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. W

    Writing Hamiltonian: Classical Mechanics

    Homework Statement I'm having some issues understanding a number of concepts in this section here. I attached the corresponding figure at the end of the post for reference. Issue 1) 1st of all, I understand that a Hamiltonian can be written as such $$H = T_2 - T_0 + U$$ whereby ##T_2##...
  2. W

    Lagrangian: Pendulum down a slope

    Homework Statement I have the answer for part a, which is: $$\theta '' + \frac{a}{r} \cos \theta + \frac{g}{r} \sin \theta$$ My issue lies with getting the following equation of motion for part b, $$\theta '' + \frac{g}{r} \cos \alpha \sin \theta = 0$$ Homework EquationsThe Attempt at a...
  3. E

    Rotating spool on table with friction

    Homework Statement I am referring to this thread and question: https://www.physicsforums.com/threads/rotation-of-a-spool-about-rough-ground.295666/ Here is the problem, restated: Homework Equations ##\tau_{net} = I\alpha## ##\tau = Frsin(\theta)## ##F_{net} = Ma_{cm}## ##\alpha = a_{cm} /...
  4. D

    Flight Mechanics - Range and Payload calculations

    Homework Statement Assume that m(fuel, climb) = 1300kg is the mass of fuel required for the climb to the cruising altitude of 10,000m, independently of the take-off weight. Assume that the distance covered during the climb is always 100km. Consider the typical payload-range diagram shown and...
  5. N

    The Simulation Interpretation of Quantum Mechanics

    It seems like every argument in favor of the Simulation Hypothesis revolves around the strangeness of Quantum Mechanics. So can the Simulation Interpretation be just as valid of an interpretation as Copenhagen or Many Worlds? If not why not?
  6. E

    Torque on Rod Due to Normal Force at a Hinge

    Homework Statement In this diagram, I wondered if there is any torque due to the normal force from the hinge, once the support stick is removed. I also want to know what the normal force would be at the hinge. The cup and ball are to be ignored here (essentially massless). Homework Equations...
  7. mcaay

    Lagrange Multipliers in Classical Mechanics - exercise 1

    Homework Statement The skier is skiing without friction down the mountain, being all the time in a specified plane. The skier's altitude y(x) is described as a certain defined function of parameter x, which stands for the horizontal distance of the skier from the initial position. The skier is...
  8. JTC

    Difference between Hamiltonian and Lagrangian Mechanics

    Hello, I am trying to "integrate into my understanding" the difference between Hamiltonian and Lagrangian mechanics. In a nutshell: If Lagrange did all the work and formulated L = T - V, they why is Hamilton's name attached to the minimization principle? YES; I KNOW about Hamilton's Second...
  9. V

    Understanding Newton's Laws: The Confusion Between II and III Revealed

    I am not a teacher, but I have made an interesting observation regarding classical mechanics education. It is surprisingly common that even students at academic level do not seem to fully understand Newton's third law (action and reaction) and confuse it with Newton's second law...
  10. D

    Find Axial Force at X: Structural Analysis Problem

    Homework Statement I have to find axial force at X for the following structure: https://i.imgur.com/8o01fkC.jpg The Attempt at a Solution These are my workings https://imgur.com/JfSfk9Z https://imgur.com/3HuDN4d I didn't work out moments because the question only asks for axial force, is...
  11. SciencyBoi

    Three Pulley - two masses system.

    Homework Statement The given system is released from rest. Assuming no friction, mass-less pulleys and ideal strings; calculate the accelerations of the pulleys. Homework Equations Constraint equations. F=ma The Attempt at a Solution Taking the above assumptions; And applying constraints...
  12. F

    Understanding Lagrangian Mechanics: Equations of Motion and Applications

    I’m a bit confused about what exactly lagranigian mechanics is. I know that L = Ke - Pe I also know the equation d/dt(∂L/∂x’) - ∂L/∂x = 0 1.) Apparentaly solving this equation gives the equations of motion. What exactly does that mean though? I solved a very simple problem and got the...
  13. ARNAV SHARMA

    Rotational Mechanics: Find Height of Stick in N Turns

    Homework Statement A student throws a stick of length l up in the air .At the moment the stick leaves his hand ,the speed of the stick's end is zero.The stick completes N turns just as it is caught by the student at the initial release point . Show that the height to which the centre of mass...
  14. Clara Chung

    Classical mechanics question (pendulum)

    Homework Statement Homework EquationsThe Attempt at a Solution I have done part a, I have no idea on part b, here is my attempt,
  15. Alexander350

    Modelling Water Tanks: Solving with Bernoulli Equation

    I tried using the Bernoulli equation to solve this. I took two points at the surface of the water in both the containers and formed this equation: gh_{b}=\frac{1}{2}v^2+gh This is assuming that the velocity of the water in the large tank is approximately zero and using the fact that both the...
  16. ang__

    How Do You Calculate the Total Inertia Matrix for a Composite Object?

    Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework EquationsThe Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them to...
  17. Krunchyman

    Teach me about classical mechanics please

    I have no prior experience in physics, but I am a math undergrad so I know calculus, differential equations, linear algebra and stuff like that. So I'm ready to move from the conceptual "bedtime story physics" to stuff with real mathematical rigor. So, what is classical mechanics all about...
  18. Alexander350

    Escape velocity and kinetic energy of the Earth

    If you had two masses, m_{1} and m_{2}, and you released them in space infinitely far apart, their kinetic energies would satisfy \frac{1}{2}m_{1}v_{1}^2+\frac{1}{2}m_{2}v_{2}^2=\frac{Gm_{1}m_{2}}{r} if they met with a distance r between their centres of mass. This equation therefore tells you...
  19. mr1batman

    How can i start in quantum physics and quantum mechanics?

    i want an article or video that i can start with at the journy of understanding the basics of quantum physics and quantum mechanics i don't want a book because in my country i would not find this types of books every where it's unique to find them thanks
  20. S

    Classical Source of Difficult Newtonian Mechanics Problems?

    I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got...
  21. C

    Collision Angle for Two Particles with Constant Velocity and Acceleration

    Homework Statement I am currently solving a problem and I am not sure if it is correct. There are two particles A and B. A has a constant velocity with |\vec{v}| = 3 and starts from y = 30 B has constant acceleration with |\vec{a}| = 0,4 The goal is to find the angle between the...
  22. Wrichik Basu

    Other Books for Non-Equilibrium Statistical Mechanics

    Can anyone refer to some good book on Non-Equilibrium Statistical Mechanics? The book should contain the basics, and can go up to any advanced level. Any level of math is acceptable.
  23. S

    Kinematics question: free-fall distance traveled during a given second

    Homework Statement An object is released from rest in the gravitational field of the Earth. Air resistance is negligible. How far does the object move during the fourth second of its motion? A. 15 m B. 25 m C. 35 m D. 45 m Homework Equations v = u + at s = ut + 1/2 at^2 v^2=u^+2as...
  24. Another

    Problem ODE from mechanics equation

    The particles are moving under force F = rK when r = 1/u and u = 1/r I tried to solve the problem by defining a variable v = u4 and u = v1/2 But I can not divide variable v out of variable u I want to find r (Radius) of orbit
  25. F

    Classical Exploring Lagrangian Mechanics: Theory, Books, and Problem-Solving

    What books include the theory of lagrangian mechanics? And where can i also find some problems?Could lagrangian mechanics help me in solving problems with oscillations?
  26. Anupama

    Linearity of time evolution in classical mechanics

    I came to know that time evolution in classical mechanics is highly non linear. Is there any case that it become linear?
  27. W

    I Hermitian Operators: Referencing Griffiths

    I have a few issues with understanding a section of Griffiths QM regarding Hermitian Operators and would greatly appreciate some help. It was first stated that, ##\langle Q \rangle = \int \Psi ^* \hat{Q} \Psi dx = \langle \Psi | \hat{Q} \Psi \rangle## and because expectation values are real...
  28. J

    Dog running on rotating ball

    <Moderator's note: Moved from a technical forum and thus no template.> We place a ball on an an inclined plane (angle ##\theta##). At the top of the ball is a small dog who always stays at the top over the course of the ball's movement. What is the motion of the ball? ------------------ I...
  29. Andrea Vironda

    Exploring the Homogeneity of Space & Time in Lagrangian Mechanics

    Hi, i know that The homogeneity of space and time implies that the Lagrangian cannot contain explicitly either the radius vector r of the particle or the time t, i.e. L must be a function of v only but the lagrangian definition is ##L=\int L(\dot q,q,t)##, so velocity appears in the definition...
  30. SciencyBoi

    A block placed in a horizontal hollow cylinder

    Homework Statement A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center...
  31. U

    Fluid mechanics - Finding force point of application

    I get how to find vertical and horizontal forces on a submerged surface (vertical = weight of fluid and horizontal = force on vertical projection). I also get how to find the point of application for the horizontal force using a moment balance. But how do you determine the point of application...
  32. grandpa2390

    Determine state of particle: Quantum Mechanics (Phase)

    Homework Statement Homework EquationsThe Attempt at a Solution This is the Solution. I am having trouble understanding parts of it. The first part I don't get is why the e^i... goes with the -z. Did my professor just choose one at random, or is there a specific reason? The second part...
  33. grandpa2390

    Question about phase factor in Quantum Mechanics

    Homework Statement I am trying to understand a solution to a problem. I may not need to post the entire question, I just need to know if ##-i = e^{\frac{-i*pi}{2}}## Homework EquationsThe Attempt at a Solution the reason for this question is that one step of the problem has a quantity...
  34. S

    I Did Paul Dirac say anything about Bohmian mechanics?

