Classical mechanics Definition and 1000 Threads

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. PhysicsRock

    I Why isn't the Lagrangian invariant under ##\theta## rotations?

    I just calculated the Lagrangian of a particle of mass ##m## in a radially symmetric potential ##V(r)##. I thought it would be a good idea to switch to spherical coordinates for that matter. What I get is $$ L = \frac{1}{2} m \left( \dot{r}^2 + r^2 \dot{\theta}^2 + r^2 \dot{\varphi}^2...
  2. Shreya

    The Definition of Torque - a proof

    I have been trying to understand this proof from the book 'Introduction to classical mechanics' by David Morin. This proof comes up in the first chapter of statics and is a proof for the definition of torque. I don't understand why the assumption taken in the beginning of the proof is...
  3. Reuben_Leib

    I Help with Euler Lagrange equations: neighboring curves of the extremum

    I tried writing this out but I think there is a bug or something as its not always displaying the latex, so sorry for the image. I have gone through various sources and it seems that the reason for u being small varies. Sometimes it is needed because of the taylor expansion, this time (below) is...
  4. Reuben_Leib

    I Why does ##u## need to be small to represent the Taylor expansion

    Necessary condition for a curve to provide a weak extremum. Let ##x(t)## be the extremum curve. Let ##x=x(t,u) = x(t) + u\eta(t)## be the curve with variation in the neighbourhood of ##(\varepsilon,\varepsilon')##. Let $$I(u) = \int^b_aL(t,x(t,u),\dot{x}(t,u))dt = \int^b_aL(t,x(t) +...
  5. R

    Coordinates of a point on a rotating wheel

    My issue is in deriving the coordinates of a point on a wheel that rotates without slipping. In Morin's solution he says that: My attempt at rederiving his equation: I do not understand how the triangle on the bottom with sides indicated in green is the same as the triangle on top that is...
  6. Slimy0233

    I Heating a tungsten filament to find out the maximum brightness emitted

    I was taking notes from a lecture on Quantum Physics and during the introduction, they gave an example of what led to the discovery of Quantum Physics: The electric bulb example where the brightness and colour of light depended on the temperature of the filament(see...
  7. Peter Morgan

    I The collapse of a quantum state as a joint probability construction

    The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...
  8. M

    Morin classical mechanics differential equation problem

    I was reading the oscillations chapter which was talking about how to solve linear differential equations. He was talking about how to solve the second order differential below, where a is a constant: In the textbook, he solved it using the method of substitution i.e guessing the solution...
  9. V

    Satellite mechanics: linear and rotational momentum

    [This is a continuation of OP's thread here: https://www.physicsforums.com/threads/satellite-mechanics-linear-and-rotational-momentum.1046963/ ] satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a...
  10. Lotto

    Can two objects moving parallel relative to a ground meet?

    I think that yes but how to explain it when someone standing on a ground sees them moving paralell? If I move properly, I can see two cars moving paralell ralative to the ground crashing, while someone on the ground do not see them crashing. Is it consistent?
  11. Lotto

    What is the smallest value of angular displacement of the raft?

    What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...
  12. V

    I Satellite mechanics: linear and rotational momentum

    satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a squared satellite weighting 100kg, 1 meter on each side. it has a thruster on it's side, shown in picture thruster quickly ejects 100g of propellant...
  13. A

    Classical A replacement for Mcauley's Classical mechanics

    Mcauley's "Classical mechanics: transformations, flows, integrable and chaotic dynamics" has a very interesting table of contents, and it has a philosophy of approaching Hamiltonian flows and chaos without using the formalism of modern differential geometry. Unfortunately, after reading the...
  14. S

    Distance travelled by a car considering only air friction?

    TL;DR Summary: Distance traveled by a car considering only air friction? How much distance would a 3-ton car travel if its initial speed was 17 km/h and we only take into account air's friction? (Assume that the car has an airfoil-like shape, so that the resistance against the air is very low)...
  15. luqman

    Coordinate Transformation (multivariable calculus)

    My Progress: I tried to perform the coordinate transformation by considering a general function ##f(\mathbf{k},\omega,\mathbf{R},T)## and see how its derivatives with respect all variable ##(\mathbf{k},\omega,\mathbf{R},T)## change: $$ \frac{\partial}{\partial\omega} f =...
  16. C

    I Variational Principles in Classical Mechanics (Douglas Cline)

    Hello, Has anyone read/heard about the textbook Variational Principles in Classical Mechanics, written by Douglas Cline? Any thoughts on whether I could use it as a replacement for Goldstein? Thank you!
  17. S

    I Water powered funicular with equal masses?

