What is Mechanics: Definition and 999 Discussions

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. P

    Conservation of energy in rotating bodies

    The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder. To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder). However, I viewed the cylinder as rotating...
  2. J

    I Origin of Probabilities in Quantum Mechanics?

    The non-normalized wavefunction of a general qubit is given by: $$|\psi\rangle=A|0\rangle+B|1\rangle.$$ The complex amplitudes ##A## and ##B## can be represented by two arrows in the complex plane: Now the wavefunction can be multiplied by any complex number ##R## without changing the...
  3. P

    Understanding basic statistical mechanics formulas

    Firstly, I would like to check my understanding of the first formula: Using velocity distribution = f(v), speed distribution = fs(v): fs(v) = f(vx)f(vy)f(vz)dxdydz, since dxdydz = 4pi*v^2*dv, fs(v) = 4piv^2f(v) The second formula is the confusing one: What does it mean? What is the...
  4. wrobel

    A Something about configuration manifolds in classical mechanics

    I think it could be interesting. Consider a mechanical system A circle of mass M can rotate about the vertical axis. The angle of rotation is coordinated by the angle ##\psi##. A bead of mass m>0 can slide along this circle. The position of the bead relative the circle is given by the angle...
  5. B

    Question concerning the mechanics of a magnet's attractive force

    Does a force exerted by a magnet change if we do not change the distance between a magnet and the body, but change the direction of the magnet (tilt)?
  6. cybernetichero

    Orbital mechanics question about Star Trek

    I'm watching the Next Generation episode Relics and Riker has just ordered the helm to "go into orbit above that point" which I took to mean geosynchronous orbit. No biggie except that the point is on the outer surface of a Dyson Sphere with a RADIUS of more than 1AU. So, assuming the sphere has...
  7. AuntyMatter

    A Shakespearean Guide to Quantum Mechanics

    When we think of the fathers of quantum mechanics we tend to think of Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger. However I think I am in solid ground in suggesting that William Shakespeare was way...
  8. D

    I Shankar Quantum Mechanics, Chapter 5, Page 160-161

    For the case of general potential V(x), what does it mean when he says that there are always one more constraint than free parameters? At each interval, ψ and ψ' must be continuous, so that is 2 constraints at each interval, and I understand that there are 2 parameters of the wavefunction in...
  9. W

    Does any classical mechanics textbook solve Kepler's Problem?

    I have several* classical physics and mechanics texts, and none solve the Kepler problem (as far as I can tell), succinctly, solving the Kepler equation, M = E - e*sin(E), for E given M and e, or more generally determining the equations of motion for an orbiting object. In fact none even...
  10. T

    On the non-applicability of Newtonian mechanics

    Hello. The questions are: Why Newtonian mechanics is not applicable to quantum mechanics and more natural phenomena in gravity? So, we needed general relativity which offers a metric theory about gravity and applies to more phenomena in nature, but how is this explained that special and general...
  11. J

    I Quantum mechanics supports solipsism?

    There is a lot of information on the Internet that quantum physics supports solipsism and that physicists believe in solipsism. I only trust this forum and the people who are here, so I want to ask you: 1. Is it true that quantum physics says solipsism is true? If this is true, then only one...
  12. binbagsss

    Drop out of PhD in fluid mechanics and switch to Mres in mathematical physics?

    A post doc in an area that differs from my PhD? I am currently doing a PhD in fluid mechanics but want to do mathematical physics tbh. In another thread I got an answer about a user who had done a PhD in accelerator physics and went to do a post-doc in condensed matter, vice versa even, but in...
  13. D

    Prerequisite mathematics for intermediate mechanics?

    I will be taking intermediate mechanics next semester, and am a bit concerned about potential gaps in my mathematical knowledge. Long story short, I used to be a physics major, switched to electrical engineering, and then decided to double major after a semester in EE. The issue is that, as a...
  14. sergiokapone

    I What does motion mean in quantum mechanics?

    Consider the Schrödinger equation for a free particle: \begin{equation} -\frac{\hbar^2}{2m} \partial_i^2\psi = i\hbar\partial_t \psi. \end{equation} Let us be interested in the motion of a free particle in quantum mechanics. We say ok, we have a solution to the Schrödinger equation for a...
  15. jay_chay22

    Engineering Frame and Machine (engineering mechanics statics)

    I have problem on this question on how to draw free body diagram. Can you please show me on how to draw free body diagram on this question ? The calculation part I think I do not have a problem with it. Thank you in advance ! I am really struggle with this question.
  16. duchuy

    Point mechanics -- Tension in a rope from a hanging mass

    Hi, I'm being asked to determine the tension of a rope only knowing that g = 9.8 m.s-2. I understand that in order to calculate tension, I would need to multiply mass with acceleration. But i don't understand how i would in this case. This is the question for reference. Thanks for your help...
  17. B

