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. N

    A Derivation of Statistical Mechanics

    Moderator's note: Spin-off from previous thread due to topic change. Because it doesn't work. Bohmian time evolution doesn't involve the coarse graining steps that are used in his calculation. A delta distribution remains a delta distribution at all times and does not decay into ##|\Psi|^2##.
  2. Salmone

    I Inner products with spherical harmonics in quantum mechanics

    Let ##|l,m\rangle## be a simultaneous eigenstate of operators ##L^2## and ##L_z## and we want to calculate ##\langle l,m|cos(\theta)|l,m'\rangle## where ##\theta## is the angle ##[0,\pi]##. It is true that in general ##\langle l,m|cos(\theta)|l,m'\rangle=0## ##(1)## for the same ##l## even if...
  3. F

    Pulling down on the string connected to a whirling block on a table

    At the time of release, the equation of motion of blocks A and B T-m_ag = m_aa and T=m_b\omega^2R respectively, where T is the tension in the string. Solving for the acceleration a then gives a=\frac{m_b\omega^2R - m_ag}{m_a}. Not sure what I did wrong or what incorrect assumptions I made...
  4. L

    Pulley system to balance the weight of a person

    Since we are dealing with an ideal rope, we have that ##T_1=T_2=T_3=F and T_2+T_3=2F=(m+m_p)g\Leftrightarrow F=\frac{m+m_p}{2}g.## ##T_4=3F+(m+m_p+M_p)g=\frac{3}{2}(m+m_p)g+(m+m_p+M_p)g=(\frac{5}{2}m+\frac{5}{2}m_p+M_p)g## and ##T_5=mg-2F.## Is this correct? If not, I woould appreciate a brief...
  5. M

    Mechanics of Materials — Torsional Stress on a Spinning Shaft

    Summary:: Torsional stress on freely spinning shaft? Hey guys, I’m having some confusion with a certain section of the “Torsion” chapter in my mechanics of materials book: “power transmission”. Please see the problem below. This is very easy to SOLVE (basically plug and chug with the...
  6. S

    Quantum 'Quantum mechanics the theoretical minimum' book

    I want to know about the book 'quantum mechanics: the theoretical minimum' book by Leonard Susskind. Is it a book worth buying
  7. T

    I Kleppner Classical mechanics: Question about stability (p.217)

    I have a question understanding the reasoning in the book. The book says in one dimension F=-dU/dr(p.185). From this, the system is stable at distance a when U'(a)=0 and U''(a)>0 where U is differentiated with respect to r.(p.217) My question arises from the instance of a pendulum where a...
  8. N

    Mechanics of materials - shear flow in built up members

    Hello! I am new to mechanics of materials and I am very confused about the problem below. So the shear formula is: tau = VQ/It From the book (Hibbeler) I understand that Q is "y'A', where A' is the cross-sectional area of the segment that is connected to the beam at the juncture where the...
  9. thedubdude

    B Special Relativity violation via Quantum Mechanics?

    We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...
  10. Santiago24

    Classical Textbooks of celestial mechanics

    Hi I'm reading classical mechanics by Taylor and there is a section about Kepler orbits that i find very interesting so i'd like to see more of classical mechanics with space applications. I appreciate rigouros mathematical books, thanks
  11. MidgetDwarf

    Classical Symon Mechanics 2nd or 3rd edition?

    Hi, was wondering if anyone is familiar with Symon Mechanics 2nd and 3rd edition. Is there a significant difference between these editions? Ie., content, quality of printing, major corrections?
  12. F

    I How to define expectation value in relativistic quantum mechanics?

    In non relativistic quantum mechanics, the expectation value of an operator ##\hat{O}## in state ##\psi## is defined as $$<\psi |\hat{O}|\psi>=\int\psi^* \hat{O} \psi dx$$. Since the scalar product in relativistic quantum has been altered into $$|\psi|^2=i\int\left(\psi^*\frac{\partial...
  13. L

    A satellite in orbit in a system with one planet and two moons

    1) Considering the forces on one of the moons, I have: ##\frac{GMm}{(10R)^2}+\frac{Gm^2}{(20R)^2}=m\frac{v^2}{10R}\Leftrightarrow v=\sqrt{\frac{G}{10R}(M+\frac{m}{4})}.## 2) Considering the initial situation in which the satellite is at rest on the surface of the planet...
  14. L

    Disk with rod attached rotating about the center of the disk

    1) Since the rod is uniform, with mass m and length l, it has a linear mass density of ##\lambda=\frac{m}{l}##, so ##I_{rod_O}=\int_{x=r}^{x=r+l}x^2 \lambda dx=\frac{\lambda}{3}[(r+l)^3-r^3]=\frac{\lambda r^3}{3}[(1+\frac{l}{r})^3-1]=\frac{1}{3}mr^2[3+\frac{3l}{r}+\frac{l^2}{r^2}].##...
  15. entropy1

    I Quantum Mechanics without time?

