Classical mechanics Definition and 1000 Threads

Homework Statement There is a metal stick that is connected to the ceiling with another one. The angle between them is 60°. Calculate the friction. Both lengths and weights are the same. Homework Equations T = f N or actually none, except trygonometry The Attempt at a Solution I tried using...

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

All copyright reserved to NPTEL, Govt. Of India and Prof. Balakrishnan.

Homework Statement N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy Homework Equations Noethers Theorem: If a...

(note: I'm going to represent the lagrangian as simply L because I don't know how to do script L in latex.) Homework Statement Two particles of equal masses m are confined to move along the x-axis and are connected by a spring with potential energy ##U = \frac{1}/{2}kx^2## (here x is the...

Homework Statement A mass m is initially at rest. A constant force $F$ (directed to the right) acts on it over a distance d. The increase in kinetic energy is therefore $Fd$. Consider the situation from the point of view of someone moving to the left at speed $V$ . Show explicitly that this...

Greg Bernhardt submitted a new PF Insights post "Classical Physics Is Wrong" Fallacy Continue reading the Original PF Insights Post.

Homework Statement A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ##r_0## with angular velocity ##w_0##, but...

Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below

Good morning. The question of the "continuous" or "discrete" nature of the universe is the subject of diatribe among the greatest physicists in the world. I would like to discuss the same topic, but asking a question about the aspect of continuum in classical mechanics. The use of mathematical...

I am looking for an undergraduate textbook on Classical Mechanics that includes Hamiltonian and Lagrangian formulations. One reason for this is that I am interested in quantization and second quantization. It should include treatment of harmonics oscillators. Thanks!

Homework Statement Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m .FInd the time...

Homework Statement Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m .FInd the time...

I'm trying to model a sphere having force applied at position P in the following diagram: I know that this applied force will have an x and y component; the y component will propel it upwards, but what I am confused about is the x component of the force. I know that the x component will propel...

I have a test coming up next week and while doing some practice questions I found one I can't wrap my head around. The question is: A pyramid (assume uniform density) is divided in two parts by a horizontal plane through its center of mass. How do the masses of the two parts compare ? There are...

Homework Statement Homework EquationsThe Attempt at a Solution what's the Fa and Fb? my logic is Fa = Wa - N = mg - ##\frac{N}{\cos \theta}## so is Fb... so the ratio is 1. But I know it's wrong. What will make the difference between Fa and Fb? can anyone give a clue please?

Homework Statement Given a graph (see below) containing the velocities of two stars with respect to the sun, I am asked to calculate the velocity of the centre of mass of a binary system. I am not given the mass of either star, nor the shape of the orbit nor the velocity of the centre of mass...

Homework Statement The carbon dioxide molecule can be considered a linear molecule with a central carbon atom, bound to two oxygen atoms with a pair of identical springs in opposing directions. Study the longitudinal motion of the molecule. If three coordinates are used, one of the normal...

Homework Statement A rocket (initial mass ##m_o##, constant exhaust velocity ##v_{ex}## needs to use its engines to hover stationary, just above the ground. a) If it can afford to burn no more than a mass ##\lambda m_o## of its fuel (##\lambda \lt##), for how long can it hover? b) If ##v_{ex} =...

This is with regard to my doubt in the derivation of the principle of least of action in Goldstein Is there any theorem in math about definite integrals like this ∫a+cb+df(x)dx = f(a)c-f(b)d The relevant portion of the derivation is given in the image.

I am solving a problem where I need to decide if an asteroids velocity is high enough to escape the planets gravitational pull. The way I did it was use conservation of energy and angular momentum to find an expression for the radial velocity and show that it remains positive as r tends to...

Homework Statement I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving. Homework Equations I = 2/5 MR^2 torque = I*alpha = R x F The Attempt at a Solution [/B] before anything, I don't get why there's a...

This question is regarding equation 6.59 in Classical Mechanics Goldstein 3rd edition. I don't understand how he reaches that step. He says he does by inverting 6.41. Is he taking the transpose matrix composed of the eigen vectors by meaning inversion ? I thought I could upload the screenshot...

