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; ...

learn more… | top users | synonyms (1)

3
votes
2answers
3k views

Confused with stress, strain and linear thermal expansion

Four rods A, B, C, D of same length and material but of different radii r, 2r , 3r and 4r respectively are held between two rigid walls. The temperature of all rods is increased by same ...
1
vote
2answers
74 views

Is rotational motion of the centre of mass impossible?

We know that for a system, the center of mass $CM$ moves as a particle as though all the forces on the system were acting on it. So does that mean rotational motion of the center of gravity ...
0
votes
1answer
48 views

Moment of inertia of orbiting sphere

Is the moment of inertia of a sphere orbiting some object equal to the moment of inertia of a point mass at the same distance away from the object?
1
vote
4answers
6k views

Direction of torque precession of a spinning wheel

Consider a spinning wheel, which is held up by one end of it's axis like this: To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is ...
4
votes
0answers
57 views

Cauchy stress tensor for a spherically symmetric problem [closed]

Given a sperically symmetric problem, I am asked to show that its Cauchy stress tensor, in spherical coordinates will assume the form: ...
0
votes
1answer
53 views

How am I able to keep my footing on an accelerating platform?

When I'm standing in a train car and the train starts slowing down relatively quickly, I instinctively flex certain muscles in my legs and that helps me keep my footing. What muscles am I flexing ...
2
votes
2answers
1k views

Find generating function $F_1$ for canonical trasformation

I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation. For example, considering the transformation $$q=Q^{1/2}e^{-P}$$ $$p=Q^{1/2}e^P$$ ...
1
vote
1answer
46 views

Does more surface area mean more traction?

I came across this question when considering new vehicle tires in a snowy environment. It appears that big off-road tires have very deep treads which greatly increase the surface area of the tire. ...
1
vote
3answers
268 views

Why do we obtain classical physics by taking the limit of Planck's constant to zero?

Why if we specifically set Planck's constant equal to zero (the limit of it) do we sometimes get classical physics? I mean, what does it mean physically to set the constant equal to zero? Or to say it ...
1
vote
2answers
65 views

Are the generalized coordinates in Lagrangian mechanics really independent?

In Goldstein's Classical Mechanics, Chapter 2.3: Derivation of Lagrange's Equations From Hamilton's Principle part of the derivation involves each of the generalized coordinates being independent. $$ ...
1
vote
0answers
18 views

Rotation, translation or both. [closed]

the square is the same material throughout, equal mass distribution. In this case, will the object rotate, translate or both and why ? Thank you.
1
vote
1answer
39 views

Force (torque) to break a bike handlebar? [closed]

Few weeks ago a neighbor manage to hit my bike with his car while the bike was parked next to a wall, check the picture. One side of the handlebar was at the wall and the door of his truck hit ...
0
votes
0answers
58 views

An intuitive explanation of the so called Galileoʼs theorem

The statement of the theorem is as follows (see Francisquini et al, Physics Education, Volume 48, Number 6, November 2013): Prove that the time taken for a particle to slide from the highest point, ...
3
votes
1answer
168 views

How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics)

I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question: "Let $S(E)$ be the area enclosed by the closed phase curve ...
1
vote
1answer
77 views

Derivation Of Euler-Lagrange Equation [closed]

I want the proof of this relation in details, $$ \frac{\rm d}{{\rm d}t}\left(\frac{\partial\vec{r}_v}{\partial q_\alpha}\right)=\frac{\partial\vec{\dot{r}_v}}{\partial q_\alpha} $$
1
vote
0answers
47 views

Internal energy in classical and quantum mechanics [closed]

What is the difference between classical and quantum mechanics of rotational, translational and vibrational energies?
0
votes
2answers
49 views

Conservation of angular momentum in a collision

Suppose I have a stick hinged to a pivot and it is released from its horizontal position and just after it becomes completely vertical, it strikes a ball completely stationary as in the given figure ...
0
votes
3answers
74 views

Why can't we define a potential energy for a non-conservative force? [closed]

We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
3
votes
1answer
108 views

Why isn't kinetic energy conserved in this rotational dynamics problem?

Consider a uniform rod which is spinning about an axis that goes through its centre, perpendicular to the rod itself. Two small rings are attached on the rod at equal distances from the centre. As the ...
0
votes
1answer
107 views

Can Newton's 3rd Law be considered as a direct consequence of the coulomb's law of electric interactions? [closed]

Let me explain my thought. Lets consider Coulomb's definition of electric force between two charges as the fundamental law. Under this consideration, forces between charges already follow What ...
0
votes
0answers
28 views

The force of a spring

I am new in continuum mechanics and I want to prove the formula which gives the force given by a spring : $$F_{max}= \frac{Ed^4(L-nd)}{16(1+\nu)(D-d)^3 n}$$ where : $E$ – Young's modulus $d$ – ...
4
votes
0answers
100 views

Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
0
votes
1answer
45 views

Spring Potential Energy [closed]

A spring whose spring constant is $k$, having an initial "free" length is $l$, is being pressed by $2$ hoops on a metal(the parabola) on his both sides. (see image below) I want to calculate the ...
1
vote
3answers
3k views

A spinning bullet

I know the rifling in a gun or rifle puts a spin on the bullet along the axis of trajectory. Now I don’t understand exactly why does it make the trajectory more stable and allow for greater travel?
0
votes
0answers
31 views

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 ...
0
votes
2answers
39 views

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 ...
0
votes
1answer
47 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 ...
1
vote
0answers
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 ...
2
votes
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 ...
1
vote
1answer
62 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 ...
3
votes
3answers
3k views

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 ...
2
votes
2answers
618 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 ...
3
votes
1answer
864 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 ...
3
votes
3answers
252 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 ...
0
votes
0answers
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 ...
0
votes
2answers
85 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 ...
3
votes
2answers
64 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 ...
1
vote
0answers
19 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 ...
3
votes
2answers
72 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 ...
4
votes
0answers
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 ...
3
votes
1answer
41 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 ...
4
votes
0answers
59 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 ...
0
votes
0answers
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 ...
1
vote
1answer
27 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 ...
1
vote
1answer
16 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 ...
2
votes
1answer
100 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 ...
1
vote
0answers
43 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 ...
0
votes
0answers
35 views

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 $\beta$ ...
2
votes
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 $$L' = L + \frac{\mathrm{d}F(q_1,\dots,q_n,t)}{\mathrm{d}t}$$ ...