    Is there a view in quantummechanics, of quantummechanics, without time as a concept?
  16. M

    I Informational Interpretation of quantum mechanics?

    I heard something today about the "informational interpretation" of quantum mechanics and a phrase used was "it from bit." Is there actually such a thing? What does it mean, and how is it distinguished from other interpretations like MWI or Copenhagen?
  17. EishaR

    Physics 101 mechanics help -- Bullet fired by a rifle barrel

    a) a= dv/dt = 2(5*10^5)t+2.8*10^5 2(5*10^5)(0)+2.8*10^5=2.8*10^5m/s^2
  18. K

    I Definition of magnetic moment in quantum mechanics

    * The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...
  19. R

    I Webb Launch Mechanics: Tangential Speed Benefits?

    When I read about the launch location, it is explained that the French Guiana launch site was chosen because it is close to the equator, which means it started with a larger tangential speed than if it were launched from a US location. However, doing the numbers, I find that an initial...
  20. Dario56

    I Action in Lagrangian Mechanics

    Lagrangian mechanics is built upon calculus of variation. This means that we want to find out function which is a stationary point of particular function (functional) which in Lagrangian mechanics is called the action. To know what this function is, action needs to be defined first. Action is...
  21. Adgorn

    Morin's mechanics problem 2.3 (motionless chain)

    In his solution, Morin solves the problem as the hint suggests: cutting the chain into small pieces, taking the component of the external forces along the curve (which is just the component of gravity here) and summing up an in integral, obtaining 0. He then claims that because the "total...
  22. S

    Shift in position of plank when a man moves on it (Centre of mass)

    Lets take the original position of the man to be our origin The plank is uniform so we can assume its mass to be concentrated at its center i.e. 4m from the origin Xcom= m1x1+m2x2/m1+m2 =50(0) +150(4) /50+150 =3m There is no external force on the system so the centre of mass does not move...
  23. Ravi Mohan

    I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective

    Hi Fellas! My first post after a long hiatus from forums. Feeling nostalgia (this is the place where it all began, my fuel for quantum fascination so to speak). I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective. I want to understand what...
  24. J

    A Is fluid mechanics (aerodynamics) still being discovered?

    Is fluid mechanics,particularly aerodynamics still being discoverd (like math for example) or everything has already done long time ago?
  25. S

    MHB A-level Mechanics Q3: Need Help w/Calculations

    It's question 3. Iam getting a bit confused with the calculations. Pls help
  26. A. Neumaier

    Insights Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics

    Continue reading...
  27. K

    I Probability in statistical mechanics

    Suppose we've an isolated box having ##N## classical distinguishable particles in it, the box being hypothetically divided into two parts, left and right with both parts identical. Its said that the probability of having the configuration of ##n## particles in the left side is given as...
  28. H

    Trouble understanding the influence of a real spring in a system

    The hypothesis is that the force of a real spring can be described as $$F = -kx + \alpha x^2$$ with x being the spring deformation and k its constant. The \alpha x^2 would be the force lost by the spring as x becomes too big. To test that, a system was build with block of mass m suspended by a...
  29. M

    Help on Learning Quantum Mechanics (Undergraduate)

    Summary:: I am in the highest level Quantum class at my university- technically considered a grad class. I am an undergrad and need advice on just how to learn it. What study tips? Good Youtubers? Physical simulations? Anything that helped you in quantum mechanics. Hello! I am an undergrad...
  30. Vectronix

    Quantum Modern Quantum Mechanics 3rd Ed: J. J. Sakurai & Jim Napolitano Review

    Is Modern Quantum Mechanics, 3rd Edition, by J. J. Sakurai and Jim Napolitano a good book to learn quantum mechanics from?
  31. chwala

    At what time will bike and car be side by side again - Mechanics

    Find the question below; For part (a), i used the graph to find ##t=22## For part (b), i considered the points; ##(8,20)##, ##(13.333,20)## and ##(0,0)## it follows that, Area=##\sqrt {25.454(25.454-21.54)(25.454-24.036)(25.454-5.333)}## ##\sqrt {2842.58}##=##53.31## There may...
  32. chwala

    Find the car's speed at point when deceleration is increased - Mechanics

    Wawawawawawa! This was a tough one...:biggrin: Find the question below; Find my approach below: We have the following equations; 1. ##v=30-0.5t## 2. ##v=30-1.5t## Now the car changes its acceleration at some point i.e from ##-\frac{1}{2}## ##m/s^2## to ##-\frac{3}{2}## ##m/s^2## ... I...
  33. S

    I A thought experiment concerning determinism in quantum mechanics

    According to the uncertainty principle, when we measure a micro-object with a measuring device, we cannot predict what value the device will show. But if we knew exactly the wave function of this device, together with the wave function of the micro-object, could we exactly predict the result of...
  34. chwala

    Find the distance between the car and the truck- Mechanics

    Find the problem and the solution below; Find my approach to the problem. Considering the motion of the car; ##v=u+at## ##33.333= 26.6667+30a## ##a=0.2222## Therefore it follows that, ##s##=## ut##+##\frac {1}{2}####at^2## ##s##=##(26.67 ×30 +(0.5×0.222×30^2)## ##s=900##metres The distance...
  35. Santiago24