    The definition of generalised momentum

    Why, in lagrangian mechanics, do we calculate: ##\frac{d}{dt}\frac{\partial T}{\partial \dot{q}}## to get the (generalised) momentum change in time instead of ##\frac{d T}{dq}##? (T - kinetic energy; q - generalised coordinate; p - generalised momentum; for simplicity I assumed that no external...
  18. F

    A First Course in Graduate Quantum Mechanics Resources

    What are some resources that you would suggest for a first course in graduate quantum mechanics? This includes textbooks, online courses such as MIT OCW(includes homework/exams), and online lecture notes?
  19. Leo Liu

    Relativity Is it worth to read the chapters on relativity in K&K mechanics book?

    Hello. I have almost finished Kleppner's Newtonian mechanics book except the part discussing special relativity. I plan to read Purcell's EM book after finishing it. I've heard some people saying that Purcell presents some of the EM concepts in a relativistic way, so I am a bit worried that I...
  20. Someone_physics

    A Thought experiment in relativistic quantum mechanics?

    Background --- Consider the following thought experiment in the setting of relativistic quantum mechanics (not QFT). I have a particle in superposition of the position basis: H | \psi \rangle = E | \psi \rangle Now I suddenly turn on an interaction potential H_{int} localized at r_o =...
  21. C

    Intro Physics Best textbook for properties of matter and fluid mechanics

    I am a First Year Undergraduate Physics student. Which will be the best textbook for me to study properties of matter (Elasticity) and fluid mechanics? I prefer a better theoretical understanding.
  22. Ali Beladi

    I What does this tricky quantum mechanics equation mean?

    I'm a current high school student and I’m aspiring to become a biochemist. I’m at the moment writing an article about adaptive mutations but there is a lot of tricky quantum mechanics in it which I simply don't get. I have asked everyone and got no answer until someone recommended to ask it in a...
  23. N

    Which is the best book for studying Rotational mechanics?

    Homework Statement:: Which is the best book that you've read for understanding rotational mechanics ? Relevant Equations:: Kindly let me know. .
  24. mattlfang

    Find the velocity and acceleration of a pulley in a mass-spring system

    This looks like a classical setup but I can't find a solution. We can calculate the energy of the system by looking at the work done by the gravity and the spring. But how do we divide the energy between the kinetic energy of the pulley and the rotation of the pulley?
  25. warhammer

    Beam resting on 2 pivots | Problem in Rotational Mechanics

    When one of the pivot is pulled, just at that moment a couple is formed due to the normal reaction from the existing pivot and the weight of the bar. From the assumptions given in the question, we can state that the distance between the two forces (N & W) giving rise to the couple is L/2. Using...
  26. kmot

    Fluid mechanics - Linearized shallow water equations

    Hi, In a text describing solution to linearized shallow water equations, I am not able to move forward. It's a 1 dimensional shallow water setup. There is a steady state (velocity) and (height of free surface). On top of this steady state there are u' and h' as disturbances. The goal is to...
  27. E

    Quantum mechanics - several constant potentials

    What I tried to do was using the fact that the wave function should be continuous. Asin(kb)=Be^{-\alpha b} The derivative also should be continuous: kAcos(kb)=-\alpha Be^{-\alpha b} And the probability to find the particle in total should be 1: \int_0^b A^2sin^2(kx) dx + \int_b^{\infty}...
  28. Frabjous

    Classical Geometrical Mechanics by Talman

    Does anyone have any experience with this book? https://www.amazon.com/gp/product/3527406832/?tag=pfamazon01-20
  29. ezfzx

    Ball rolling within a rolling cylinder

    Cylinders rolling down inclines are a common demo. But how do you model the movement of a sphere rolling within a rolling cylinder? I teaching a physics class and this question came up and my dynamics math is a little rusty. But I haven't found anything like this in any book or online. There's...
  30. ricles

    Cylinder rotating on a support

    This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...
  31. Muthumanimaran

    I Exploring the Physics of LASER: Classical vs Quantum Mechanics

    My question is the physics behind the LASER such as stimulated emission can be only explained by quantum mechanics only. We can represent LASER as coherent state in quantum mechanics only. Then how can we say LASER can be thought of a classical light source?
  32. fluidistic

    Quantum Schwinger's Quantum Mechanics: Symbolism of Atomic Measurements

    I had never heard of Schwinger's Quantum Mechanics: Symbolism of Atomic Measurements until very recently. I wonder what you people think about that QM textbook. Is it a good introduction to QM? A reference? Or, possibly an outdated and bad book? At first glance, it seems a masterpiece to me...
  33. Santiago24

