What is Classical mechanics: Definition and 1000 Discussions

Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond earlier works, particularly through their use of analytical mechanics. They are, with some modification, also used in all areas of modern physics.
Classical mechanics provides extremely accurate results when studying large objects that are not extremely massive and speeds not approaching the speed of light. When the objects being examined have about the size of an atom diameter, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. To describe velocities that are not small compared to the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. However, a number of modern sources do include relativistic mechanics in classical physics, which in their view represents classical mechanics in its most developed and accurate form.

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  1. R

    A The Lagrangian a function of 'v' only and proving v is constant

    Hi everyone. So I'm going through Landau/Lifshitz book on Mechanics and I read through a topic on inertial frames. So, because we are in an inertial frame, the Lagrangian ends up only being a function of the magnitude of the velocity only (v2) Now my question to you is, how does one prove that...
  2. T

    B What is the force acting on a seesaw?

    Here's a question that I've been trying to solve for a while but keep on running into dead ends, and I can't seem to find any info on the internet to help me. Anyways I was wondering what the integral of torque is? For my specific example I have a rod that is not equally balanced on a fulcrum...
  3. C

    Difficulty with Mathematical Methods of Classical Mechanics

    Homework Statement A friend and I are going through Vladimir Arnold's Mathematical Methods of Classical Mechanics, but I think my lack of a background in pure math / proofs is seriously hampering my ability to do any of the problems in the first chapter. For example: PROBLEM. Show that if a...
  4. Salvador_

    Classical mechanics differential equation F(x) = -kx

    Homework Statement A particle of mass m is subject to a force F (x) = -kx. The initial position is zero, and the initial speed is v0. Find x(t). Homework Equations F = m*v*dv/dx = -kx v = dx/dt The Attempt at a Solution I'm new to differential equations, so please excuse me if I make any...
  5. T

    Intro Physics Kleppner Mechanics: am I ready?

    I just finished my junior year in high school. In college, I hope to major in physics and was interested in the honors versions of freshman introductory physics. These all have the prerequisite of a calculus-based mechanics course and use Kleppner as their mechanics textbook. I have so far only...
  6. V

    Continuum mechanics in physics education

    I came across this article about the near absence of continuum mechanics in university-level physics education: http://www.troian.caltech.edu/papers/Gollub_PhysToday_Dec03.pdf I have wondered this issue myself: why is continuum mechanics mainly studied by engineers rather than physicists, even...
  7. J

    Classical mechanics: Jacobi variational principle

    An isolated mechanical system can be represented by a point in a high-dimensional configuration space. This point evolves along a line. The variational principle of Jacobi says that, among many imagined trajectories between two points, only the SHORTEST is real and is associated with situations...
  8. A

    About centripetal acceleration

    I've been thinking about centripetal force and its effects on motion in uniform circular motion. I've actually found it difficult to accept that velocity magnitude can ever be maintained constant. Here is why: if this is our velocity vector, v, at the top of the circle: → Then the centripetal...
  9. unseeingdog

    B Coefficient of Restitution in x and y

    I am currently studying collisions in high school and my teacher told us that, in order to calculate the direction of each object after a 2-body collision, we could change the values in the relative velocity terms of the equation of the coefficient of restitution to the components in x and y. Is...
  10. Val Antthony

    Classical Which classical mechanics book has better content?

    Hey guys! I'm currently on my junior year and I will be taking advanced classical mechanics next semester. My lectures will consist mainly on Lagrangian and Hamiltonian mechanics and I am currently in need of a good book in classical mechanics. I have used Kleppner and Kolenkow's An Introduction...
  11. Dimani4

    Classical mechanics -- Throwing a balloon up into the air....

    Hi people. Here the situation. Balloon filled with air I throw in the air. Balloon starts to move upstairs. It slows down and then is starts to fall down to the Earth. I'm interesting only in the movement of upstairs. Here the picture. In the first case (left) I choose the direction of...
  12. H

    Calculating the equations of motion for particle in parabola

    I made the problem up myself, so there might very well not be a rational answer that I like! Homework Statement A point-particle is released at height h0 is released into a parabola. The position of the particle is given by (x, y) and the acceleration due to gravity is g. All forms of friction...
  13. A

    Tension on the rope (classical mechanics problem)

    Homework Statement The situation is that of Goldstein's problem 1.21 (or 1.19 in some editions): "Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table and m2 hangs suspended. Assume m2 moves only in a vertical line."...
  14. C

    Classical Which Classical Mechanics book to get?

