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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The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
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In a vacuum, given two identical objects, if one is stationary, what would happen if the two objects collide?

Given these two identical objects, if one is stationary, and the centre of mass of the other object collides head on with the centre of mass of the object that is stationary, i.e it does not come into ...
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1answer
49 views

How are unbalanced forces even possible, given Newton's 3rd law? [duplicate]

The notion of an unbalanced force seems to contradict Newton's third law, entirely. For instance, apparently, if you push a rock, then an unequal force is being applied in the opposite direction with ...
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26 views

Height of water in vessel containing gas [closed]

The question reads- Thin walled Cylinder of height h, mass m and cross section A filled with gas and floats on water. Now due to leakage depth of submergence increases by $\Delta h$. $P_o$ is the ...
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1answer
40 views

Why is the potential independent of the generalized velocity?

In Goldstein, Classical Mechanics, Chap. 1.4 we derive Lagrange's equations from D'Alembert's Principle. My question is regarding the last part of the derivation, specifically the part where he ...
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1answer
63 views

How is it possible to vary time without affect the coordinates or their derivatives?

In the context of Noether's theorem , the Hamiltonian is the constant of motion associated with the time-translational invariance of the Lagrangian. Time-translational invariance is equivalent to the ...
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3answers
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Why does friction cause a car to turn?

I've had a lot of difficulty conceptually understanding the physics of how a car turns on an unbanked curve, so I'm hoping you could help me out. When a car is moving in uniform circular motion, we ...
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2answers
620 views

Virtual displacement and generalized coordinates

I have a doubt regarding the expression of a virtual displacement using generalized coordinates. I will state the definitions I'm taking and the problem. The system is composed by $n$ points with ...
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1answer
867 views

Is there any case in classical mechanics where Newton's (strong) third law doesn't hold?

Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system ...
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3answers
254 views

Is angular velocity parallel to axis of rotation?

I'm reading the Wikipedia page on angular velocity. It says here of the angular velocity vector in three dimensions that “[t]he magnitude is the angular speed, and the direction describes the axis of ...
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35 views

What is the probabililty that a fair coin lands on its side?

This is a popular gag in movies, but I wonder how likely it really is. What is the probability that a uniform cylindrical coin (with radius $1$ and height $h$) lands on its side? If the ground were ...
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2answers
86 views

Intercept of 2 moving objects at constant acceleration

I have to make a simulation in which a guided missile has to hit an incoming enemy missile.The enemy missile "T" is the one which has to be intercepted and is only affected by gravity, the guided ...
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2answers
66 views

What is the difference between translation and rotation, in the Lagrangian/Hamiltonian frameworks?

This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian ...
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20 views

Finding maximal angle after elastic collision [closed]

Let $m_1=400gr, m_2=600gr$ represent the masses of two balls. the two balls are hanging from the ceiling ($m_1$ is right to $m_2$), and then someone pull to the right side the $m_1$ ball in an angle ...
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2answers
73 views

Energy of Falling chain

Can someone explain this solution for the motion of a falling chain? My Question is based on the above mentioned question on PSE. Suppose we have a chain attached on one end, while the other end is ...
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33 views

What kind of torques cause an object to precess?

In studying precession, my textbook (Taylor's Classical Mechanics) makes the assumption that a top spinning about its symmetric axis, but tipped at an angle $\theta$, will precess nicely so long as ...
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1answer
43 views

Birkhoff Method for Harmonic Oscillator Perturbation

Problem: Given Hamiltonian $$H = \frac12 (p^{2}+q^{2})+q^{3}-3qp^{2}$$ make a perturbative canonical transformation $(q,p) \rightarrow (Q,P)$ such that the new Hamiltonian, apart from terms of degree ...
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60 views

Falling Raindrop with Asymptotic Acceleration [closed]

I am given a falling raindrop that is gaining mass proportional to the product of its surface area and its velocity. I am assuming down is the positive direction. So, $m'=4\pi\alpha r^2v$. From ...
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54 views

What is an intensive property of a fluid?

Let's assume we are considering a fluid which occupies the bounded domain $\Omega_t\subseteq\mathbb R^d$ at time $t\ge 0$. Let $c\in\Omega_0$ be a particle of the fluid and $$x_c:[0,\infty)\to\mathbb ...
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1answer
28 views

Does *advection* describe the change of density of massless infinitesimal tiny *thingies* injected into a fluid?

I'm considering an incompressible Newtonian fluid with uniform density and try to figure out what's meant by the term advection. Let $\Omega_0\subseteq\mathbb R^d$ be an (infinitesimal small) bounded ...
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1answer
17 views

Expressing 3D orientation in alternative to Euler angles for 3D rigid body dynamics

I was unsure whether it would be best to post this in Physics, Maths, or other forums, so please say if this question is suited better elsewhere. I am trying trying to create a physics engine for a ...
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1answer
101 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
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45 views

Is time-1 map of a Hamiltonian vector field on a cylinder always twist?