    Could you, please, give me reference to any paper or talk by Paul Dirac where he expresses his views about or give comments to the de Broglie-Bohm theory (Bohmian mechanics)?
  35. B

    Mechanics of Materials Question

    Homework Statement Homework Equations G = Shear Stress/Shear Strain G = E/(2(1+n)) n being poissons ratio The Attempt at a Solution So I know the easiest way to solve is simply to manipulate the first equation a little bit >>> Shear Stress = G * Shear Strain >>> Shear Stress = P/A >>>> P...
  36. C

    A Symplectic geometry of phase space

    What is a symplectic manifold or symplectic geometry? (In intuitive terms please) I have a vague understanding that it involves some metric that assigns an area to a position and conjugate momentum that happens to be preserved. What is 'special' about Hamilton's formulation that makes it more...
  37. O

    Distance of two moving particles

    Homework Statement There are two particles. There are moving equally on two intersecting lines to intersection. On time t=0 is the distance of two particles d. The velocity of one particle relative to the other has a projection u in the direcion of d. In direction perpendicular to d is the...
  38. O

    Projection at an angle - throwing stones

    Hello everyone. I have this problem: 1. The problem statement, all variables and given/known d I throw stone from height h at an angle α, then at an angle β (so I know h, α, β). I throw it with same velocity v. The stones fall in same distance d. The question is: find the d (distance) and v...
  39. M

    Find the time dependence.... (Mechanics)

    Homework Statement I am not looking for a solution to the problem, as much as I need a clarification on what it's asking for. The problem: "A particle of mass m slides down an inclined plane under the influence of gravity. The particle is starting its motion from rest. Find the time dependence...
  40. M

    Factor of Safety and load/stress linearity

    Why can we calculate factor of safety using Strain (fail)/ Strain (allow) only if the load applied is linearly related to the stress developed within the member? What happens if the two are not related? Also, my textbook says factor of safety can also be calculated by stress (fail)/ stress...
  41. C

    I Hamiltonian as total energy for natural systems?

    Could someone please prove that the H=T+V for systems where the transformation from Cartesian to Generalized coordinates is time independent. I have read through the proofs in Taylor's classical mechanics and Goldstein's but do not understand them.
  42. V

    What is the acceleration of the blocks in a pulley constraint problem?

    Homework Statement Need to find the acceleration of the blocks, all surfaces are smooth : https://drive.google.com/file/d/0B5bF4yPQOejoazhWeEgySmtfSnc/view?usp=drivesdk Homework Statement Need to find the acceleration of the blocks Homework Equations a1 + a2 + a3 =0 (acceleration of strings...
  43. L

    "Shifting" non-inertial frame in Accelerating Atwood Machine

    Hello, I was referring to this thread: https://www.physicsforums.com/threads/accelerating-atwoods-machine-problem.44305/ to solve a problem on accelerating atwood machines in which, naturally, one attempts to find the acceleration of each of the individual masses. Although I now understand how...
  44. B

    Taylor Mechanics Problem 5.13

    Homework Statement This is the problem verbatim: The Potential energy of a one-dimensional mass m at distance r from the origin is U(r) = U0 ((r/R) +(lambda^2 (R/r)) for 0 < r < infinity, with U0 , R, and lambda all positive constants. Find the equilibrium position r0. Let x be the...
  45. B

    Classical Mechanics Textbooks: A Must-Have for Physics Students

    I'm sophomore in physics looking for best free books for classical mechanics and for vibrations and waves. Anyone with references pleaseThank you
  46. K

    B How is Bohr's atom model convenient with quantum mechanics?

    Hi. From what I read, according to Quantum mechanics "even though it looks like objects are in definite places, when we get down to ridiculously tiny objects (like electrons) they seem to be not he in anyone place. And everything looks like a hazy clouds of probability."...
  47. N

    Mean Square Fluctuation (Q.M.)

    Homework Statement A state of a particle in the potential box of width a with infinitely high walls is described by the wave function: Ψ(x)=Ax(x-a) Find the probability distribution of various value of particle energy, mean value and mean square fluctuation of energy. Homework Equations...
  48. U

    Lifting a Beam with a uniform weight distribution

    Homework Statement Hi There, I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems) If I have a hinged beam (of uniform weight) and I lift it from one end and stay...
  49. X

    Question about statistical mechanics

    Hello, first of sorry for asking what maybe a stupid question. I am teaching myself physics by watching lessons about QM, Classical Mechanics, EMT etc. I was watching Susskind's lectures about statistical mechanics lately and he derived equation of energy E= 3/2 x k x T. 3 in 3/2 came from...
  50. J

    Classical The best mechanics books from the bottom to the top + math

    Hey there, there may be many threads about this problem, but I would want you to recommend me few books to read about mechanics from the bottom to the top. I mean, I don't have that much of a problem in calculus, but I'm not excellent in it either. So I would want a good textbook or bunch of...
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