    Hi all, I am looking for a good introduction to classical mechanics. I have looked at some book recommendations online but I am having trouble choosing the right book for me. Right now, I know no physics, so I need to start from the very beginning which I think is classical mechanics. I am self...
  15. G

    Looking for a Classical Mechanics Book by Goldstein?

    I need a book written just on the style of Classical Mechanics by Goldstein. I don't remember the book name and author but it is just the copy of the book Classical Mechanics by Goldstein. Please guide.
  16. R

    Calculating the moment of inertia of a solid sphere

    Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...
  17. R

    Simple Harmonic Oscillator behaviour when a potential term is added

    Homework Statement A simple harmonic oscillator has a potential energy V=1/2 kx^2. An additional potential term V = ax is added then, a) It is SHM with decreased frequency around a shifted equilibrium b) Motion is no longer SHM c)It is SHM with decreased frequency around a shifted equilibrium...
  18. N

    How weight affects surface bending over time

    Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...
  19. benny91xp

    B Walter Lewin videos -- why ± 0.5 cm uncertainty why not ± 0.1?

    here is the link to walter lewin video lecture please jump to 13:13 8.01x - Lect 2 - 1D Kinematics - Speed, Velocity, Acceleration i thought that all meter ruler/ meter stick use ± 0.1 cm as uncertainty .how did he get ± 0.5 cm?
  20. S

    A One Hamiltonian formalism query - source is Goldstein's book

    In 3rd edition of Goldstein's "Classical Mechanics" book, page 335, section 8.1, it is mentioned that : In Hamiltonian formulation, there can be no constraint equations among the co-ordinates. Why is this necessary ? Any simple example which will elaborate this fact ? But in Lagrangian...
  21. S

    Rolling ball and generalized co-ordinates

    Consider a sphere constrained to roll on a rough FLAT HORIZONTAL surface. A book on classical mechanics says it requires 5 generalized co-ordinates to specify sphere's configuration: 2 for its centre of mass and 3 for its orientation. I did not understand why 3 for orientation. I guess only 2...
  22. N

    I Classical v. quantum dynamics: Is spin the key difference?

    I'm interested in understanding the key physical differences between classical and quantum dynamics. I understand that spin (intrinsic angular momentum) is one major physical difference.* So I wonder whether all else flows from this? Or are there other major (unrelated) physical differences...
  23. Mind----Blown

    Significance of terms of acceleration in polar coordinates

    How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction? from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ; (where er and eθ are unit vectors in the radial direction and the direction of increase of the...
  24. 1

    Help finding the vibrational frequencies and normal modes

    Homework Statement Let's say that I have a potential ##U(x) = \beta (x^2-\alpha ^2)^2## with minima at ##x=\pm \alpha##. I need to find the normal modes and vibrational frequencies. How do I do this? Homework Equations ##U(x) = \beta (x^2-\alpha ^2)^2## ##F=-kx=-m\omega ^2 x## ##\omega =...
  25. T

    Rigid body orientation using Euler angles confusion

    Hello, Homework Statement I'm given the following exercise: "A rod with neglected thickness exists. What is the relation between the α,β angles to Euler angles of orientation? α is defined as the angle between the rod and its projection on the XY plane. β is defined as the angle between the...
  26. zwierz

    A Classical Mechanics challenge for fun

    I composed a problem and propose it here. I know the solution so it just for fun of the participants. There is a cylindrical bobbin of radius ##r##; the bobbin rotates about its central axis with angular velocity ##\omega=const>0##. An inextensible weightless string is coiled around the...
  27. J

    I Difference between statistical and dynamical properties

    Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...
  28. L

    Why is Newton's equation of motion invariant to time reversal

    Is there any deep reason behind this? per example the principle of least action or something else?
  29. L

    I A question about Noether theorem

    How can I derive that the work of a force perpendicular to velocity is always zero from the theorem of Noether? I have heard that there is a relation between these two but in Google I found nothing. Thank you very much
  30. smodak

    Classical Found a great resource on Theoretical Mechanics (free)

    Classical mechanics: a minimal standard course by Sergei Winitzki. It is not probably going to help you if you already did not know the subject but is a great refresher nonetheless. He also includes a differential equations refresher that I found invaluable. Looks like he has a ton of other...
  31. T

    Classical mechanics electrostatics and charges

    Homework Statement hi i was doing a practice physics junior olympiad paper when i got stuck in question 11 in this link [/B] https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf Edit by moderator: Inserted relevant extract of the PDF so that helpers do not have to...
  32. durant35

    I Many Worlds vs Classical Mechanics

    I have a question regarding the ontology of the many-worlds interpretation which by my assumption shows some deficiencies in this way of thinking. When many worlders describe branching and effects giving rise to multiple worlds they typically invoke Schrodinger cat-type experiments where from a...
  33. L

    Derivation of Rocket Equation Using Relative Velocity

    Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...
  34. Xell

    Classical What is a good, basic classical mechanics textbook?

