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. Jozefina Gramatikova

    Classical mechanics: Square well with Bounded particle

    My question is can we have negative energy in classical mechanics? Also I would need help for finding the velocity in part b)
  2. SpaceIsCool

    Transverse velocity and real/imaginary parts?

    Homework Statement The transverse velocity of the particle in Sections 2.5 and 2.7 is contained in (2.77), since By taking the real and imaginary parts, find expressions for v_x and v_y separately. Based on these expressions describe the time dependence of the transverse velocity. Homework...
  3. SpaceIsCool

    Can This Differential Equation Be Solved by Separation of Variables?

    Homework Statement We solved the differential equation (2.29), , for the velocity of an object falling through air, by inspection---a most respectable way of solving differential equations. Nevertheless, one would sometimes like a more systematic method, and here is one. Rewrite the equation...
  4. hilbert2

    Delta potential in classical mechanics

    In quantum mechanics, there exist some systems where the potential energy of some particle is a Dirac delta function of position: ##V(x) = A\delta (x-x_0 )##, where ##A## is a constant with proper dimensions. Is there any classical mechanics application of this? It would seem that if I...
  5. J

    MHB Challenging Classical Mechanics Problems: Can You Solve Them?

    Hello i have the difficulty in solving this two problems..thank you for your help math help boards :-)
  6. C

    Spring with oscillating support (Goldstein problem 11.2)

    Homework Statement A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to ##z=a\cos(w_1t)##. By treating a as a small quantity, obtain a first-order solution to the motion of m in time...
  7. TachyonLord

    Find the average force at distance x

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  8. R

    Why does the axis of rotation pass through the metacentre?

    When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is called the...
  9. John McAndrew

    Acceleration of mass depends upon K and L of a spring?

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  10. D

    Hamilton Jacobi equation for time dependent potential

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  11. sams

    Questions Regarding the Inertia Tensor

    In Chapter 11: Dynamics of Rigid Bodies, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, pages 415-418, Section 11.3 - Inertia Tensor, I have three questions regarding the Inertia Tensor: 1.The authors made the following statement: "neither V nor ω...
  12. K

    On Newton's first and second laws

    I'm reading Scheck's book about Mechanics and it says that Newton's first law is not redundant as it defines what an inertial system is. My problem is that we could say the same about Newton's second law. Indeed, Newton's second law is only valid, in general, for inertial systems, so it also...
  13. R

    Moment of Inertia of an Ammonium Molecule

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  14. M

    How to calculate rebound speed of ball hitting a wall?

    Homework Statement A ball of mass 0.075 is traveling horizontally with a speed of 2.20 m/s. It strikes a vertical wall and rebounds horizontally. Due to the collision with the wall, 20% of the ball's initial kinetic energy is dissipated. Show that the ball rebounds from the wall with a speed of...
  15. M

    Change in momentum when given the speed (not the velocity).

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  16. J

    Discrepancy in Lagrangian to Hamiltonian transformation?

    I know, $$ L=T-V \;\;\; \; \;\;\; [1]\;\;\; \; \;\;\; ( Lagrangian) $$ $$ H=T+V \;\;\; \; \;\;\;[2] \;\;\; \; \;\;\; (Hamiltonian)$$ and logically, this leads to the equation, $$ H - L= 2V \;\;\; \; \;\;\...
  17. L

    Lagrange equation of second kind - find solution's constant?

    Homework Statement This could be a more general question about pendulums but I'll show it on an example. We have a small body (mass m) hanging from a pendulum of length l. The point where pendulum is hanged moves like this: \xi = A\sin\Omega t, where A, \Omega = const. We have to find motion...
  18. D

    Rest energy in classical mechanics

    [Moderator's note: Post spun off from another thread.] That is correct but it doesn't mean Eo=0. The rest energy is unlimited in classical mechanics. Therefore it is impossible to find a relation between total energy and momentum.
  19. O

    Energy conservation and friction

    Hi, I just started learning physics at university and so I'm looking for help on a simple energy conservation problem. On the bottom right-hand of the image I attached below, you should see that it asks whether the initial speed would increase or decrease if the object was of a greater mass...
  20. M

    Can 3 forces of 9N, 4N, and 6N be in equilibrium?