Homework Statement An artist must push with a minimum of 75N at an angle of 45° to a picture to hold it in equilibrium. The coefficient of friction between the wall and the picture frame is 0.30. What is the mass of the picture? Homework Equations ΣF=0 Ffr=μFN F=ma The Attempt at a Solution I...

I am self studying Classical Mechanics and I am a bit confused about this. After reading Kleppner Kolenkow Mechanics can I read Symon's Mechanics or do I need to read anything in between like Fowels or Marion&Thornton? I already studied the Maths portion upto Multivariable Calculus,Real...

I need a book with exercises, to try to excel my next classical mechanics, I really to get a good grade. Thank you very much!

I’m felling demotivated because I had a bad grade, I don’t know how I got such kind of grade. However, I’m looking to get a very good grade in the next test, that will count 100%. I’m in the first year of physics, what advices do you have on how to study(CM), which exercises? What books should...

Homework Statement Referring to the attached diagram, the object ABCD is kept in an isolated system where it is under no external influence of any kind. A· An instantaneous force F acts along the edge BC of the block ABCD, where M is its mass, with its center of mass located at O...

Well, my physics teacher taught us about rotation the other day and I came across a scenario where a sphere and a ring roll down a friction-less inclined plane from a point of absolute rest. I found it counter-intuitive as I started to think about why would they start rolling in the first place...

1.Why does the angular speed of small gear depend only on larger gear only? 2.Why does the length of linkage connecting two gears does not have any influence on the angular speed of smaller gear? The first question can be answered by looking at slack and tightening of chain caused by rotation...

Is the following logic correct?: If you have an hamiltonian, that has time has a variable explicitly, and you get the lagrangian,L, from it, and then you get an equivalent L', since L has the total time derivate of a function, both lagrangians will lead to the same equations euler-lagrange...

is there a way for me see EVERY solution from goldstein's book? i already have some solutions, but not every one

Homework Statement The Attempt at a SolutionSo I first tried by saying consider a time t in which mass m is directly above the origin O. I.e., mass m at the Cartesian coordinate (0, 4l/3). I wrote a = a(t) as the extension function of the spring, which has 0 natural length. So, I applied the...

how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 ) Thank You

Homework Statement Now these two blocks are pulled separately by x1 and x2 distance. Find the frequency of shm Homework Equations a = -w^2 x The Attempt at a Solution Now after m1 being pulled, it moves with acceleration a1=Force of spring/m1. acceleration of block 2 = a2=/force of...

Homework Statement I'm having some issues understanding a number of concepts in this section here. I attached the corresponding figure at the end of the post for reference. Issue 1) 1st of all, I understand that a Hamiltonian can be written as such $$H = T_2 - T_0 + U$$ whereby ##T_2##...

Homework Statement [/B] A mass ##m## travels in a straight line with velocity ##v_0## perpendicular to a uniform stick of mass ##m## and length ##l##, which is initially at rest.. The distance from the center of mass of the stick to the path of the traveling mass is ##h##. Now the traveling...

Homework Statement The skier is skiing without friction down the mountain, being all the time in a specified plane. The skier's altitude y(x) is described as a certain defined function of parameter x, which stands for the horizontal distance of the skier from the initial position. The skier is...

Homework Statement A spring with spring constant k is attached to a box of mass M in which is placed a small body of mass m. The system is displaced a distance A from equilibrium and released from rest. Find the normal force between the box and the small mass as a function of time. For what...

Homework Statement Homework EquationsThe Attempt at a Solution I have done part a, I have no idea on part b, here is my attempt,

Homework Statement The problem is to take a small ball of mass m on a uniform rod of mass m which is hung on a hinge vertically downward, they're asking to find the velocity to be imparted for it undergo a complete rotation. I have the kinetic energy bit worked out but I'm getting the wrong...

I have no prior experience in physics, but I am a math undergrad so I know calculus, differential equations, linear algebra and stuff like that. So I'm ready to move from the conceptual "bedtime story physics" to stuff with real mathematical rigor. So, what is classical mechanics all about...