Mechanics Definition and 999 Threads

Mechanics (Greek: μηχανική) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in displacements, or changes of an object's position relative to its environment.
This branch of physics has its origins in Ancient Greece with the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics.
It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light.
It can also be defined as a branch of science which deals with the motion of and forces on bodies not in the quantum realm. The field is today less widely understood in terms of quantum theory.

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  1. CuriousLearner8

    A Eigenvalue Problem of Quantum Mechanics

    Hello, I hope you are doing well. I had a question about the eigenvalue problem of quantum mechanics. In a past class, I remember it was strongly emphasized that the eigenvalues of an eigenvalue problem is what we measure in the laboratory. ##A\psi = a\psi## where A would be the operator...
  2. A

    How much statistical mechanics is enough for a physicist?

    How much statistical mechanics do I need to know to study QFT, astrophysics, black hole thermodynamics, and other advanced topics? And where should I study it in your opinion? So far I have only read Tong's notes however I don't think it is enough. Some quantum statistical mechanics is also...
  3. B

    I Checking if a stationary point is a minimum using Lagrangian Mechanics

    I'm having trouble understanding how to find out whether or not a stationary point is a minimum and I'm hoping for some clarification. In my class, we were shown that, using Euler's equation, the straight-line path: with constants a and b results in a stationary point of the integral: A...
  4. C

    Advice for self-study Intro to Mechanics course?

    TL;DR Summary: Is there a mental model for setting up equations of motion and related mathematical equations when tackling mechanics problems? Hi there, I'm going through a first year mechanics textbook (An Introduction to Mechanics by Kleppner et al) from MIT OpenCourseware as I'm interested...
  5. G

    I How can I integrate variable velocity in fluid mechanics?

    Do you know of any place where I can look up things about the momentum (linear momentum) in fluid mechanics? It's just that when I have a variable velocity and it has to be integrated, I don't quite understand how to do it. I have looked for videos and things and I can't find that they are...
  6. Yossi33

    Engineering Mechanics of materials -- deformation problem

    Hi, i'm struggling with that problem , i need to find the distance that point N went down.My way of thinking is that the structure is twice not statically determined because of the beam MN and beacuse of the left support which is also unnecessary in order for equilibrium. My 2 equations of...
  7. G

    Fluid mechanics: water jet impacting an inclined plane

    I was looking at an example of fluid mechanics and I don't understand this. Statement figures: CONTINUITY EQUATION $$\left. \dfrac{dm}{dt}\right]_{MC}=(\dot{m}_2+\dot{m}_3)-\dot{m}_1=0$$ $$\dot{m}_1=\dot{m}_2+\dot{m}_3$$ $$\rho c_1A_1=\rho c_2A_2+\rho c_3A_3$$ $$\rho c_1 h1=\rho c_2 a1+\rho...
  8. I

    I QED/Quantum Mechanics: Probability or Spatial Function?

    In "QED, The Strange Theory of Light And Matter" Richard Feynman describes the probability path of a single photon emitted from a source, reflected from a mirror surface, and finally reflected to a probe detector. This path is the least time path relative to the probe/viewer, determined by the...
  9. Omega0

    B Lagrangrian and Hamiltonian mechanics: A historical picture

    Hi, I believe that I have an acceptable level of understanding where SRT, GRT, QM and QFT come from. This is not true for me regarding the "good old stuff". Newton, okay, this is relatively (:wink:) clear to me but do you know something about the historical motivation for Lagrangian and...
  10. T

    Mechanics of Spinning Around (effects on inner ear)

    Suppose I stood up and spun around in a circle for about twenty seconds and stop. Then, I ask my friend to look into my eyes (as I try to look into his). He sees my eyes go back and forth and back and forth (and I cannot stop that). I vaguely recall someone telling me there is a hair (or...
  11. 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...
  12. Argonaut

    I Don't Ever Mention "Centrifugal Force" to Physicists

    I've just come across the following line while studying (Young & Freedman) and found it amusing. It sounds like a dirty family secret we discuss once and then should never mention again :biggrin:
  13. 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...
  14. Paul Colby

    A Recent papers refuting real-valued quantum mechanics

    So, in a rare instance I actually read APS News, I came across “New Experiment Suggests Imaginary Numbers Must be Part of Real Quantum Physics.” In November 2022, Volume 31, Number 10. Since complex numbers are isomorphic to a real 2x2 matrix algebra, I was confused how such a claim can be...
  15. L

    Solving a Celestial Mechanics Task with Velocity Vector Scattering

    Hi, the task is as follows Unfortunately, I am not getting anywhere at all with task c. I have now proceeded as follows: I assume that the calculation takes place in the reference system of the sun. In the task the following is valid, $$\vec{v}_{si}=-s\vec{v}_p$$ I have now simply assumed...
  16. H

    Allowed energy for a potential in quantum mechanics

    Hi, I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html, which is similar of what I'm doing. I'm using mathematica to find the values of E. However, I'm not sure how...
  17. Ashish Somwanshi

    Measurement problem quantum mechanics

    Is the answer 0.748?
  18. 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...
  19. G

    Calculating ##F_{DB}##: Equilibrium in a Machine

    Figure: My attempt at a solution: For the calculation of ##F_{DB}## we consider the equilibrium in the whole machine. $$\left. \begin{array}{r} h\rightarrow h=6\cdot \sin \theta +3=6,44\, \textrm{ft} \\ d\rightarrow d=6\cos \theta -1,5=3,41\, \textrm{ft} \end{array}\right\} \,\, \alpha =\arctan...
  20. Q