I have a one degree of freedom analytic Hamiltonian $H(q,p)$ defined on a semi-infinite cylinder, i.e. $(q,p) \in \mathbb{T} \times \mathbb{R}^{+}$, such that all level sets $H(q,p)=c$ are closed ...
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Canonical transformation question

Let $(\vec{r},\vec{p})$ denote set of canonical variables. Assume a system is described by the following Hamiltonian $$H(r,p) = \frac{1}{2m}(p_1^2 + (p_2 - \beta*x_1)^2 + p_3^2),$$ where $\beta$ ...
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1answer
57 views

Lagrangian isn't unique [closed]

If $L$ is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations, show by direct substitution that $$L' = L + \frac{\mathrm{d}F(q_1,\dots,q_n,t)}{\mathrm{d}t}$$ ...
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1answer
59 views

Change of internal energy to kinetic energy

Why do we feel tired while running as during running we are increasing our kinetic energy. I understand that the energy inside us(from food or something else) is being converted to KE while running ...
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3answers
149 views

Work done changes between reference frames?

(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent ...
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1answer
49 views

Rate of applied force versus material failure?

Question: Does the rate at which a force is applied to an object determine the maximum force reached that mechanically fails the object? If so, what are the concepts that need to be understood to ...
2
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1answer
842 views

Hamilton's characteristic and principle functions and separability

Just hoping for some clarity regarding Hamilton's characteristic function (W). When we take a time independent Hamiltonian we can separate the Principle function (S) up into the characteristic ...
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1answer
27 views

In golf, is there a rotational mechanical advantage of using a thicker grip?

I was asked to migrate this question to the physics exchange. Ok, so many professionals are now using the new SuperStroke golf grips. I am basically thinking about the concept of a bigger grip, but ...
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1answer
54 views

Harmonic oscillator and cyclic coordinates

I am reading goldstein there is some comment I don't understand. Consider the following hamiltonian $$H = \frac{p^2}{2m} + \frac{kq^2}{2}$$, which can be rewritten as follows $$H = \frac{1}{2m}(p^2 ...
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A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
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160 views

Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and ...
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1answer
63 views

How does a pop pop boat work?

I have been reading about the pop pop boat on wikipedea. What I don't understand is after the hot water is ejected the vacuume gets created, so when the same amount of water will be sucked in the boat ...
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2answers
24 views

Torsion and twist in solid cylindrical beam

Well given a beam (as shown), a solid cylinder with radius R. A Torque $T$ applied to it, I need to solve the angle of twist ($\theta$) at the position where the torque is applied ($z$). The basic ...
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1answer
104 views

Why does a particle fall in a straight line?

In Lagrangian Mechanics we choose the path of least action. Given a uniform gravitational field, and a particle of finite mass; and fixing two points the start & end-point we consider all paths ...
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2answers
78 views

Simple Plane pendulum

So, I am having a lot of troubles visualizing the following system. The point of suspension of a plane simple pendulum of mass m and length l is constrained to move along a horizontal track and is ...
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5answers
919 views

Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
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0answers
27 views

Integral of Forces is the Velocity

I am self learning classical mechanics. I have the following problem: At time $t$ we have a force $f(t)$ acting on a particle with mass $m$ that is at distance $x(t)$ from $0$. We also assume ...
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0answers
44 views

An object on a conveyor belt

Let's say a bag (30kg) is sitting on a moving conveyor belt and at the end of the conveyor belt, there is a wall. Since the belt is moving at a constant speed (say 2.0 m/s), when the bag hits the ...
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0answers
45 views

What does the Hamilton-Function have to do with conservation of Energy in Lagrangian Mechanics?

I am currently doing Lagrangian Mechanics and I am having difficulties with deriving conservation laws from the Lagrangian. I have tried to understand this by reading the explanation in three ...
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1answer
24 views

What is the effect of torque transmitted through a gear system to the angular acceleration of a flywheel?

For a school project, I am trying to design a system that will spin a flywheel at a high rpm to store energy. My initial idea was to accelerate the flywheel via a compound gear train with an ...
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0answers
31 views

How much torque would it take to tip over a Christmas tree?

I had an, ah, incident in the house last night (need I say more? That has led to me wondering about how much torque I would need to apply to tip over a tree to the point where gravity causes the tree ...
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1answer
45 views

Force Exerted on a Rocket

I am reading Spivak's "Physics for Mathematicians". He has the following setup up: We let $m(t)$ be the mass of a rocket and its fuel at time $t$. And, we let $q(t)$ be the velocity at which the ...
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1answer
492 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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0answers
64 views

What is “Accumulated plastic strain rate” in Current yield Norton law?

I'm doing FEA of steel under high strain rates and using Elasto-ViscoPlastic material model, with Von-mises yield criterion along with Isotropic hardening. The strain rate sensitivity is addressed by ...
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1answer
261 views

Effect of Eath's rotation on a ball thrown upwards [duplicate]

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
2
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1answer
1k views

Lagrangian, Kinetic & Potential energy with two masses connected to three springs

Two masses $m_1$ and $m_2$ are on a frictionless surface. They are connected by three springs with constants $k_1,k_2,k_3$. $k_1$ and $k_3$ are attached to walls and $k_2$ is between the masses. $k_1$ ...
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2answers
58 views

Is this an error?

The teacher wrote the following: There is a dot missing where the green arrow is, right? After applying Euler's theorem, the term in brackets becomes $x_j$, but we need it to be $\dot{x_j}$, don't ...
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4answers
81 views

Relativistic acceleration in sinusoidal electric field

Consider a relativistic charge $q$ moving with an oscillating electric field $E_z$ with phase velocity $v_p=c$ in direction $\hat{z}$ (e.g. radially polarized laser coprogating with electron). What ...