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)

1
vote
1answer
307 views

Classical mechanics from Quantum mechanics

I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator $K(x,x_0;t)=\langle x|e^{-i ...
0
votes
1answer
550 views

Three-mass, two springs copled oscillator NOT attached to walls

Int he three-mass coupled oscillator problem, we often see it stated that you have three masses, (they can be equal or not, but we'll assume they are equal here) connected by two springs and then ...
5
votes
2answers
260 views

Is it normal for physical functions to lack a 2nd derivative?

My question is about the appearance of a non-analytic function in the formula for the resistive force in air or other medium. Considering the 1-dimensional case as covered by Walter Lewin in his 8.01 ...
0
votes
0answers
314 views

Work done by rolling vs skidding friction force

Two identical bicycles having equal weight riders are traveling along a level road adjacent to each other with the same non-zero velocity. Bike A, (the "skidder"), applies the rear brake strongly ...
3
votes
1answer
147 views

Determinant and adjunct of $k-\omega^2m$ in terms of natural frequencies

Given is a mechanical multiple degree of freedom system described by the following matrices and equation: mass matrix ${\bf{m}} = \left[\begin{matrix} m & 0 & 0 \\ 0 & m & 0 \\ 0 ...
0
votes
1answer
732 views

Non-rigid body rotational dynamics

I'm attempting to solve the following problem: Two friends hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about an axis through the center of the ...
0
votes
2answers
542 views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: ...
1
vote
0answers
139 views

Canonical transformation problem

(Apologies if HW questions are not allowed -- I couldn't really find a definite answer on this) Question Let $Q^1 = (q^1)^2, Q^2 = q^1+q^2, P_{\alpha} = P_{\alpha}\left(q,p \right), \alpha = 1,2$ ...
1
vote
0answers
195 views

Force from a HEMIspherical shell [closed]

I am working on this problem and just trying to figure out what my prof/ TA did in the solution sheet -- but also to make sure I understand what I am doing and some of the mathematics involved. A ...
1
vote
1answer
255 views

Constrained motion in a parabolic tube [closed]

A smooth parabolic tube is placed with vertex downwards in a vertical plane. A particle slides down the tube from rest under the influence of gravity. Prove that in any position, the reaction of ...
3
votes
1answer
191 views

Why can we assume independent variables when using Lagrange multipliers in nonholonomic systems?

I'm studying from Goldstein's Classical Mechanics. In section 2.4, he discusses nonholonomic systems. We assume that the constraints can be put in the form $f_\alpha(q, \dot{q}, t) =0$, $\alpha = 1 ...
6
votes
3answers
333 views

Angular momentum of particle rolling around inside of sphere

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity $v_o$. It travels halfway around the sphere and reaches point B, which is ...
2
votes
4answers
487 views

how to represent the effect of linking rigid-bodies together?

I have 2 rigid-bodies (b1,b2) if i linked one to the other (as if they are conjoined together) , how to represent b1 effect on b2 and b2 effect on b1 Is there any LAW that affect the ...
1
vote
0answers
316 views

Can a Research Paper on Classical Mechanics make it to a good journal? [closed]

I am starting University in September, 2014. I have some knowledge already on classical mechanics as I took optional Applied Math courses (called Mechanics 1 and Mechanics 2) in my mathematics ...
1
vote
1answer
475 views

Using Lagrange's Equations with Generalized forces

I am a bit confused on how this works. For instance if I wanted to look at an object moving in 2 dimensions only subject to gravity (and assuming that the potential is just mgy), I get that my ...
3
votes
1answer
143 views

Hamilton-Jacobi formalism and on-shell actions

My question is essentially how to extract the canonical momentum out of an on-shell action. The Hamilton-Jacobi formalism tells us that Hamilton's principal function is the on-shell action, which ...
7
votes
1answer
249 views

Phase Space Flow

Phase space flow shares characteristics with fluid flow such as incompressibility by Liouville's theorem. Extending the similarities one might be curious, does phase space flow have a characteristic ...
1
vote
0answers
179 views

Derivation of Scattering Equation 9.88 in Thornton & Marion

I am confused as to how a particular equation in Thornton & Marion's 'Classical Dynamics of Particles and Systems' was derived. It is equation 9.88, on page 354 of the fifth edition. An incoming ...
0
votes
0answers
32 views

best fundamental physics book [duplicate]

Good evening. I'd like to know, in your opinion, what would be the best fundamental physics book for a freshman? I want to start all over again. Thanks in advance.
0
votes
1answer
56 views

Force experienced on two particles in a rotating system?

I've a system of two particles of the same mass who rotate in a circle about the centre of mass of the two particles. Is the force experienced by the particles $F=MV^{2}/r$ or should I use ...
1
vote
0answers
125 views

Buoyancy Correction for a Kater Pendulum

Question: Consider a Kater pendulum: that is, a rod with two cylindrical masses at both ends, with a knife edge between the two masses and another between one ...
2
votes
2answers
596 views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
2
votes
2answers
1k views

Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
1
vote
2answers
120 views

Classical Mechanics - Allowed systems

I've edited my question to clear any possible confusing parts: This an exercise from the book "The Theoretical minimum", I'm paraphrasing. In classical mechanics, dynamical laws must be reversible ...
1
vote
1answer
79 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 ...
2
votes
1answer
286 views

Time it takes two oppositely charged particles to collide

I think this is supposed to be a simple problem but I am having a hang up converting it to a one-body problem. It's one-dimensional. +q and -q a distance d apart, held stationary then let go at t=0. ...
5
votes
5answers
4k views

Difference between torque and moment

What is the difference between torque and moment? I would like to see mathematical definitions for both quantities. I also do not prefer definitions like "It is the tendancy..../It is a measure of ...
0
votes
2answers
4k views

When does not Newton's 3rd law apply?