    Quantum Advanced Quantum Mechanics Textbooks: Derivations of Equations

    Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.
  21. 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...
  22. samy4408

    I Relationship between viscosity and velocity in fluid mechanics

    hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?
  23. I

    Quantum Mechanics problem: Determine the value of the constant

    I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.
  24. huc369

    Analysis of the mechanics of skydiving

  25. Argonaut

    Relative Velocity and Angles of Movement (Sears & Zemansky's Exercise)

    The official solution says ±25.4°, but I'm having trouble reproducing it. Here is my solution: 1) The components of the velocity of firework F with respect to the ground G in the moment of explosion are the following (Notice, I'm using sin, because the statement says 30.0° from vertical.)...
  26. Al-Layth

    Resource Request for Relativistic Mechanics

    I am aware of the Newtonian model of Gravitation and I am interested in Relativistic Mechanics. I do not know anything about relativistic mechanics other than its more "accurate" at modelling gravitation and that it "reduces" to the classical formulation in some cases. I only want to be able...
  27. Ashish Somwanshi

    Measurement problem quantum mechanics

    I was not able to attempt since I don't know which formula or method can be used to solve the problem
  28. T

    I About photon-polariser interaction quantum-molecular-level mechanics

    I'm quite interested in the aforementioned topic, and would like to take a look at more literature about it, and to learn more about it, and would like to ask if you know more about it, or know interesting aspects about it, you can suggest the titles of the materials, or share the links to the...
  29. H

    I Quantum mechanics stationary state

    Hi, I have hard time to really understand what's a stationary state for a wave function. I know in a stationary state all observables are independent of time, but is the energy fix? Is the particle has some momentum? If a wave function oscillates between multiple energies does it means that the...
  30. 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!
  31. 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)...
  32. Ira_anabelle

    Using Seismic Waves detected at 4 Seismometers to determine the Epicenter

    My first attempt was to work with the the difference in arrival times, but that didnt account for the focus to be under the epicenter. So I tried again in combination with the angle between the stations but have not arrived at a clear solution.
  33. lavalite

    Thin-walled sphere and fluid mechanics question

    Suppose you had a thin-walled sphere fully submerged in a liquid. The sphere is filled to the equator with a liquid of sufficient density to reach buoyant equilibrium. Will the lateral cross-sectional areas of the thin-walled sphere experience tensile stresses in the longitudinal axis? Why or...
  34. 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
  35. AJSayad

    Engineering Experimental Fluid Mechanics Vs. Computational Fluid Mechanics

    Hi everyone, I just started graduate school and I've been working in an experimental fluid mechanics lab. We have a shock tube and run tests on studying supersonic and hypersonic airflow under different conditions. We use Schileren imaging and transducers to take measurements during tests. We...
  36. sol47739

    I Exploring Electromagnetism & Quantum Mechanics

    In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is...
  37. E

    I Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics

    Hello, I'm hoping someone can help me understand a statement in Sakurai Modern Quantum Mechanics (3rd edition). In particular, in the section that describes free particle in infinite spherical well (page 198, section 3.7.2), after the text has shown that for a given ##l## value, the energy...
  38. Graham87

    Quantum Mechanics - Matrix representations

    I have found J^2 and Jz, but I am not sure how to find Jx and Jy. I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results. Thanks!
  39. A

    Fluid mechanics - Additional liquid capacity due to compression

    A cylindrical tube (diameter = D, width = L) is completely filled with a liquid (density = ρ). A pump pressurizes the system with a pressure P. Consequently, 1) the solid tube is compressed and deformed according to Hooke's law (σ = ε.E), and 2) the liquid is compressed and deformed, following...
  40. mopit_011

    B Equivalence of Frictional and Applied Force

    The following passage is from Halliday Resnick Krane in Chapter 3 which is about dynamics in one dimension. "We can measure frictional forces. By placing the body on a horizontal surface where it experiences a frictional force, we could attach a spring and pull the body with just the right...
  41. Graham87

    Intro to quantum mechanics - Spin and linear algebra

    So this expression is apparently in Sz basis? How can you see that? How would it look in Sy basis for example? The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here? Thanks
  42. Graham87

    Intro to Quantum Mechanics - Formalism normalisation

    I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared. Thanks
  43. sachin

    Motion of center of mass under gravity

    While solving this question I could not figure out the concept of two blocks sticking together. the question is, Two particles A and B of masses 1 kg and 2 kg respectively are projected in the directions shown in figure with speed uA =200m/s and uB =50m/s. Initially they were 90m apart. They...
  44. Kinetic cyclic scissors

    Kinetic cyclic scissors

    Fun with tiled cyclic quadrilaterals
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  45. G

    I At which point is gravity inconsistent with quantum mechanics?

    I'd like to understand how gravity does not combine with quantum mechanics. At least there is no accepted theory of quantum gravity, so I assume it is not solved? I'm only starting to learn QFT and eventually GR. Maybe, someone can already outline where those theories fail to combine and comment...
  46. 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.
  47. Graham87

    Plot the Expectation Value of Spin - Intro to Quantum Mechanics Homework

    I have found an answer to all of them (a-e) but I don’t know how to plot the function. Thanks!
  48. Graham87

    Intro Quantum Mechanics - Dirac notations

    I am learning Dirac notations in intro to quantum mechanics. I don’t understand why the up arrow changes to down arrow inside the equation in c). My own calculation looks like this:
  49. Graham87

    Quantum mechanics - Find S_x and S_y

    I have a lecture slide that shows how to find S_x and S_y. I get all the steps except the last row. Where did 1/2 come from? I think my linear algebra needs polishing. Thanks!
  50. 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...
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