    I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...
  18. M

    B Irreversibility of Aristotle's law

    "Reversibility means that we never lose information, that at a fundamental level we can always retrodict the past as well as predict the future in the laws of physics". Susskind in his Theoretical minimum Lecture 2 describes about the laws which are true and which are not. He tells the law of...
  19. becks1

    Classical mechanics problem for a free particle

    Summary: The initial problem states: Consider a free particle of mass m moving in one space dimension with velocity v0. Its starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1 at time t = t1 > 0. and this info is to do the 3 problems written out. a)...
  20. Al-Layth

    I Comprehensive List of Mechanics Formulations

    beyond 1.) the Newtonian formulation 2.) The lagrangian formulation 3.) The Hamiltonian formulation What other formulations are there
  21. S

    I Receding movement of a stopped object in an accelerating universe?

    Imagine we attach an imaginary cosmological scale rope to an object that is very far away from us. Before attaching the string, the object would be receding from us due to spacetime expansion. After attaching it, tension would form in the string and we would eventually stop the object. After...
  22. P

    Maximum duration of Solar eclipses

    The result I get is 2 hours and 10 minutes. My reasoning is down here. But! Checking the map for the 2024 Solar eclipse, https://www.timeanddate.com/eclipse/map/2024-april-8, in many locations you can see a partial eclipse of over 2 hours 40 minutes. What is the main source of error here? Here...
  23. D

    Getting wrong answer in an (angular) impulse momentum problem

    I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α) And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.
  24. SaintRodriguez

    Please help me pick a topic for an essay about classical mechanics

    I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.
  25. bigmike94

    Prerequisites for John Taylor classical mechanics

    Inside the textbook, the prerequisites state first year mechanics and some differential equations, although it continues to say the differential equations can be learned as you’re working your way through the book, as differential equations were basically “invented” to be used for applied...
  26. H Ucar

    A Magnetic bound state in classical mechanics

    Seven years ago, I wanted to share and discuss my experiments results there but it was not possible since there was no published peer review paper yet and apparently not fulfilling forum requirements. Now we have such a publication, but still not sure the subject can be discussed here. Anyway...
  27. Physicsphysics

    I Understanding Classical Mechanics: Acceleration

    I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an...
  28. M

    B Why is KE not conserved when momentum is?

    Its clear in elastic collision that both KE and momentum is conserved. Bodies exchange their velocities. It is seen clearly in this video. There is no decrease in speed. Total KE is constant. But in an inelastic collision momentum is conserved again but not the KE. There is loss in KE (I guess...
  29. A

    What causes knots and stress when untwisting ropes?

    [Mentor Note -- thread moved from the schoolwork forums to GD as it seems like a more general question] Homework Statement:: Topoisomerases help in relieving strain in the DNA ahead of the replication fork caused by the untwisting of the double helix (Topoisomerases are enzymes that...
  30. AF Fardin

    Moment of inertia of a double physical pendulum

    I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below
  31. M

    B Does a body behave as a point mass even at rest?

    Hi, A body with center of mass behaves as a point mass when a force is applied. So when ##F_{ext}=0## then does it also behave as a point mass with ##a_{com}=0##, at rest. If yes, How can we prove this? (And can somebody please answer my other question I posted a week ago...
  32. M

    B K Energy & Momentum: Driving Force or Lost Heat?

    https://www.physicsforums.com/threads/conservation-of-momentum-and-loss-of-energy-in-inelastic-collisions.311037/post-2182192 If I understand correctly mathematically the momentum of the system remains unchanged but individual momentums decreases always. In an inelastic collision the momentum...
  33. bigmike94

    I Topics covered in John R Taylor Classical mechanics

    I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics? Would it be similar to what’s covered in Newtonian mechanics, but obviously more advanced. Cheers in advance 👍
  34. P

    Calculate tilt angle of a bar lifted via two ropes on fixed points

    Summary: How to calculate the equilibrium angle of a bar that is lifted on its two ends with ropes attached to fixed lifting points? Hello and good day all, First of all I would like to apologize in advance for my english, I am not a native speaker so some grammar errors may be left. My...
  35. Dario56

    I Why is it Impossible to Solve the Three Body Problem Analytically?

