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. H

    Help with classical mechanics question

    Homework Statement A nucleus of mass 20mu (where mu is the atomic mass unit 1.66*10^-27) is moving with a velocity of 3*10^6 ms^-1 when it breaks into two fragments. In the course of this process internal energy is released from within the nucleus and the kinetic energy consequently increases...
  2. P

    A bunch of Classical Mechanics online Resources( lecture notes)

    Tell me you love me. http://www.phys.psu.edu/~lammert/419/notes.html" http://www.physto.se/~ingemar/anmek.pdf" http://www.phy.ohiou.edu/~rollinsr/phys605/" http://farside.ph.utexas.edu/teaching/336k/336k.html" http://www.damtp.cam.ac.uk/user/tong/dynamics.htm"...
  3. A

    Classical mechanics reference book

    Hi All, Kindly suggest me an alternative book for "Classical Mechanics by Goldstein". I am finding it little bit difficult to understand so if i can find any alternate book which is little less complicated than Goldstein it will be helpful for me. I am concentrating on the below mentioned...
  4. L

    Why Can't Stefan-Boltzmann Law Be Explained in Classical Mechanics?

    I've looked all over the internet, and can't find a decent explanation. Could someone please explain why the stefan-boltzmann radiation law of I = oT^4 be explained in classical mechanics rather then quantum? It's urgent, sorry to be pushy. Cheers.
  5. J

    Relativistic covariance in classical mechanics?

    Hi friends, long time ago I noticed the following interesting similarity between classical mechanics and relativity. Consider particle moving in an external field and the action defined as a function of actual time t and position q: S(t,q) = \int_0^t L(q^r,\dot q^r,t´)dt´ The motion q^r is...
  6. J

    Hydrogen atom obeying classical mechanics rather than quantum mechanics

    Suppose that the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum? So far I have: quantum mechanics deals with the smallest possible piece of a system...
  7. N

    Is it reasonable to go straight from general physics to classical mechanics?

    I'm a biochemistry major with most of my requirements out of the way. Fall term my schedule will be: Physical chemistry, intro to real analysis (junior level). This is 8 credits, but to maintain full financial aid I need 12 credits. I recently found out that I am 12 credits away from a physics...
  8. V

    Cannot see where potential enegy comes from in classical mechanics

    Homework Statement F=force, a=acceration, m=mass, U potential energy, P momentum, E=energy How do derive 2 and 3 from 1( see below). Homework Equations 1) F=ma, 2) E= (p^2)/(2m) + U, 3) ma = -del U The Attempt at a Solution I try to understand why U pop into the...
  9. J

    Lectures on Classical Mechanics - J. Baez

    Graduate course lecture notes - Excellent! http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf" jf
  10. T

    Classical Mechanics - Pulleys System

    Homework Statement Consider the pulleys system in the picture. Assume both pulleys are frictionless. Assume the rope is massless and inextensible. Find the acceleration of the mass m_2 Homework Equations The Attempt at a Solution I have solved the same problem with massless...
  11. T

    Classical Mechanics - Block Friction Problem

    Homework Statement A block of mass M is placed on a horizontal plane with kinetic friction coefficient equal to \mu. A particle with mass m and velocity \vec{v_0} hits the block in a completely inelastic collision (i.e. the two bodies get stuck together). Knowing that the angle between...
  12. O

    Uncertainty principle in classical mechanics boundary

    Hallo, Why does dp*dx>>h represents classical mechanics state? Thanks, Omri
  13. P

    Tetherball - Classical Mechanics

    Homework Statement A small ball is attached to a massless string of length L, the other end of which is attached to a very thin pole. The ball is thrown so that it initially travels in a horizontal circle, with the string making an angle \theta_0 with the vertical. As time goes on, the string...
  14. S

    Testing Physics GRE without classical mechanics

    Howdy! I am taking Phyiscs GRE next semester and won't have taken classical mechanics by the time I take the test. I am not comfortable with the situation. Can anyone please suggest me a good preparation strategy for me ?
  15. G

    How Do You Model a Damped Harmonic Oscillator with External Forces?

