Classical mechanics Definition and 1000 Threads

Hello all. I know both books cover some different topics, but for the topics they share, which one do you think is better? I have checked the first chapters in both books, and, for the time being, I can't decide. So, if anyone of you have used these textbooks, maybe you can give me a piece of...

Homework Statement We have a spring of length l0 tied to two vertical non moving sticks. We place a mass m at 0,45l0 and let it oscillate. If we measure the period of an oscillation, we can find the angular frequency and calculate k. The question is, how can I calculate k1 and k2, the constants...

As seen in the picture, this question is about an object moving in the x-y plane. But I don't get why in equation 8.9 the cross terms vanish? If anyone can help me, that would be really nice.

I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : \begin{equation} E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial v(x,t)}{\partial...

I'm wondering if it's possible to send a man to the moon using only classical mechanics. If not, where would the classical equations fail?

Homework Statement A point particle of mass m moves on a frictionless surface. Its position can be described with polar coordinates r and phi. The particle is connected to the origin of the coordinate system by a spring with spring constant k and unstretched length zero, which provides a force...

I am a secondary student who is in grade 10, which means that I am only beginning to learn physics and calculus (e.g. Newton's Laws and Binomial Theorem). I have a passion for physics and has been getting relatively good grades but recently I started to lay my hands on Newton's Laws and I am...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

Dear All, I am often get confused when four terms STATICS,DYNAMICS,KINEMATICS and KINETICS are used in physics Mechanics.can someone please differentiate between these four terms.i will be thankful.

Homework Statement - The force acting on a particle m = 3kg is given by the following force equation: F = (v/9)(3 - x2), the particle begins at a position of x = 1m with a speed of v = 0 m/s at time t = 0s. Find the displacement of the particle at time t = 5 s. Homework Equations F =...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

I've been asked to find the conserved quantities of the following potentials: i) U(r) = U(x^2), ii) U(r) = U(x^2 + y^2) and iii) U(r) = U(x^2 + y^2 + z^2). For the first one, there is no time dependence or dependence on the y or z coordinate therefore energy is conserved and linear momentum in...

In classical physics , specifically in rotational mechanics we have concepts of torque , angular momentum and their extensions. We widely use them in problem solving but how were they defined , what was the basis of their definition , was all that purely experimental and most importantly who did...

Homework Statement A point particle is moving in a field, where its potential energy is U=-α/r. Find first motion integrals. Homework Equations How to derive it The Attempt at a Solution I only figured out that all of this is related to the conservation of energy, but i don't know even the...

I would like to use the Buckingham-Pi theorem in order to "algorithmify" non-dimensionalization of existing equations. I can get things to work for very simple problems, but am running into issues with a harder example. I posted my question on physics.stackexchange.com the day before yesterday...

Hallo Everyone, What are the most important unsolved problems in Classical Mechanics especially related to mechanics of rigid body mechanics, deformable-body mechanics and, fluid mechanics.

hey there, i need your help, I am a student in physics and electricity engineering, and i have a bit of a problem with the changing mass materiel, well in first look he's pretty easy but i want to learn how to create my own equations and I am never getting the same result. so ill be glad if...

Hello all, I'm currently taking an upper undergraduate two part Mechanics course using the above mentioned book by its author. He's a great professor and I was wondering if anyone else has checked out this book? It's very math heavy and I'm struggling with some of the language since I haven't...

Do you guys know of any website that has solved problems of Lagrange Mechanics?

I was wondering if anyone could suggest any books that would describe and explain basic and some more advanced mechanics with a reasonable amount of mathematical content? Cheers

Homework Statement Given a uniform bar of length L, which point should you hang it from (between 0 and L) so that you get maximum frequency for small oscillations? Homework Equations ... The Attempt at a Solution It seems like a basic problem, but I don´t know how to start. Could you guys...

I am trying to dig deep into classical mechanics. Among many suggestions, this was an odd one to me. I know of Arnold Sommerfeld and his work, but I have not read any of his works(books, papers, .etc). I tried to find reviews of this book online to no avail. If there are people who have read the...

There will be a competition in classical mechanics and I need a good book to prepare. The competiton was also held last year and i ended up thir, so I dear to say that I know classical mechanics very well. The competition will include kinematics, dynamics, law of conservation of energy, Newton's...

I need a reference book to read the following topics- a) Generalized coordinates; b) D'Alembert's principle and Lagrange's equations; c)Hamilton equations; d) Motion of rigid bodies in two dimensions. The topics need to be covered only at graduation level. Thanking you in anticipation.

This is Newton's law of universal gravitation. $$F=G\frac{m_1.m_2}{r^2}$$ Gravitational field $$g$$ is derived from this formula $$g=G\frac{m_1}{r^2}$$ This is named gravitational "field" strength. If Newton knew nothing about "field concept" and formulated his formula in the form of "action...

I've finished my institution's sequence on classical mechanics and am wanting to keep reading the subject. Does anyone have a standard suggestion after Fowles/Cassiday "Analytical Mechanics"? We covered almost the entire book except for the very last chapter and a few sections on oscillations...

In 'Introduction to Mechanics' by Kleppner and Kolenkow...motion of ionospheric electron under non-uniform acceleration is x = (a0/w)t - (a0/w^2)sin wt...my question is when there is non-uniform acceleration, it makes sense to have sinusoidal part in the motion...but how come there is uniform...