    Three (many) body problems where three or many bodies (particles) interact are impossible to solve analytically. First one appeared in classical mechanics where equations of motion of planets were tried to be found by applying Newton's 2nd law for system of planets and stars interacting via...
  36. rudransh verma

    Accelerating wedge with a block at rest on it

    I have drawn a fbd and the logic I think is that at rest the block moves down the wedge but when a force P is applied vertical force becomes zero and the horizontal force ##F_N\sin \beta## = P?
  37. rudransh verma

    B Why does friction decrease with repeated force application?

    Suppose you have a heavy body placed on a surface. We apply a horizontal force such that it is on the verge of moving (maximum static friction). We measure this force and note it down. Now we cut the body from the top and remove a thin layer and again do the same thing. We apply a force and...
  38. rudransh verma

    B Understanding Friction: The Impact of Inter-Molecular Bonding on Movement

    Imagine a solid body big and heavy. It will have friction between it and the surface when tried to move. Somehow the cluster of molecules opposes the push. When free these molecules stick on surface and can be moved by a mere blow of wind but when bonded into a solid body the structure of large...
  39. rudransh verma

    B Why does ice have more friction when it's solid compared to when it's melting?

    Water is made up of loose molecules but a body like ice is bonded strongly into a shape. Imagine a ice brick. It will have friction between it and the surface when tried to move. Now it slowly starts melting. The molecules of ice will start sticking on the surface. Somehow the cluster of...
  40. rudransh verma

    B What is the relationship between force and distance in planetary motion?

    https://www.feynmanlectures.caltech.edu/I_09.html 9-7 "From this figure we see that the horizontal component of the force is related to the complete force in the same manner as the horizontal distance x is to the complete hypotenuse r, because the two triangles are similar. Also, if x is...
  41. rudransh verma

    B Analysis vs arithmetic approach to solving motion

    https://www.feynmanlectures.caltech.edu/I_10.html https://www.feynmanlectures.caltech.edu/I_09.html Using Mathematical approach we can describe the motion of a falling body whose gravity is 32 m/s^2. Analysis shows that this is simply ##s-s_0=ut+1/2at^2##. Similarly we can describe the motion of...
  42. D

    A classical mechanics problem involve rotating

    I came up with these: (especially not sure if second is right)
  43. mohamed_a

    I Classical analogy approach to quantum mechanics

    I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...
  44. rudransh verma

    B Confusion with orientation of coordinate axis in inclined plane

    When we take the x-axis parallel to incline surface its clear that the horizontal component of weight is causing the block to come down but when we take the standard orientation its not so clear to me. Is horizontal component of ##F_N## causing the block to come down? <Moderator's note: Use of...
  45. rudransh verma

    What is the minimum force needed to move a block with friction present?

    We know the minimum force to move the body in presence of friction will be ##F>\mu F_N## But it’s not right.
  46. rudransh verma

    B Understanding Weight and Inertia: A Comparison of Mars and Earth

    https://www.feynmanlectures.caltech.edu/I_09.html “Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student. On Mars, weights would be different but the amount of force needed to overcome inertia...
  47. rudransh verma

    Potential energy in case of Atwood machine

    ##T-2mg=2ma_1## (acceleration of heavier mass) ##T-mg=ma_2## (##-a_1=a_2##) On solving the eqns, ##a_1=-g/3=-a_2## ##s=1/2at^2## ##s=-g/6## , distance covered by heavier mass. ##s=g/6## , covered by lighter mass. Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass) ##\Delta...
  48. rudransh verma

    A block coming down the incline

    ##W_{ext}=mgh+KE_f+0=-20(5\sin 37)+(1/2)2(10^2)## ##W_{ext}=-60.18+100=39.81J## But it’s not consistent with ##W=F.d=20*5=100J## I can’t figure it out.
  49. rudransh verma

    Block pulled up the incline problem

    a) $$v=u+at$$ $$v=0+(F/m)t$$ $$v=-10$$ Now $$v^2=0+2as$$ $$s=-5$$ $$W=F.d=(-20)(-5)=100J>40$$ b) $$W=-mgh$$ $$W=-20(3)$$ $$W=-60$$
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