Classical mechanics Definition and 1000 Threads

These images have been taken from Goldstein, Classical Mechanics. Why do we need Lagrangian formulation of mechanics when we already have Newtonian formulation of mechanics? Newtonian formulation of mechanics demands us to solve the equation of motion given by equation 1. 19. for this we need...

Where in this though-experiment do I get it wrong? Even though no mass can travel faster then c, maybe information can? And I'm not talking about quantum entanglement etc. Consider a pipe, filled with balls that are very tightly arranged. If I push the outermost ball on one side of the pipe...

Rehashing this topic because I believe a clear misconception is stated in many threads. Classical mechanics is an incorrect ( by the definition of correct ) theory which is only an approximation that uses incorrect assumptions ie. Constant time but yet makes accurate predictions in its regime...

I’m a high school student reading through Young and Freedmans University Physics. The book has gotten my very interested in classical mechanics, and I wish to read more about it outside the textbooks. However, I don’t know where I can read more about it. Sure, there are books that I can read...

1. A weightless rod carries towards of masses M and M. The roads Hinge Joint to vertical axis OO', which rotates with an angular velocity ω. Determine the angle φ formed by the rod and there vertical. The attempt at a solution If I am not wrong, the two ways to ensure equilibrium are...

Hi everybody! I've just finished my 4th year of physics degree (1st year of the masters degree, to be more exact) and I feel that I've spent most of my time reading theory and studying proofs and very few time on actual problem solving. In order to change that, I decided this summer go through...

In the last paragraph of these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes3.pdf, it says how a state with large number of photons is not classical. Why is that? I thought quantum mechanics' laws were most applicable when we...

Homework Statement A uniform cylinder of mass ##M## and radius ##R## is released from rest on a rough inclined surface of inclined surface of inclination ##\theta## with the horizontal as shown in the figure. As the cylinder rolls down the inclined surface, what is the maximum elongation in...

A very simple question. How do we represent a vector with Newton's notation (writing the arrow symbol with the overdot notation)? Can we write them both above each other. First, the overdot notation and then the arrow symbol? Thank you a lot for your help...

Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta $$ $$T = mgcos\theta $$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...

When a classical field is varied so that ##\phi ^{'}=\phi +\delta \phi## the spatial partial derivatives of the field is often written $$\partial _{\mu }\phi ^{'}=\partial _{\mu }(\phi +\delta \phi )=\partial _{\mu }\phi +\partial _{\mu }\delta \phi $$. Often times the next step is to switch...

Homework Statement Freight car and hopper* An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track. Find the speed when a mass of sand m has been transferred.Homework...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Homework Statement Homework Equations $$\mathcal{L}=T-U$$ $$\omega= \frac{d\phi}{dt}$$ $$I=mr^{2}$$ The Attempt at a Solution My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following: $$K.E...

My question is related to the book: Classical Mechanics by Taylor. Section 7.8 So, In the book Taylor is trying to derive the conservation of momentum and energy from Lagrange's equation. I understood everything, but I am struggling with the concept and the following equation...

In Section 7.6 - Equivalence of Lagrange's and Newton's Equations in the Classical Dynamics of Particles and Systems book by Thornton and Marion, pages 255 and 256, introduces the following transformation from the xi-coordinates to the generalized coordinates qj in Equation (7.99): My...

Homework Statement This is derivation 2 from chapter 8 of Goldstein: It has been previously noted that the total time derivative of a function of ## q_i## and ## t ## can be added to the Lagrangian without changing the equations of motion. What does such an addition do to the canonical momenta...

My question is simple. Why do we need 9 different quantities, ie 1 normal stress and 2 shear stresses on 3 different planes, to define stress at a point? example: http://www.geosci.usyd.edu.au/users/prey/Teaching/Geol-3101/Strain/stress.html I think it should be enough to define the 3 stresses...

The potential energy of a particle of mass $m$ is $U(r)= k/r + c/3r^3$ where $k<0$ and $c$ is very small. Find the angular velocity $\omega$ in a circular orbit about this orbit and the angular frequency $\omega'$ of small radial oscillation about this circular orbit. Hence show that a nearly...

A particle of mass m in xy plane is attracted toward the origin with the force $$\begin{align}\vec{f} = - \frac{k^{2} m}{r^{6}}\vec{r}\end{align}$$ where ##\vec r## is position vector of particle measured from origin. If it starts at position ##(a,0)## with speed $$v=\frac{k}{\sqrt{2} a^{2}}$$...

I am preparing for an exam which requires me to solve problems in electrodynamics and electrostatics problems along with classical mechanics and geometrical optics problems. The concern is that I do not have electrodynamics in my course in school so I have to study it completely on my own. I...

I'm working through Gregory's Classical Mechanics and came across his derivation of energy conservation for a system of N particles that is unconstrained. We get to assume all the external forces are conservative, so we can write them as the gradient of a potential energy. There's a step he...

Hello, all. These are not the circumstances under which I would have preferred to have made my first post, but unfortunately, as the question suggests, this semester (second semester of freshman year), I earned a C in my calculus-based Intro to Classical Mechanics course. Not really for lack of...

Hello, When we applying the principle of least action, we require ##\delta S=0##, which corresponding to the action S being an extremum. I am just wondering why do we say that the action is a minimum instead of a maximum for a physical path? Can I use the path integral to explain this problem...

Homework Statement Show that the ratio of two successive maxima in the displacement of a damped harmonic oscillator is constant.(Note: The maxima do not occur at the points of contact of the displacement curve with the curve Aeˆ(-yt) where y is supposed to be gamma. 2. Homework Equations The...

Homework Statement so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3, I've uploaded the page here The rotation matrix associated with 1.2a and 1.2b is \begin{pmatrix} \cos\theta &...

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Copyright reserved to Prof. Balakrishnan and NPTEL. Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Homework Statement Consider a rocket subject to a linear resistive force, $$f = -bv$$, but no other external forces. Use Equation (3.29) in Problem 3.11 to show that if the rocket starts from rest and ejects mass at a constant rate $$k = -\dot{m}$$, then its speed is given by: $$v =...

I am getting correct equations on using the Lagrangian method in Systems with no non conservative forces, but when I use it in Systems with friction, sometimes I get correct equations, and sometimes I do not. Most of the equations have some problem with the coefficients of the frictional forces...

Homework Statement Homework Equations The Attempt at a Solution

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Copyright reserved to NPTEL, Government of India, and Prof. Balakrishnan.

Homework Statement A model yacht runs on a horizontal frictionless oval track as shown (viewed from above) in the figure. The curved parts of the track are semi-circles of radius ##R = 0.5 m##; the straight sides have length ##L = 1 m##. The mass of the yacht is ##m = 0.5 kg.## A force of...