    Homework Statement A mass of 3kg is acted upon by three forces of 4.0 N, 6.0N, and 9.0N and is in equilibrium. The 9N force is suddenly removed. Determine the acceleration of the mass. Homework Equations F=ma. The Attempt at a Solution My main problem with this question is that I cannot think...
  21. chmodfree

    I Generalized Momentum is a linear functional of Velocity?

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  22. C

    Escape Velocity and the Motion of Two Massive Bodies

    Hey there, If body 1, mass M1 has escape velocity V_e1 = (2GM1/r)**.5 but M2 is more massive than M1 is this relation still valid? In this case, the subordinate body really isn't the subordinate body so does this still hold? And r (distance b/t the two) changes not only due to the motion of M2...
  23. sams

    A Summation Index Notation in the Transformation Equations

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  24. F

    Energy and motion from ##R^6 \rightarrow R##

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  25. G

    Given force as a function of x, how do I find the total energy?

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  26. sams

    Scleronomic or Rheonomic Mechanical System?

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  27. H

    Any good lecture notes for classical mechanics?

    Any good lecture notes for classical mechanic?
  28. D

    Two falling rods connected by a hinge

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  29. D

    Linearize a function about a solution to check for stability

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  30. sams

    Why is a negative sign included in Equation (6) for central-force motion?

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  31. Samama Fahim

    Frequency of Undamped Driven Oscillator near Zero

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  32. Amitayas Banerjee

    What is the Lagrangian, equations of motion for this system?

    <<Moderator's note: Moved from a technical forum, no template.>> Description of the system: The masses m1 and m2 lie on a smooth surface. The masses are attached with a spring of non stretched length l0 and spring constant k. A constant force F is being applied to m2. My coordinates: Left of...
  33. sams

    A Difference between configuration space and phase space

    Lagrangian Mechanics uses generalized coordinates and generalized velocities in configuration space. Hamiltonian Mechanics uses coordinates and corresponding momenta in phase space. Could anyone please explain the difference between configuration space and phase space. Thank you in advance for...
  34. Pushoam

    Solving the Rotating Wire Problem

    Homework Statement A circular wire hoop rotates with constant angular velocity ! about a vertical diameter. A small bead moves, without friction, along the hoop. Find the equilibrium position of the particle and calculate the frequency of small oscillations about this position. Homework...
  35. Pushoam

    Why do we need the Lagrangian formulation of Mechanics?

    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...
  36. P

    Classically communicate information faster then light?

    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...
  37. W

    The approximation of classical mechanics

    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...
  38. E

    Other Physics Journals/Articles About Classical Mechanics

    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...
  39. Amitayas Banerjee

    Equilibrium Conditions for a Rotating Rod with Two Point Masses

    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...
  40. M

    Classical Improving my problem solving skills....

    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...
  41. P

    Why is a state with large number of photons not classical?

    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...
  42. U

    Rotational Mechanics question with spring

    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...
  43. sams

    Representing Vectors in Newton's Notation: How to Use Overdot and Arrow Symbols?

    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...
  44. Safder Aree

    Simple Pendulum undergoing harmonic oscillation

    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...
  45. Q

    I Derivative of a Variation vs Variation of a Derivative

    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...
  46. MARX

    Momentum Kleppner Classical Mechanics Freight Car and Hopper

    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...
  47. sdefresco

    Torque and Angular Momentum Vector Question.

    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...
  48. Phylosopher

    Bead on a Helix, angular velocity

    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...
  49. Phylosopher

    Conservation laws from Lagrange's equation

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  50. sams

    A Partial Differentiation in Lagrange's Equations

    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...
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