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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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Number of collisions with block [on hold]

The problem is given in David Morin's Classical mechanics. Here is the screenshot: Now, I jumped to solve part b of question. To find the number of bounces,we note that mass losses momentum of -2mV ...
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1answer
26 views

Different action-angle variables for a 2D harmonic oscillator

Consider a bidimensional harmonic oscillator. Ref. 1 says that, when the frequencies are commensurable, separating the variables in cartesian or polar coordinates leads to different action-angle ...
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34 views

Regarding change in kinetic energy [on hold]

When does change in kinetic energy equals zero? Also, is the initial velocity is zero for all the bodies ? Please explain.
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3answers
48 views

Changing Coordinate System Changes derivation (mechanics, dynamics)

I'm reviewing some mechanics, and having an issue where my choice of coordinate system results in an incorrect derivation, one that is clearly incorrect. I suspect there's a missing step in my ...
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2answers
38 views

Solving elastic 2-dimensional collision problems where the resultant angle is not provided [on hold]

Having real trouble with the question below that is part of my engineering course. I've sussed question 6 but making no headway with Q7. A ball of mass 0.2 kg collides elastically with a heavier ball ...
2
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3answers
152 views

What's the point of momentum?

I know this may sound like a strange question but I have always wondered what exactly the mathematical point of momentum is. I have understood energy to be an attempt to reformulate Newton's 2nd law ...
1
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1answer
66 views

Explanation of a spring using “Artistotle's law of motion”, $\vec{F}=m\vec{v}$

So I was watching Susskind's Classical Mechanics lectures and I didn't understand something in the second lecture. He was telling about Aristotle's Law of motion which is $$\vec F = m\vec v.$$ He ...
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1answer
43 views

D'Alembert's principle and equation of motion

Is obtaining proper equation of motion from D'Alembert's principle a mere coincidence or there is some logic behind this? This is asked because while we are finding the equations in a regime where ...
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0answers
22 views

Does brake help in preventing wheel spin

Once I came across a technique that supposed to help 2WD cars with regular open differentials in situations where one drive wheel has no traction and car is not equipped with electronic assistants ...
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0answers
21 views

How to generate force with air pressure [on hold]

I am trying to figure out how to generate a substantial force for a short period of time by releasing pressure in a small high-pressure air tank. A rough estimate of the force required is 40 ...
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0answers
94 views

Is it possible to jump in space [on hold]

A system of nonlinear equations can have many branches of roots, for example, a system of equations of general relativity by substituting $$g_{pq}=\sum_{k=1}^N c_{pqk} \phi_k (t,x^1,x^2,x^3),c_{pqk}=...
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3answers
104 views

What is the physical content of the principle of least action?

Say the world is governed by the Principle of Least Action (or Hamiltonian mechanics) and let's not worry about quantum mechanics too much. Independently of any Lagrangian or Hamiltonian, does that ...
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0answers
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Is there any formula or existing theory for how long it takes objects to fall through just the surface of a liquid?

I was watching Lecture 12 in Walter Lewin's 8.01 series (https://www.youtube.com/watch?v=djCCno4Cbcw), and the phenomenon at 19:26, as the ball bearing breaks through the surface, struck me. I have ...
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2answers
67 views

Are there such things as internal-external forces?

An example of an internal force is the tension in the spring of a harmonic oscillator. An example of an external force is the gravity on a pendulum. Are there any forces that are both internal and ...
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0answers
32 views

Newtonian mechanics relation with QM [duplicate]

QM is the best theory we have to date for the microscopic world. Can quantum mechanics explain also the motion of an object? In other words can we derive Newtons law of motion from QM?
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0answers
21 views

How to set setup of a torsion pendulum/balance physics experiment [on hold]

@Moderator: Per your meta data: "What about experimental physics and laboratory equipment? Physics is not just theoretical, and experimental physics is on topic here. This includes questions about ...
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1answer
24 views

Chirikov standard map derivation

This might be a stupid question, but I am having trouble understanding the derivation of Standard map by integrating Hamilton's equation of motion over one period. I am going through this dissertation ...
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2answers
31 views

What makes a collision 2D?