    Homework Statement Give the equations of motion of the following system: http://www.jelp.org/imagenes/mech.jpgHomework Equations So, i assume the following cases (the diagram i so deficient). 1) Black Point (x1) is fixed 2) There's a force applied at x1 (black dot) 3) The position of the...
  16. X

    Searching for Classical Mechanics book

    So everyone here already knows how important understanding classical mechanics is so that brings me to my question; What is a good introductory mechanics book that has nice complete mathematical derivations, good well-written physics explanation, and large breadth in terms of subject matter. In...
  17. V

    Classical Mechanics Textbook Recommendation

    Hey guys, I am an undergraduate junior physics major currently enrolled in PHY3220 (Classical Mechanics) and we are using the textbook by Fowles and Cassiday titled, "Analytical Mechanics." However, I am looking for a second Classical Mechanics textbook that I could use as a reference since...
  18. B

    Air friction on a A4 paper ( Classical Mechanics )

    Homework Statement How could u find the drag/friction due to air on a A4 size page dropped perpendicular to the ground. There are about 20 sheets and is dropped about waist height. The tricky thing is no instruments are aloud. Only your senses... Homework Equations F=-cv where c is...
  19. J

    Solving the Problem of an Infinite Chain Slipping Down a Table

    Hello all, I'm having trouble with the following problem: Pb: A chain with constant density and infinite length is slipping down from the table without friction. Determine the position of the tip of the chain at time t. I know there are a few ways to approaching this problem, namely from...
  20. N

    Is Using the Tangent Direction to Determine dl in Work Calculation Incorrect?

    Homework Statement Hi all. We have that the work W equals Ui - Uf (respectively the initial and final potential energy). Let us say that a stone has a height 10 m, and falls down. We say that positive x is upwards. Now W = \int F \cdot dl = F(x_f-x_i)=U_f-U_i, since F and dl both point...
  21. X

    Which Classical Mechanics Book Should I Choose for Next Semester?

    I'll take classical mechanics next semester and I want a book for this course. I choose two books but, unfortunately, I can buy only one, Kibble or Goldstein. I know Goldstein is going to be better but Kibble's book is much cheaper (17 pounds @ amazon.com). Does Goldstein worth it? Could you...
  22. A

    Classical Mechanics: Solving for x(t) from V(x) = const.

    Homework Statement An object is moving in one-dimensional space with a potential funciton V(x) = constant. Find the equation of motion, x(t). Use x_0 as the initial position and v_0 as the initial velocity at t=0. Homework Equations initial position = x_0 initial velocity = v_0 The Attempt...
  23. P

    Top Classical Mechanics Texts for Self-Study | Physics, Calculus, ODEs, and More

    Hi, I'm looking for a good classical mechanics text for self study, roughly around my level. So far I've taken courses in calculus based physics courses, ( first year mechanics and E&M ) multi-variable calculus, ODE's and linear algebra. I have self taught myself real analysis, and a...
  24. L

    Classical mechanics - Lagrange multipliers

    Homework Statement A disk moves on an inclined plane, with the constraint that it's velocity is always at the same direction as it's plane (similar to an ice skate, maybe). In other words: If \hat{n} is a vector normal to the disk's plane, we have at all times: \hat{n} \cdot \vec{v} = 0. Also...
  25. J

    Classical Mechanics: linear resistance

    Homework Statement Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*vext+Fext show that if the rocket starts from rest and efects mass at a constant rate k= -m' then its speed is given by v=(k/b)vex[1-(m/m0)^b/k] The...
  26. P

    How Does the Decreasing Mass of the Sun Affect Earth's Orbital Radius?