    I would like one that is not very mathematically intense, and not to advanced, thanks for any replies.
  35. E

    Relative Acceleration - Particle and Wedge

    I would be very grateful for help with deriving the following equation... "A smooth fixed plane is inclined at 30 degrees to the horizontal. A wedge of mass M and angle 30 degrees is held on the surface so that its upper face is horizontal, and a particle of mass m rests on this face. The...
  36. Mikkel

    Classical Mechanics - Find angular velocity of two rods

    Homework Statement Hello! I apologize for my poor setup, first post. I am given a system of two rods, hope you can see my image.http://file:///C:/Users/Mikkel/Downloads/Mek2_exam_Jan2016_final.pdf One along the x-axis with mass = 2m and length = 2l Another perpendicular with the other with...
  37. Elvis 123456789

    A rope falling off an inclined plane

    Homework Statement A rope of length L is falling off an incline. Part of the rope is still on top of the horizontal surface. There is no friction between the incline and the rope. The incline is at an angle theta above the horizontal. a) What is the magnitude of the acceleration of the rope...
  38. yesudeep

    How Does Physics Impact Tennis Performance?

    Namasté, I'm an avid tennis player trying to deepen my understanding of tennis and its equipment. I hope to learn more about this subject. Thank you. :) Cheers, Yesudeep.
  39. J

    I Connection between Foucault pendulum and parallel transport

    Hello! I try to think about the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel transported represents(for example, is it the normal to the plane of oscillation vector?). In...
  40. hadsox

    Rotating and translating spool across a table

    Homework Statement A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its center of mass is a distance l from the edge...
  41. D

    How to find the average potential energy given V(x,y) and E?

    Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...
  42. G

    Work-Energy for Bead on Rotating Stick

    Homework Statement Verify the Work-Energy Theorem W=ΔK for a bead of masd m constrained to lie on a frictionless stick rotating with angular velocity ω in a plane. Homework Equations W =∫ F⋅dr, K =m/2 v^2 [/B] The Attempt at a Solution Adopting polar coordinates the velocity is v = r' +r*Θ'...
  43. Lujz_br

    Question 6.9 Taylor: Classical Mechanics

    Homework Statement Hello, I solved others but not 6.9: Find the equation of the path joining the origin O to point P(1,1) in the xy plane that makes the integral ∫(y'2 +yy' + y2) dx stationary. ∫ from O to P. y' = dy/dx Homework Equations I need use ∂f/∂y = d/dx (∂f/∂y') (euler-lagrange...
  44. C

    Quantum What is the Born approximation and how does it relate to quantum scattering?

    Hi i am trying to understand Borh's scattering but i need article that will teach me step by step. Do you know any?
  45. A

    Where can I find lectures on classical mechanics online?

    I am a high school student looking for some amazing lectures online to study classical mechanics for a regional qualifying camp for ipho.
  46. S

    Harmonic oscillation in classical mechanics

    Homework Statement An object of mass m = 300g is attached to a spring with a constant k = 3.0Nm-1 and is at rest on a smooth horizontal floor in a fluid where the resistive force is assumed to be linearly proportional to the velocity v. the object is then displaced 10mm to the right of the...
  47. Unteroffizier

    Centripetal Force - same thing as gravitational force?

    First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me. I recently took...
  48. K

    Classical mechanics formulations?

    Hi, when do we use hamiltonian vs. Newtonian mechanics or even lagrangian formulations? pros and cons? I am thinking molecular dynamics codes
  49. AD MCFC

    Studying Review for Upper Division Class Mechanics course?

    Hello, I will take Classical Mechanics I (upper division) course fall of 2017. I have not seen Mechanics material since fall of 2014 and would like suggestions on how to review the concepts prior to taking the class. I was pretty good in that class and do not need to "re-learn" anything per...
  50. CassiopeiaA

    A Symplectic Condition For Canonical Transformation

    I am reading Chapter 9 of Classical Mech by Goldstein.The symplectic condition for a transformation to be canonical is given as MJM' = J, where M' is transpose of M. I understood the derivation given in the book. But my question is : isn't this condition true for any matrix M? That is it doesn't...
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