In my mechanics course, we've covered 1D and 2D collisions. However, what physical factors determine whether a collision will be 1 or 2 dimensional? To make the question more precise, consider a ...
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1answer
30 views

Logarithmic decrement of damped oscillatory system and energy [on hold]

I'm having a hard time trying to find connection between the logarithmic decrement of damped oscillatory system and the energy of that system. I need this to solve the following problem : Find the ...
0
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1answer
32 views

Viscoelastic Constitutive Relation

In the Mori-Zwanzig formalism, the following identification for the generalised shear viscosity $\eta(t)$ is given: $$ \eta(t) = \frac{V}{k_B T} \langle \sigma(t) \sigma(0) \rangle, $$ identified as ...
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1answer
16 views

Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?

I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question). Following Landau and Lifshitz's Mechanics, on page 110 ...
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0answers
17 views

Deriving kinematic equations for the slingshot maneuver using Lagrangian mechanics

I have an assessment/investigation coming up in my math class for which I plan to derive the equations of motion for the slingshot maneuver/gravity assist using Lagrangian mechanics. So far, I am ...
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0answers
23 views

Simple harmonic motion and rotation [closed]

A wooden rod rotates with an angular speed w, while the rod is making an angle x with the horizon or x axis . At the rod there is a ring of mass m which can slip up and down the rod . The coefficient ...
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0answers
28 views

Simple Harmonic Motion analysis [closed]

Can anyone help me solving this question
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0answers
49 views

If gravitation force varied with $r^{-3}$ instead of $r^{-2}$ what would happen to Kepler's laws [duplicate]

2nd law wouldn't change as it is LCAM. 3rd Law would change. But I'm confused about first law. Does any body under influence of any central force move in an ellipse?Can anyone give a simple proof/...
2
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4answers
88 views

Why is a temperature gradient set up in a heated rod?

Suppose a cylindrical rod is maintained at 100 degree Celsius and the other at 0 degree Celsius. My book says that after reaching "Steady State" the rod will have developed a constant temperature ...
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1answer
25 views

Potential energy of a charge in a magnetic quadrupole field

I have a charged particle of charge $q$ that moves with velocity $\vec{V}$ from a position $\vec{r}$, inside a magnetic quadrupole field of the form: $$\vec{B}=B_{0}(x,y, -2z)$$ The Lorentz force acts ...
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0answers
50 views

Spring with oscillating support (Goldstein chapter 11, problem 2)

The problem: A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to $z=a\cos(w_1t)$. By ...
0
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1answer
43 views

Position of a particle sliding down an arbitrary curve as a function of time

Given a curve in a frictionless environment with parameterization $\displaystyle \mathbf{r}(\theta)=x(\theta)\hat{\mathbf{i}}+y(\theta)\hat{\mathbf{j}}$ for $\theta\in[0,\theta_f]$, how can I find the ...
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1answer
50 views

Does the axis of rotation of a rigid body depend on the frame of reference?

When studying the kinematic motion of a rigid body, angular velocity $\omega$ is a vector that not seem to specify a unique axis of rotation... When looking at the free rigid body motion of a wheel ...
1
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1answer
54 views

Non-conservative forces in Lagrangian mechanics

In the Lagrangian formalism with a dissipative frictional force $F$, we can write $$\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial\dot{q}_{k}}-\frac{\partial\mathcal{L}}{\partial q_{k}}=Q^{(nc)}_{k}...
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0answers
22 views

What are the starting units to perform the Gauss method?