Is Newton's 3rd law valid in non-inertial frames? If so, then are there other cases for which Newton's 3rd law is not applicable?
1
vote
1answer
1k views

Explicit time dependence of the Lagrangian and Energy Conservation

Why is energy(or in more general terms,the Hamiltonian) not conserved when the Lagrangian has an explicit time dependence? I know that we can derive the identity: $\frac{\partial ...
0
votes
4answers
2k views

4th equation of motion

Ive been given the 4 equations of motions The fourth being: $$s=ut+\frac{1}{2}at^2$$ If rearranged it forms the quadratic equation $$at^2+2ut-2s=0$$ But that means that t has 2 values. Will ...
0
votes
1answer
353 views

General Solution of Mechanics Problem

I had a homework problem that Given velocity, $v^2(t)=\frac{K}{x(t)}$, where $x(t)$ is distance, find $v$ as a function of $t$. Of course if we assume a positive root, it is easy but what if ...
4
votes
3answers
1k views

Formula for implementing a simulated weighing scale

Background: I'm on the pledge drive committee for a non-profit group, and there is an issue that is always contentious within this group; thankfully the group is amicable, although competitive, about ...
1
vote
1answer
271 views

Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
4
votes
1answer
381 views

Can force be transferred through objects in a chain to the last object without any displacement of objects in the middle?

sorry for terrible graphical representation, I did an experiment, i took 6 coins fixed 4 of them in one place by placing some real heavy objects on them , then i took a 5th coin placed it in the ...
10
votes
3answers
961 views

What happens when a ball stops bouncing?

If I were to drop a bouncy ball onto a surface, each successive bounce will be lower in height as energy is dissipated. Eventually, however, the ball will cease to bounce and will remain in contact ...
0
votes
1answer
137 views

Missing centrifugal acceleration

I am trying to get correct equations for acceleration of a point in reference frame A, given position, velocity and acceleration in rotating reference frame B. Let $\mathbf{x}_A(t)$, ...
2
votes
2answers
225 views

Can a massless rope accelerate?

Suppose I have an Atwood machine, that is, two different masses connected with an inextensible, massless rope over a pulley. Assuming no friction between the rope and the pulley, the heavier mass will ...
3
votes
1answer
364 views

D'Alembert's principle

Actually I have some troubles to understand what this principle is all about, so I want to use the simple pendulum in order to get the idea. Since I have read a few passages that dealt with this ...
0
votes
1answer
166 views

What is the tension in the string of a spherical pendulum? [closed]

Can some one solve it by using Lagrange's undetermined multiplier method or any other method that explains the physics in spherical pendulum system? book references: 1) Classical mechanics by ...
1
vote
0answers
79 views

How to analyze this constraint question

Let $\gamma$ be a smooth curve in the plane, and introduce curvilinear coordinates $q_1,q_2$ on a neighborhood of $\gamma$; $q_1$ is the direction of $\gamma$ and $q_2$ is distance from the curve. ...
-2
votes
1answer
72 views

Attraction of a Bullet due to Gravity in a Perfect Vaccum

I realise that this might be conventially very difficult to answer because there's no KG or Newtons in space, only particles. As far as I understand, every object creates a 'pull' due to the forces ...
2
votes
1answer
98 views

Can all systems be put in equilibrium?

I'm in a first year statics course. We have spent the whole semester solving for forces and moments so that the system is in equilibrium. When we are given a system, we immediately begin solving for ...
1
vote
3answers
4k views

Would a pendulum swing indefinitely in a frictionless vacuum?

I am attempting to settle a friendly bet. Would a pendulum swing indefinitely in a hypothetical vacuum (i.e. no air resistance) having a hypothetical frictionless bearing (i.e. no energy lost due to ...
-2
votes
1answer
324 views

What is the maximum mass that the airplane can have and still maintain enough lift to fly? [closed]

A commercial airplane travels at a speed which is 85% of the speed of sound. The wings of the airplane are designed such that the bottoms of the wings are flat and the tops of the wings are curved ...
0
votes
1answer
1k views

Problem with Velocity of efflux [closed]

I am stuck in this problem- I need to find the velocity of efflux at the hole of the container. [We can assume that the area of the hole is negligible in comparison with the base area of the ...
3
votes
1answer
606 views

What is a bilateral constraint?

In the realm of mechanics/rigid body dynamics, can anyone tell me what a bilateral constraint is? Can't seem to find any information on the exact definition, just uses of it such as "considering only ...
0
votes
2answers
262 views

Curve object in liquid under pressure [duplicate]

I would like to know how red forces are compensate in this study. A black solid object is put in a liquid (helium or hydrogen for example). It's a curved solid. Solid don't move up or down, imagine it ...
0
votes
2answers
196 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
4
votes
0answers
93 views

Do vortex tubes work with a reversed end plug?

Would a vortex tube still work if instead of a cone plugged into the 'hot' end you had a smaller hole on the 'cold' end? As I understand it, the point of the cone on the hot end is to only allow the ...
11
votes
3answers
2k views

Why do we use operators in quantum mechanics?

In classical mechanics, physical quantities, such as, e.g. the coordinates of position, velocity, momentum, energy, etc, are real numbers, but in quantum mechanics they become operators. Why is this ...