on hold]

Forces arising from magnetic fields do violate Newton's third law of motion under certain circumstances. What other forces violate the third law?
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0answers
27 views

The ideal structure shape that can withstand the most pressure [on hold]

If one were to build a structure of maximum weight 1 kg solely out of newspapers and tape, what do you thing would be the best structure that can withstand the most pressure? (high weight-to-force ...
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1answer
24 views

Difference between kinematic momentum and conjugated momentum in purely mechanical setup

I don't know much about physics, but I wanted to understand what was the difference between the "kinematic momentum" and the conjugated momentum. As I understand it, kinematic momentum is mass times ...
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1answer
25 views

Can Momentum of an object change without net acceleration on the object? [on hold]

Comfy with single variable calculus and basic concepts of classical mechanics.
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0answers
29 views

classical physics, problem number 6 [on hold]

[the question number 6 has to be solved of this given picture] (https://i.stack.imgur.com/yTezc.jpg) please solve the problem as soon as possible
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1answer
6 views

Lateral (bending) stiffness of a helical compression spring

Does a helical compression spring have uniform lateral (bending) stiffness throughout its length? Suppose I exert a force radially along a certain height of the spring, and that force rotates along ...
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0answers
26 views

Converting a discrete statistical energy distribution to a continuous version

The probability of finding a particle at a particular energy level when energy is considered discrete is according to Boltzmann: $$P(E_j) = \frac{g_j\cdot e^{-\beta E_j}}{\sum_{j=1}^\infty g_j \cdot ...
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2answers
32 views

Kinematics of particles

Do particles have to move in a straight line to apply Suvat equations? I always perceived that they do because acceleration can mean a change in the magnitude of velocity, a change in direction or a ...
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1answer
40 views

Energy in central force orbit

Given a mass $m$ moving under the central force $$F(r) = -k/r^n$$ and a circular orbit passing through the force center, I want to show $n$ must equal 5. I ultimately arrive at the expression $$E = \...
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1answer
17 views

Horizontal force on a fluid surface

I was doing some problems involving calculating the thrust due to pressure on curved surfaces. One way, of course, was to integrate over the surface to find the thrust. I noticed that the answer ...
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1answer
41 views

Not parabolic falling

Suppose a small mass m is launched from height h with horizontal initial speed v0; if the ground is horizontal, it's easy to calculate the equation of movement (parabolic), because the coordinates of ...
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0answers
22 views

Can we also Legendre transform the Lagrangian using $\frac{\partial L}{\partial q}$ instead of $\frac{\partial L}{\partial \dot q}$? [duplicate]

We calculate the Hamiltonian as the Legendre transform of the Lagrangian $$H(q,p,t) = p \dot q - L(q,\dot q,t), $$ where $p$ is the slope function $$p \equiv \frac{\partial L}{\partial \dot q} .$$ ...
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1answer
81 views

Question (mostly) About Relativity

Before I get into the actual question, I'd like to say that my only knowledge on Einstein's Theory of Relativity (both Special and General) have been obtained through about an hours worth of videos ...
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0answers
39 views

Solving time evolution equations in Hamiltonian formalism

I have 4 time evolution equations and the Hamiltonian $H(X_{1},X_{2},P_{1},P_{2})$ that generates the time evolution depends on 4 canonical coordinates but I would like to solve the differential ...
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0answers
46 views

Please read the question from the image and answer [closed]

A photograher at a distance l from a railway track wants to photograph a train travelling at a speed v , at the instant when his line of vision makes an angle alpha with the railway track (What ...
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0answers
31 views

Show, from first principles, the equation of motion of a mass (m) on a spring? [closed]

Show, from first principles, the equation of motion of a mass (m) on a spring, subjected to a linear resistance force R, a restoring force S, and a driving force G(t) is given by $(d^2x/dt^2)$ + $2K(...
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1answer
21 views
+50

Calculating the power of a pneumatic piston vibrator

I am using a pneumatically-driven piston vibrator to compact a tank filled with granular material. The intensity of the vibrator can be regulated by changing the pressure of the pressurized air fed ...
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1answer
30 views

The correlation between scales of time and space

I guess it is quite well known that there is an empirical correlation between scales of time and space. That means that small things are usually move / rotate relatively (compared to its sizes) ...
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0answers
40 views

What if $\omega =0$, which is the frequency of the perturbation term?

In analytic mechanics, when we found a equilibrium position of the system, to determine the stability of that configuration, we apply $q \to q_0 + \epsilon \eta$ with $|\eta| \ll 1$ s.t $q_0$ is the ...
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2answers
55 views

Can we define potential for all conservative forces?

I know that defining potential for non-conservative forces is not possible and we can define potential and potential energy for conservative forces only. But can we define it for all conservative ...
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0answers
39 views

Time reversal invariance of physical laws stated mathematically

There is a logical argument stated in many physics books that laws of physics obey time reversal invariance. A common example that is given is two colliding balls in a snooker game. If we observed ...
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2answers
45 views

Why is the work done by friction zero when body is rolling? [duplicate]

Why is the work done by friction zero when body is rolling? Does it mean no energy is dissipated by friction.
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0answers
21 views

How to calculate the amplitude increase by resonance?