    Classical Recommend books about classical mechanics please

    Hi! i need some textbooks recommendations to learn by my self about classical mechanics in a undegraduate level. I don´¨¨t know what kind of math is required, i have knowledge about calculus by my high school classes and i learned more with the book "Calculus" by Gilbert Strang. I wait for your...
  34. K

    Probability density in statistical Mechanics

    First of all, I've calculated the partition function:Z=1h3∫e−βH(q,p)d3pd3q=1h3∫e−β(p22m−12mrω2)d3prdrdθdz=2πL(2mπh2β)3/2e12βmω2R2−1ω2mβThe probability of being of one particle in radius $r_0$ is: p(r=r0)=1Z∫e−βHd3pd3q=∫1Z2πL(2mπh2β)3/2eβmrω22rdr So I've thought that because, by definition, the...
  35. A

    Does a statistical mechanics of classical fields exist?

    The usual presentation of classical statistical mechanics are based on the Liouville equation and phase space distribution. This, in turn, is based on the Hamiltonian mechanics of a system of point particles. Real undulatory systems, specially non-linear ones, have to be complex to study...
  36. T

    Quantum Mechanics determining the normalized constant of a particle

    In my book it has the following example, A particle confined to the surface of a sphere is in the state $$\Psi(\theta, \phi)= \Bigg\{^{N(\frac{\pi^2}{4}-\theta^2), \ 0 < \theta < \frac{\pi}{2}}_{0, \ \frac{\pi}{2} < \theta < \pi}$$ and they determined the normalization constant for ##N##...
  37. qnach

    A Partition function in number theory and statistical mechanics

    Is the partition function used in number theory and statistical mechanics the same thing?
  38. A

    Analytical Mechanics: Regularity Conditions on Constraint Surface

    Hi, In my course in analytical mechanics, it is said that for a system of n particles subjected to r constraint equations, it is necessary to impose regularity conditions on the constraint surface defined by G = 0 where G is a function of the position of the position of the particles and time...
  39. patric44

    A Would it matter which inner product I choose in quantum mechanics?

    hi guys i was thinking about the inner product we choose in quantum mechanics to map the elements inside the hilbert space to real number which is given by : $$\int^{∞}_{-∞}\psi^{*}\psi\;dV$$ or in some cases we might introduce a weight function dependent on the wave functions i have , it seems...
  40. I

    I Quantum Mechanics Wave Function in 3D

    I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?
  41. Vivek98phyboy

    Reflection of inverted waves to form a standing wave

    Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?
  42. Vivek98phyboy

    Contradiction in Phase of reflected sound

    While studying the fundamentals of sound waves in organ pipe, I noted that the fact about phase of reflected waves is contradicting while referring multiple sources This book of mine describes the reflection from a rigid surface/closed end to be in phase Whereas this one describes the...
  43. E

    Classical Prerequisites for Arnold's Methods of Classical Mechanics

    I've finished with Gregory's classical mechanics and was looking for something a bit more challenging. I thought Arnold's methods of classical mechanics look pretty interesting, but it's definitely more mathematically complex than anything I would have done before, especially the bits about...
  44. WMDhamnekar

    MHB Is the Given Answer for the Classical Mechanics Problem on Earth Correct?

  45. thaiqi

    Quantum Which books are best for learning Bohm's mechanics?

    Hello, everyone. Which books best for learning Bohm's mechanics?
  46. thaiqi

    Deriving Statistical Behavior of Particles via Classical Mechanics

    Hello, using computation simulation, can the statistical behavior of many particles be derived through deterministic classical mechanics?
  47. TechieDork

    Courses I think I won't get an A in Quantum Mechanics I

    This is by far the hardest undergraduate class I have ever take. The majority of class got less than 40% on the midterm. Unfortunately, I was sick during the exam hours too ,so it's hard for me to concentrate and think clearly Thank god,the professor uses the norm-referenced grading and My...
  48. JD_PM

    Classical Book on discrete mechanics (particularly interested in Lagrangian)

    Hi.I am looking for a book to learn about discrete mechanics (i.e. working in a 3D lattice instead of ##n## generalized coordinates). I am particularly interested in how to derive the discrete E-L equations by extremizing the action. I have checked Gregory and Goldstein but they do not deal...
  49. E

    Griffiths Quantum Mechanics 2nd edition Chapter 8 equation is confusing

    In Griffiths Quantum Mechanics 2nd edition, in Chapter 8 he calculates the following integral on page 323 and he gets I disagree with this result, I think the integral should be since Maybe somebody can explain why I am wrong? Also, from equation 8.24 to 8.25, he makes the assumption that...
  50. Boolean

    Lug FBD and simple mechanicals

    Pretty simple FBD of a lug in a pull test that I solved using FEA software, but I’m having trouble checking with a hand calc. Back end is fully supported in a test fixture Feel free to make up numbers where not given
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