    1. The mass of the sun is decreasing as dM/dt=-constant .M Find [dr/dt]/r for the earth Homework Equations [b]3. I tried using M=M0-alpha. t and then separating the variables in the equation GMm/r^2=mdv/dt. I don't knot the right way to solve this. Plz tell me how to solve this...
  27. H

    Yet another problem from classical mechanics

    Homework Statement THis time it is rather 3 problems, you are required to solve two of them before tackling third. So, in the first problem is about hoffman transfe. YOu are asked to calculate the velocity of the spaceship when it leaves the Earth and at it's encounter with juputer. It...
  28. H

    Looking for help with one problem. Classical Mechanics Kibble

    [b]1. It is problem for kibble book, classical mechanics. I star with mass M traves through cloud of particles with density ro. Particles that collide with a star are trapped by it. Derive the expression for mass increase of the star dM/dt. The Attempt at a Solution Since all particles that...
  29. J

    Rocket science in classical mechanics

    Homework Statement a rocket propelled car has total mass m0 and empty mass (after all of the fuel is burned) of m1. the car's exhaust speed is u and it has a constant burn rate of a=-dm/dt. ignore friction of wheels on the road, assume road is horizontal, and ignore air res. the driver fires...
  30. G

    Lagrangian in classical mechanics

    Hello: In Classical mechanics, the lagrangian of a system is defined as the kinetic energy minus the potential energy, but is there any physical meaning of the lagrangian ?, and if there is, What is it? Regards
  31. S

    Understanding Gravitational Time Dilation in Classical Mechanics

    Homework Statement I am self studying Chow's Classical Mechanics. I have realized that I am at my best if I leave no stone unturned Homework Equations \hat e_t . \hat e_t = 1 Understood d(\hat e_t. \hat e_t)/dt =0 Also understood But 2\hat e_t .d\hat e_t/dt=0 Not...
  32. D

    A question about Marion&Thornton book on Classical Mechanics (year 2)

    Dear all, I am wondering if Introduction Classical Dynamics of Particles & Systems (5 ed.) by Marion and Thornton is any good? I have already studied year 1 Classical Mechanics course, using University Physics by Young and Freedman. May I know if Marion&Thornton book is of higher level and...
  33. D

    Finding Forces on Supports in Classical Mechanics

    Homework Statement Find the expression for the forces on support A and B. Fax, Fay, Fbx and Fby. Homework Equations I'm thinking; Moment , M=F*l Fa^2=Fax^2+Fay^2, same for b Fax=Fbx The Attempt at a Solution (1) M = F*L1 Since I know that the sum of moments around the...
  34. E

    Calculating Mass and Tension: Classical Mechanics Problems Solved

    Hi, If these questions have been asked before, then please point me in the right direction. 1) Find the Mass of an object that is suspended by two strings. The tension on String one is 34 N and is held at a 40 degree angle with the horizontal (i.e., if a line was drawn through the center of...
  35. D

    Leonard Susskind : Classical Mechanics

    http://www.youtube.com/view_play_list?p=189C0DCE90CB6D81
  36. J

    Preparing for Classical Mechanics

    I'm an EE student and I am going to take modern physics next semester, and then would like to take classical mechanics. I was enrolled for about a half week in a classical mechanics class but it seemed really hardcore and I wasn't prepared for it. (The first homework problem was: Describe the...
  37. M

    Rotational group SO(3) in classical mechanics

    Hi! This is my first post here. I'm currently studying analytical/classical mechanics and have some problems understanding how the Lie algebra is formed in relation to the SO(3) group of rotations. My problem is this: Given a matrix representation R of some rotation around a fixed axis, we...
  38. N

    Structure and Interpretation of Classical Mechanics

    This is an unusual book which uses the Scheme programming language to functionally describe the various components of classical mechanics. I would say it is at the level of a graduate mechanics course (think Goldstein), however students with a strong programming background will find it easier...
  39. E