If you know the natural frequency of an object, how would one calculate how much the amplitude increases because of resonance? I would imagine it would depend on the material?
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0answers
16 views

What happens when an impulse is applied at right angles to one end of a rod (free to move on a frictionless surface)? [duplicate]

What will be the difference if we apply this impulse at the center of the rod? Will the translatory motion be same in both the cases?
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2answers
127 views

Infinitesimal Rotation under Orthogonal Similarity Transformation

I’m reading charpter 4.8 of Goldstein’s classical mechanics 3rd edition that deals with infinitesimal rotations, and the following is the part I got stuck: (p.166~167) If $d\boldsymbol{\Omega}$ is ...
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0answers
37 views

Euler applies the principle of least action to projectile motion

I was reading my physics book and became interested in the origin of the Principle of least action. After some historical research I arrived at Euler's historical text A method for finding curved ...
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2answers
84 views

Will a wheel keep rolling in perfect vacuum? [duplicate]

I have a query which I cannot resolve by finding enough arguments. A perfectly round wheel that also doesn't have any contractions due to gravity is placed in a perfect vacuum, so no drag is present. ...
12
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2answers
2k views

In the quantum hamiltonian, why does kinetic energy turn into an operator while potential doesn't?

When we go from the classical many-body hamiltonian $$H = \sum_i \frac{\vec{p}_i^2}{2m_e} - \sum_{i,I} \frac{Z_I e^2 }{|\vec{r}_i - \vec{R}_I|} + \frac{1}{2}\sum_{i,j} \frac{ e^2 }{|\vec{r}_i - \vec{...
14
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3answers
2k views

How does Ehrenfest's theorem apply to the quantum harmonic oscillator?

Ehrenfest's theorem, to my level of understanding, says that expectation values for quantum mechanical observables obey their Newtonian mechanics counterparts, which means that we can use newton's ...
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1answer
22 views

Running water and stand still water impact [closed]

I jumped from height $\:\rm h$ into a moving water canal of breadth $\:\rm b$ and infinite length with velocity $v$ and in a different fall, I'm plummeting into a swimming pool of length $l$ breadth $...
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2answers
54 views

Is rigid body mechanics included in classical mechanics?

Can rigid body mechanics be derived from Newtonian, Lagrangian or any other formulation of classical mechanics? Or do we need some extra axioms or laws?
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2answers
134 views

Is Action Always “Locally” Least?

In general, I know it's true that the Principle of Least Action is more properly called the Principle of "Stationary" Action. However, there are results which seem to suggest that for sufficiently ...
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4answers
84 views

Does rotational kinetic energy always implies translational kinetic energy?

I always thought that whenever there's rotational kinetic energy, there's also translational (linear) kinetic energy. The opposite is not true. There can be translational kinetic energy without having ...
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0answers
26 views

What is the difference between Non-Conservative and Dissipative?

We often hear these terms. However, they are often confused to be synonyms, but they are not. What are the rigorous definitions of them?
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2answers
64 views

What is the origin of this formula $\vec B = -\frac{1}{c^2}\vec v \times \vec E=-\frac{1}{ec^2}\vec v \times \nabla V(r)$?

For context, this is from the beginning of the proof for the Spin-orbit interaction term in atomic physics. Classically, the magnetic field seen by a particle of charge $e$ moving with a velocity $...
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0answers
18 views

Theorem of relative derivatives, Mozzi Equations and Theorem of relative motion

I am currently studying Kinematics in a Mechanics course and I am unable to find sources besides college material to help me studying what I learn in classes, probably due to my ignorance regarding ...
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2answers
89 views

How is mass defined by special relativity?

I am eagerly interested in all kinds of areas of physics. As the question of mass has been around for a pretty long time, I am interested about what modern physics namely special relativity says about ...
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1answer
21 views

Speed that a galaxy-sized newton's cradle would propagate motion

This doesn't necessarily have to be a newton's cradle, but the important point is that the length of the chain of spheres is exceptionally large (on the order of light years). Ignoring the effects of ...
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1answer
59 views

What is the meaning of $d$? [duplicate]

What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
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0answers
19 views

Energy quantization in macroscopic world [duplicate]

Is energy quantized in macroscopic world according to principle of correspondence ? Can an object have quantized kinetic or potential energy ?
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0answers
19 views

What are the dynamics of a rope wrapping around a pole of given radius?

Suppose we drop a mass m from an initial angle $\theta_o$ connected to the pole of radius r with a rope of initial length $l_o$. As the system is released, the rope wraps around the pole, decreasing ...
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1answer
41 views

What does conservation of probability mean in Classical Mechanics and why is it true?

In the context of the Liouville equation, regularly the conservation of probability is invoked. (Of course, the overall probability is always conserved but this is a truism and not what is meant here. ...
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2answers
103 views

What does $\frac{d\rho}{dt} =0$ but $\frac{\partial \rho}{\partial t} \neq 0 $ mean intuitively?

For concreteness, let's say that $\rho(q,p,t)$ describes the probability density in phase space. On a superficial level both $\frac{d\rho}{dt}$ and $\frac{\partial \rho}{\partial t} $ tells us how $\...
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2answers
28 views

Do you have an idea for two easy experiments to measure the coefficients of static and sliding friction of a rope wrapped around a steel rod?

I'm researching a phenomenon dependent on the Capstan/Euler-Eytelwein-Equation. To model a simulation, I need the friction coefficients. I came up with the idea of hanging one mass $m_1$ on one side ...
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1answer
17 views

Mechanics of a stationary grain resting on the surface of a granular bed which is subject to a collision

Consider the following stationary configuration of three disks (in 2d): I would like to consider the two supporting (lower) disks as entirely static, but the upper disk can move, and it only rests in ...
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1answer
50 views

How can you use tensors in theory of elasticity? [closed]

I am interested in physics and Icame across the usage of tensors in elasticity. How do you do that? How can tensors be useful?