Classical mechanics Definition and 1000 Threads

Homework Statement This is a problem from K & K, but I changed it very slightly. A light plane weighing 2,500 lb makes an emergency landing on a short runway. With its engine off, it lands on the runway at 120 ft/s. A hook on the plane snags a cable attached to a 250 lb sandbag and drags...

Homework Statement I'm doing past a past exam (2003) and I'm stuck on the first exercise. Here it is: Consider a helix centered in the z-axis, of radius R and fixed step a, given in cylindrical coordinates by z=\frac{a\theta }{2 \pi }, r=R. A particle of mass m slides without rolling over the...

What would be your go-to textbook for Classical Mechanics at the undergraduate level? It must also cover the Lagrangian and Hamiltonian formulation. My school uses "Analytical Mechanics" by Fowles & Cassiday but I find it not very complete and doesn't cover all topics. I've also read parts...

Homework Statement A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point x = √3 when it is projected towards the origin with speed 2. Find the equation of motion describing x(t). Homework Equations x=Asin(ωt+θ) The Attempt at a Solution At t=0...

Classical Mechanics: Finding force, equilibrium points, turning points... Homework Statement The potential energy between two atoms in a molecule is U(x) = −1/x^6 +1/x^12 Assume that one of the atoms is very heavy and remains at the origin at rest, and the other (m = 1) is much less...

Could someone demonstrate to me how in Landau's Mechanics book, he gets from equation (16.5) tan θ = (v_0 sin θ_0) / (v_0 cos θ_0 + V) to equation (16.6) cos θ_0 = -(V/v_0) sin^2 θ ± cos θ √[1 - (V/v_0)^2 sin^2 θ] I am using the quadratic formula, and the first term on the right...

Homework Statement An Instrument carrying a projectile accidentally explodes at he top of its trajectory.The horizontal distance b/w the launch point and the point of explosion is L. The projectile breaks into 2 pieces which fly horizontally apart. The larger piece has three time the mass of...

Homework Statement I have a problem regarding to lagrangian. 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{d F(q_1,...,q_n,t)}{d t} also satisfies Lagrange's equations where F is any ARBITRARY BUT...

I like your explanation, and I agree. However, why does it not work for the case of gravity? To be more specific, I'm talking about the mainstream classical justification for the equivalence principle as it applies to active gravitational mass. Let me give an analogy that applies to the OPs...

I'm learning mechanics right now via an extension course. In the absence of an "on-demand" teacher I've found multiple textbooks and online resources to be useful. When I studied calculus, Paul's online calculus notes (http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx) were a great...

Homework Statement A mass, m, is attached to a support by a spring with spring constant, k. The mass is hanging down from the spring, so there is a gravitational force on the mass as well. Neglect any resistive or frictional force. The support is then oscillated with an amplitude of A and...

Hey guys, First time posting. I was thinking of starting an extra credit paper for my Physics 1A course, and was wondering if anybody could think of any noteworthy and recent applications of classical mechanics that I could do some research on. I was thinking of maybe pursuing dark matter as...

Hi, I'm a bit confused wit the concept Configuration Space. First, the professor defined generalised coordinates as such: U got a system of n particles, each particle has 3 coordinates(x,y,z), so u got 3n degrees of freedom. If the system has k holonomic constraints, u got 3n-k degrees...

This is really simple but I can't figure it out. I was on a bus when I thought of this: Say I'm sitting in the back of a bus which is traveling on a flat surface, and accelerating with a constant acceleration (forward). Now I get up from my seat in the back and make my way to the front of the...

Homework Statement Set up the equations of motion for the system shown in Fig. 4.16. The relaxed lengths of the two springs are l1, l2 . Separate the problem into two problems, one involving the motion of the center of mass, and the other involving the "internal motion" described by the two...

Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.

Im pretty good at Mechanics but I need a "feel good" book which can complement and help me strengthen my concepts of mechanics very well. I like thorough explanations so I can be conceptually good and in a position to attempt most questions. Also needs to have good worked examples. Please let me...