    Classical mechanics marion and thornton

    [SOLVED] classical mechanics marion and thornton Homework Statement At the beginning of section 12.4 in marion and thornton, they say that \dot{q}_k and [itex]\ddot{q}_k[/tex] are both 0 at equilibrium, where these are generalized coordinates. Can someone please explain how they got that the...
  40. Greg Bernhardt

    Classical Mechanics: An introductory course

    A complete set of lecture notes for an lower-division classical mechanics course. Topics covered include one-dimensional motion, three-dimensional motion, Newton's laws of motion, energy and momentum conservation, circular and rotational motion, statics, planetary motion, oscillations, and wave...
  41. E

    How to Find Normal Mode Frequencies for Three Masses in an Equilateral Triangle?

    Three equal masses arranged in a equilateral triangle are connected by 'springs' with force constants 'k' the coordinates of the masses are: mass 1 at [0, \sqrt{3}/2*L] mass 2 at [L/2, 0] mass 3 at [-L/2,0] find the normal mode frequencies. The only part i am having trouble with...
  42. B

    Should I learn Classical Mechanics before Electricity & Magnetism?

    I will probably be taking both CM I/II and E&M I/II before I graduate, but I'm wondering is it a bad idea to take E&M before taking CM? I don't think I can take both at the same time this coming year so I have to pick just one.
  43. B

    Classical mechanics: ball rolling in a hollow sphere

    [SOLVED] Classical mechanics: ball rolling in a hollow sphere Homework Statement This problem is from Gregory: A uniform ball of radius a and centre G can roll without slipping on the inside surface of a fixed hollow sphere of (inner) radius b and centre O. The ball undergoes planar...
  44. B

    Gregory’s Classical Mechanics Mass on a spring

    [SOLVED] Mass on a spring Homework Statement This problem is from Gregory’s Classical Mechanics A light spring of natural length a is placed on a horizontal floor in the upright position. When a block of mass M is resting in equilibrium on top of the spring, the compression of the spring...
  45. N

    Classical Mechanics: Lagrangian of a falling yo-yo

    Homework Statement A uniform circular cylinder (a yo-yo) of radius a and mass M has a string wrapped around it that can unwind without slipping. The yo-yo moves in a vertical straight line and the straight part of the string is vertical as well. The other end of the string is fastened to a...
  46. N

    Is the Eigenvalue Equation Correct for 3D Small Oscillations?

    Homework Statement Problem: Derive eigenvalue equation of motion of a system undergoing free small oscillation in three dimensional space. Homework Equations The Attempt at a Solution I want to know if I have correctly written the values of T and V--- \ T=\frac{1}{2}\ m...
  47. C

    Classical Mechanics Dynamic Drag Resistance

    i'm not even sure where to get started with this one because the thorton and marion classical dynamics book is really awful. BEGIN PROBLEM Suppose a baseball, which has a mass of 150 g and a diameter D of 7 cm is released from rest. For a sphere in air, the dynamic drag is F_d=.25 D^2 V^2...
  48. K

    Classical mechanics, angular momentum and velocity not parallel, why?

    Homework Statement A single particle of mass m is revolving at steady speed in a circle of radius a about the z axis at a height h above the origin. In this situation the particle has angular velocity w = wz 1 Show that the angular momentum L is not parallel to w 2 If a second particle...
  49. D

    Want help regarding my classical mechanics assignment

    Homework Statement I need to write a C program to simulate physics problems. My job is to write a code , in which I give the user a function F(x) = ax^n + bx^(n-1) + ... , and user inputs the coefficients a,b,c ... and my computer code should tell whether the given force F(x) is conservative...
  50. E

    Where is the Definition of Apsidal Vectors? Goldstein's Classical Mechanics Book

    Homework Statement My classical mechanics book (Goldstein) talks about apsidal vectors in the context of central force problems and elliptical orbits. I cannot find where the book defines this term and it is nowhere on the internet. Has anyone heard this term before? Homework Equations...
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