    Quantum Introductory quantum mechanics textbook for self-study

    Hi! I want to self study some of quantum mechanics so i need introductory textbook. I've taken courses on linear algebra that covers all "Linear algebra done right" by Sheldon Axler, multivariable calculus, two courses on general physics and the basics of differentials equations. I really like...
  36. chwala

    Find the time taken to travel from top of slope to base - Mechanics

    Now this is a textbook example with solution. I understand working to solution...my only reservation is on how they used acceleration. The cyclist, i understand was traveling at a constant acceleration of ##2## ##m/s^2## before reaching the top part of the slope. Now, if he is descending...
  37. chwala

    Find speed of the racing car as it crosses finish line - Mechanics

    This is a textbook problem (Mechanics). Attached find the question and respective solution. This is fine with me, i like trying different ways of solving math related problems. My approach is as shown below. Using the graph sketch It follows that, ##s##= ##(35×12)##+##\frac...
  38. A

    Is Throwing a Knife with No Spin Actually More Effective?

    They say that a rotating knife thrown is more dangerous than a knife thrown straight I find it weird If the knife is rotating, it will experience more air drag than if thrown straight which will also depend on plane of rotation(For some reason, I don't know, it experiences more drag if...
  39. curiousPep

    I Lagrangian mechanics - generalised coordinates question

    I think I undeerstand Lagrangian mechanics but I have a question that will help to clarify some concepts. Imagine I throw a pencil. For that I have 5 generalised coordinates (x,y,z and 2 rotational). When I express Kinetic Energy (T) as: $$T = 1/2m\dot{x^{2}}+1/2m\dot{y^{2}}+1/2m\dot{z^{2}} +...
  40. D

    Need help with this unequal length bifilar pendulum

    [Mentor Note -- Three threads on the same problem have been merged into this one] Hi, I'm doing a lab report on the relationship between the period of oscillations in an unequal length bifilar pendulum. The set up is like below Can anyone help me derive a formula for the period of oscillations...
  41. K

    Quantum Finding the Perfect Self-Study Book for Intro Stats & Quantum Mechanics

    Can you please suggest a good introductory statistical and quantum mechanics book which can be self studied. My math background : I've done multivariate calculus, vector calculus, linear algebra ,some complex analysis all at the usual undergraduate level. The books I've self studied thus far...
  42. tworitdash

    A Applications of weak measurement of quantum mechanics in other domains

    This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean and standard deviation of a variable). The sensor measures this once in a while (like once in a...
  43. R

    Boats in a triangle colliding after some time

    Assume that three boats, ##B_1##, ##B_2## and ##B_3## travel on a lake with a constant magnitude velocity equal to ##v##. ##B_1## always travels towards ##B_2##, which in turn travels towards ##B_3## which ultimately travels towards ##B_1##. Initially, the boats are at points on the water...
  44. A

    Moment of Inertia of a 4 rod system

    This was the question (The line below is probably some translation of upper line in different language) For disc it was ma^2/2 For ring it was ma^2 For square lamina it was 2ma^2/3 For rods It was different Please explain Thank You🙏
  45. brochesspro

    Relative Velocity of a Passenger Hitting the Dashboard in a Car Crash

    Where exactly have I gone wrong? I think it is the part where I assume that the person gains the deceleration of the car, but I have no other way to proceed in this case. Also please only use the equations that I have posted below, and it would help if you would not use the equation for...
  46. Shreya

    Phase factor in quantum mechanics

    Please be kind to help.I would be grateful
  47. jonas_biermann

    B Calculating the torque needed to rotate a drum

    Imagine this: You have a drum with a radius of 12cm, around that drum is a toothed belt which is connected to a motor. The drum weighs 10kg The motor should be placed under the drum How would I calculate the amount of torque needed to rotate the drum I don't have any idea how to calculate this...
  48. TheBigDig

    Forces acting on a car on an incline

    For part 1, I got ## tan \alpha = 1/30 ## ##\alpha = 1.9^{\circ}## ##mgcos(1.9) = 10774N## I'm a little thrown off by the second part. Are we supposed to assume that in the absence of friction, F = N and then substitute F = ma to solve for this?
  49. Hamiltonian

    Quantum Buying my first Quantum mechanics book

    I recently started studying some quantum mechanics, so far I have been using online resources(like MIT OCW 8.04/8.05, and Tongs notes I think I have reached a stage where I understand the Schrodinger eqn and can solve it for various potentials(including for the H-atom) but I don't know anything...
  50. L

    I Benefits of Lagrangian mechanics with generalised coordinates

    I have sometimes seen the claim that one advantage of Lagrangian mechanics is that it works in any frame of reference, instead of like Newtonian mechanics which will hold only in the inertial frame of reference. However isn't this gain only at the sacrifice that the Lagrangian will need to take...
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