Hi! I am a very mathematically-oriented physicist. Since I never plan in making contact with "dirty" mechanics like robotics, structural problems or force diagrams, I want a book that prepares me for the mathematical/theoretical foundations of mechanics so that I can transition more smoothly to...

The principle of least action applicable in an uniform field can be obtained as follows: Particle A \vec{a}_A = \vec{a}_A \int \vec{a}_A \cdot d\vec{r}_A = \int \vec{a}_A \cdot d\vec{r}_A \int \vec{a}_A \cdot d\vec{r}_A = \Delta \; {\textstyle \frac{1}{2}}\vec{v}_A^2 \int \vec{a}_A...

I'm working on a project for a space habitat, and I want to have the math to back it up. Sorry if some of these seem obvious or too simple, but I'm here to learn. By the way this is not homework, it's just something I do in my spare time. And if you have the links where I can learn more about...

Terminal Velocity In Glycerin 2.10 in "Classical Mechanics" Homework Statement For a steel ball bearing (diameter 2mm and density 7.8g/cm3) dropped in glycerin (density 1.3g/cm3 and viscosity 12 N s/m2 at STP) the dominant drag force is linear drag given by flin = 3*pi*n*D*v where D is the...

Homework Statement This is a fairly general problem that came up while trying to model a system. Given a rotating disk and an inertially fixed object, how is the fictional coriolis force handled? For example, if there is a dot on the ground below a sheet of transparent plastic rotating at...

Homework Statement "A passenger (mass m) initially at rest steps out of an airplane. Assume down is the positive x-axis and put the origin at the airplane. Assume the air resistance force is linear in the velocity so F(air)= -mbv. Find the distance D he has fallen when his velocity is...

Homework Statement A particle has a velocity u = -V0 i + V0 j and position (d,0) at t=0. At any time t its position in polar coordinates is (r,theta) and velocity V = V0 cos theta i + (V0-V0sin theta) j. At t =t, angular velocity of the particle at the origin will be -----------------...

Hi, I'm currently a physics major attempting to earn my bachelor's degree. I was just told by the tiny physics department at my school that they won't be offering the classical mechanics course that I need in order to graduate before that fateful date, they suggested that I add an additional...

A block is resting on a frictionless surface as shown in the figure attached with this post. Calculate the minimum force F required so that the block will topple? The dimensions of the block, free body diagram and other details are there in the picture attached. Now, since the surface is...

Homework Statement A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion m\ddot{z} = -m\gamma\dot{z} + F(t) to find v(t) = \dot{z}(t) for the initial velocity \dot{z}(0) = v_0 Hint: what is the time derivative of...

Homework Statement A point mass m is exposed to a time dependent force F(t). Determine the position r(t) of the point mass for the initial conditions r(0) = r_{0}and v(0) = v_{0} Homework Equations The Attempt at a Solution \sumF= ma F_{z}(t) - mg = ma a = 1/m F_{z}(t) - g...

I am taking calculus based physics I (classical mechanics) in a few days. I'm shooting for 100s on my tests so I need to be diligent. What is the best way to study classical mechanics? What I plan to do is take notes on the chapter before lecture, and after I will do all the problems (not...

Why do first-year grad students take classical mechanics, besides those wanting to analyze mechanical systems? This would be a course along the lines of Goldstein, etc. Do some of the concepts/methods show up later in quantum mechanics, nuclear physics? If they skipped this mechanics...

Can anyone give me some suggestions?Thanks.

Wondering if it is only the formulae of quantum mechanics that routinely include complex numbers (a real component plus an imaginary one, e.g. i (the square root of -1)). If so, doesn't this immediately suggest (or even demand) that the (un)reality of the quantum realm is fundamentally unlike...

Classical Mechanics Homework question Question - A light elastic string AB of natural length L and spring constant K, lies slack on a horisontal plane. A particle of mass m also at rest, is attached to end A of the string. The other end B is pulled along the plane with constant velocity V...