Homework Statement I'm really looking for a verification on parts a) and b), but I'll add what I did with part c) without going to into too much detail. I'm posting this question mainly due to part d). I feel that I have every part before this right, but I'm not getting any symmetric...

Background: I am an upper level undergraduate physics student who just completed a course in classical mechanics, concluding with Lagrangian Mechanics and Hamilton's Variational Principle. My professor gave a lecture on the material, and his explanation struck me as a truism. Essentially, he...

I am about to read the book Classical Mechanics by Herbert Goldstein. The prerequisites that it says in the book are advanced calculus and vector analysis. Would that mean multivariable calculus? Also there are a lot of things about transformation matrices and tensors. Would I need to review...

Homework Statement The potential energy function of a particle of mass m is V(x) = cx/(x2+a2), where c and a are positive constants. Qualitatively sketch V as a function of x. Find two equilibrium points: identify which is a position of stable equilibrium, and find the period of small...

Homework Statement A bird of mass 2 kg is flying at 10 m/s in latitude of 60° N, heading due East. Find the horizontal and vertical components of the Coriolis force acting on it. Homework Equations The Coriolis Force, F = 2mw∧v. Where ∧ shows the cross product between angular frequency...

I was recently reading the strange world of classical mechanics. It prompted me to calculate some round trip times for things moving near the speed of light (classically, with an aether). I found that the predictions it makes are awfully similar to relativity, and I can't think of an experiment...

I know Single variable Calculus and I have a basic understanding of multivariable calculus. I also happen to know basic linear algebra. What are the mathematical pre-requisites needed in order to self-study theoretical mechanics? I'm planning to take this course...

Classical Mechanics by Herbert Goldstein is one of the most used textbooks on this subject, perhaps the most used one. However, I found a couple of errors in Section 4.9 (in 3rd ed, written with Charles Poole and John Safko) about rotations. First, at p. 172, the angular velocity vector ω is...

When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...

Well, I know that Hooke's law establishes that the force applied on a spring is proportional to the displacement. However, I've got a little bit confused about the formula. My textbook manages the formula as the following: F=-kx Whereas some websites manage it as this: F=kx I still don't...

PROBLEM: Show that Special Relativity predicts a precession of π(GMm/cl)2 radians per orbit for any elliptic orbit under a pure inverse-square force. where G is gravitational constant, M is mass of larger body, m is mass of smaller orbiting body, c is speed of light and l is angular momentum...

Homework Statement A solid hemisphere with radius b has its flat surface glued to a horizontal table. Another solid hemisphere with radius a rests on top of the hemisphere of radius b so that the curved surfaces in contact. The surfaces of hemispheres are rough, meaning no slipping occurs...

Hello everyone, my name is Silkia and I'm a new member. I am a pediatrician but as with Alejandro in another thread my real love has always been physics. In three occasions I had decided that this was my career choice but long "stories" short, I ended up in medical school. As an undergraduate I...

Homework Statement [/B] A solid cylinder of mass m and radius r lies flat on frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The...

Hello, I am a second year undergrad student majoring in Astronomy and Computer Science. I am having a hard time with my physics courses for the following reasons: 1) SmartPhysics is the text we use (if you can call it a text...). Basically it is an online HW and "pre-lecture" system that...

I have a course next semester on Classical Mechanics (mostly Lagrangian problems), for a second time. I'm ok for the theoretical preparation, but I'm trying to work ahead on problems and exercises, which was badly explained and without much of any resources. So, one of the sources to exercise on...

Hi everybody, The question sounds dumb, but I asked it, probably someone had the same experience, and can help me or give advice on it about what I'm going to do next ! I know calculus until the double integrals and I don't know enough about Lagrange multipliers ( Indeed, looking for intuitive...

Please let me know if I did this wrong or right, and if I did it wrong, please correct me :) 1. Homework Statement The biceps brachii, a muscle in the arm, connects the radius, a bone in the forearm, to the scapula in the shoulder (see below). The muscle attaches at two places on the scapula...

I've read a couple of places that a hamiltonian can be a tool used in classical mechanics and that it's eigenvalues are useful pieces of information. I've tried finding info on the subject matter, as I want to see something that actually requires linear algebra, or at least makes good use of it...

Homework Statement Consider a transformation to a relatively uniformly moving frame of reference, where each position vector ri is replaced by rli = ri − vt. (Here v is a constant, the relative velocity of the two frames.) How does a relative position vector rij transform? How do momenta and...

Hello Physics Forum! I have a question: The problem: For a lightly damped oscillator being driven near resonance in the steady state, show that the fraction of its energy that is lost per cycle can be approximated by a constant (something like 2pi, which is to be determined) divided by the Q...

Homework Statement In certain situations, particularly one-dimensional systems, it is possible to incorporate frictional effects without introducing the dissipation function. As an example, find the equations of motion for the lagrangian ##L = e^{γt} (\frac{m\dot{q}^2}{2} - \frac{kq^2}{2})##...

I'm currently going over some mechanics notes and am confused about the following situation: In the book I'm looking at, it describes two particles absent of external forces, only exerting a force on each other. In deriving a potential energy equation for the two, it goes on to say that if the...