To calculate the Gauss method, we need : the respective geodetic latitude the equatorial radius of the body (here earth) the respective local sidereal time the respective declination the respective ...
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3answers
46 views

Why does a rotor move at a constant angular speed? [closed]

If a there is a net torque on a rotor of an electric motor produced by the electromagnetic force, then why does it rotate at a constant angular speed? This is in reference to problem 10.35 of ...
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0answers
25 views

Rolling mechanism

Suppose a ball is rolling on a flat platform.The ball is in a state of pure rolling i.e the point of contact of ball with the surface is having an instantaneous tangential velocity of zero relative to ...
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0answers
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How are time period and amplitude related in the oscillation given by $U(x) = k* |x|^3$? [duplicate]

Answer is of the form if time period is proportional to amplitude^(n). Then find n. This is a 2 mark question from 1998 IIT JEE paper. And I have come across a method that can be used to get the ...
1
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1answer
34 views

Derivation of the inertia tensor

I am trying to understand the inertia tensor of rigid bodies but I don't quite understand how it is derived. This is what I tried: Consider a rigid body consisting of $N$ point masses acted upon by ...
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3answers
59 views

Where does linear momentum go in angular momentum conservation? [closed]

This question is a continuation of another question, found here: Does conservation of angular momentum break conservation of momentum? The first part of this question is exactly the same as the other ...
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1answer
53 views

Resultant effect of orthogonal motion of electric charges

*If two charges are moving uniformly with parallel velocity vectors that are not perpendicular to the line joining the charges, then the net mutual forces are equal and opposite but do not lie along ...
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0answers
47 views

A problem on degree of freeedom?

[The problem is roughly] Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges of the ...
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0answers
24 views

What is degree of freedom in thermodynamics? [duplicate]

I have read a lit bit of degree of freedom in classical mechanics and hope to understand as if the number of variable used to describe a system in the configuration space. But in thermodynamics I read ...
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0answers
22 views

What is the formal definition of Degree of Freedom? [duplicate]

Is the degree of freedom defined in classical mechanics same as the degree of freedom in thermodynamics? If not what is the formal definition of degree of freedom in thermodynamics?
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1answer
41 views

Why can't I derive the rocket equation this way?

Suppose I'm considering both the rocket, its unburnt fuel and the exhaust all of them combined as my system. Also suppose that the rocket was initially at rest. Then according to momentum conservation,...
11
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2answers
258 views

Why does an ice-cube turn faster and faster while melting in water?

Whenever I put an ice-cube into a glass of hot water, so that it melts quickly, and it is initially rotating slowly, I noticed that its rotational speed increases as it melts and 'shrinks'. Why? I ...
0
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0answers
41 views

Invariance of Space and Time in Different Reference Frames

I'm studying dynamics by Anil Rao's book. He said something that made me really confused. The citations below construct the problem. [...] An assumption of Newtonian mechanics is that space is ...
0
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1answer
25 views

Non-relativistic limit of the cosmological constant

Usually, when we apply the non-relativistic limit ($c \rightarrow \infty$) to relativistic equations, the cosmological constant $\Lambda \sim \mathrm{L}^{-2}$ is simply offhandedly neglected by ...
2
votes
1answer
43 views

How can the action can describe a movement? What is the argument behind? [duplicate]

We define the action of a system as $$S(q)=\int_{t_1}^{t_2}L(t,q(t),q'(t))dt,$$ where $q(t)$ is the evolution of the system and $L$ is the Lagrangien. How can a stationary point of $S$ can describe ...
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0answers
22 views

Euler three body problem, what exactly is it? [closed]

I have a question about the 'Euler three-body' problem. I have to write an essay about this subject for the course 'chaos theory', which is about dynamical systems and chaos. Does anybody know what ...
0
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1answer
30 views

Formula for Power from Kinetic Energy

Work Done = $Fd$ Power = $Fv$ If the (net) Work Done = Change in Kinetic Energy, and the object starts from rest: Work Done = $\frac{1}{2} mv^2$ Power = $\frac{1}{2} m av$ Power = $\frac{1}{2} ...
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3answers
62 views

What is the direction of normal? [closed]

What will be the direction of normal and friction in a case where a spherical body is just about to fall off a table?
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0answers
21 views

How to calculate Hamiltonian when Lagrangian has higher order derivatives? [duplicate]

If we have a Lagrangian density $\mathcal{L}$ for a scalar field $\phi$ depending on $\phi$, $\partial _{\mu} \phi$, and $\partial _{\mu} \partial _{\nu} \phi$, what is the Hamiltonian? Additionally, ...