I'm beginning a directed study in QFT this fall and my supervising instructor told me I'd need to know some basics of Lagrangian and Hamiltonian Mechanics before we began (he also told me I needed to go back and review Perturbation Theory) since I'd need to know the formalism I guess? I've...

Homework Statement Using the corresponding constraints conditions, calculate the kinetic energy of 1)A homogeneous cylinder of radius a that rolls inside a cylindrical surface of radius R>a.Homework Equations My toughts: I hope they meants "roll without slipping". Let's consider this case...

Homework Statement Determine the principal moments of inertia of a circular cylinder with radius R and height h. Homework Equations Not sure. The Attempt at a Solution This is the first problem of this kind I attempt to solve. From what I've read on wikipedia, the tensor of...

Homework Statement Determine the possible trajectories of a particle into the following central potential: U(r)=U_0 for r< r_0 and U(r)=0 for r>r_0.Homework Equations Not sure. What I used: Lagrangian+Euler/Lagrange equations.The Attempt at a Solution I used polar coordinates but I'm not sure...

I'm an aerospace engineering major. I'm wondering if, in the future (perhaps after graduation), a treatment of classical mechanics under Taylor's book would be useful to me. I will be taking classes on statics and dynamics, but after that, there doesn't seem to be any further treatment of...

Homework Statement A particle of mass m moves under a uniform gravitational field along a rod which moves in a vertical plane with a constant angular velocity \vec \Omega. Write down the motion equations of the particle and calculate the constraint force. Is the energy conserved...

Homework Statement The cycloid pendulum consists of a particle under the effect of a constant gravitational field (\vec g = -g \hat y) that moves without friction over a curve described parametrically by x=a(\theta + \sin \theta) and y=a(1-\cos \theta ). 1)Write down the Lagrangian and the...

What is the typical material covered in such classes? Is there a common textbook used by most colleges that I could look through? Can someone suggest a good book from Dover publications that I can pickup cheaply to serve the same purpose? Much appreciated.

Homework Statement I try to solve the problem 3.5 in Kleppner Kolenkow ”An introduction to Mechanics” using various approaches but end up with wrong answers. The problem is: 3.5 A circus acrobat of mass M leaps straight up with initial velocity v0 from a trampoline. As he rises up he takes...

Homework Statement Calculate the Cartesian expressions and the value of the modulus of the angular momentum in cylindrical coordinates of a particle whose coordinates are (r, \phi, z).Homework Equations L=T-V, \vec P = \sum _i ^3 \frac{\partial L}{\partial \vec {\dot q_i}}, \vec M = \sum _i^3...

I am a Physics major, just completed my junior year. During my fall semester I took the first level to the upper level Classical Mechanics sequence and received a C. I know that this was because I was working part time at that time so I was not able to put in as much time as I should have into...

Hi, I looking for books that have practice problems (with explanations would be nice) on general introductory level Calc. based Classical Mechanics. And for Electromagnetism I'm looking for an introductory book that has practice problems. I haven't taken Multivariable Calc. yet (I'll be...

Imagine that I have a system that is described classically by a given Hamiltonian which is a function of a given set of parameters q and their canonical conjugate momenta p=\frac{\partial L}{\partial \dot{q}}. Then, I will say that the quantum description of the same system is guided by setting...

I'll be attending college in a few months, and I would like to know what mathematics to study in order to understand my classical mechanics class. Could anyone help me? I've heard that I should know ODEs and PDEs but I didn't think such math was required. Is this true? And what should I be...

Okay, I have this textbook about Classical Mechanics. It is NOT a high school textbook, it's like a college textbook, which requires beyond algebra. I also have calculus textbook, but I have not mastered multivariable calculus yet. If I do master this, will it help me finish Classical Mechanics...

So, I am about to read Landau's and Lifschitz's textbook on Classical Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material? Would real-variable calculus and linear algebra be sufficient for the task? Thanks for all...

Looking at a path of system state (x(t),v(t)) as a vector, the Lagrangian strangely is a scalar function of pairs of coordinates of the vector. If, on the other hand, the complete state of a system was captured in a single complex number x+iv, a complex analogue of the Lagrangian would simply...