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. hadsox

    Rotating and translating spool across a table

    Homework Statement A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its center of mass is a distance l from the edge...
  2. D

    How to find the average potential energy given V(x,y) and E?

    Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...
  3. G

    Work-Energy for Bead on Rotating Stick

    Homework Statement Verify the Work-Energy Theorem W=ΔK for a bead of masd m constrained to lie on a frictionless stick rotating with angular velocity ω in a plane. Homework Equations W =∫ F⋅dr, K =m/2 v^2 [/B] The Attempt at a Solution Adopting polar coordinates the velocity is v = r' +r*Θ'...
  4. Lujz_br

    Question 6.9 Taylor: Classical Mechanics

    Homework Statement Hello, I solved others but not 6.9: Find the equation of the path joining the origin O to point P(1,1) in the xy plane that makes the integral ∫(y'2 +yy' + y2) dx stationary. ∫ from O to P. y' = dy/dx Homework Equations I need use ∂f/∂y = d/dx (∂f/∂y') (euler-lagrange...
  5. C

    Quantum What is the Born approximation and how does it relate to quantum scattering?

    Hi i am trying to understand Borh's scattering but i need article that will teach me step by step. Do you know any?
  6. A

    Where can I find lectures on classical mechanics online?

    I am a high school student looking for some amazing lectures online to study classical mechanics for a regional qualifying camp for ipho.
  7. S

    Harmonic oscillation in classical mechanics

    Homework Statement An object of mass m = 300g is attached to a spring with a constant k = 3.0Nm-1 and is at rest on a smooth horizontal floor in a fluid where the resistive force is assumed to be linearly proportional to the velocity v. the object is then displaced 10mm to the right of the...
  8. Unteroffizier

    Centripetal Force - same thing as gravitational force?

    First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me. I recently took...
  9. K

    Classical mechanics formulations?

    Hi, when do we use hamiltonian vs. Newtonian mechanics or even lagrangian formulations? pros and cons? I am thinking molecular dynamics codes
  10. AD MCFC

    Studying Review for Upper Division Class Mechanics course?

    Hello, I will take Classical Mechanics I (upper division) course fall of 2017. I have not seen Mechanics material since fall of 2014 and would like suggestions on how to review the concepts prior to taking the class. I was pretty good in that class and do not need to "re-learn" anything per...
  11. CassiopeiaA

    A Symplectic Condition For Canonical Transformation

    I am reading Chapter 9 of Classical Mech by Goldstein.The symplectic condition for a transformation to be canonical is given as MJM' = J, where M' is transpose of M. I understood the derivation given in the book. But my question is : isn't this condition true for any matrix M? That is it doesn't...
  12. Elvis 123456789

    Courses Partial Differential Equations vs Classical Mechanics 2?

    Hello everyone. So I wanted to get some opinions on what some of you thought was a better choice, as far taking PDE's or classical mechanics 2 goes. First let me start off by giving a little info; I've already taken calc 1-3 and ordinary differential equations, physics 1 & 2...
  13. K

    Thoughts Experiment about Frame of References

    Homework Statement The Observer (me) is at Inertial Frame of Reference: 1) I am sitting at a car moving east v=30 km/h relative to earth A bird flying east v = 10 km/h relative to earth What is the speed of bird for me? 2) I am sitting at a car moving east v=30 km/h relative to earth A bird...
  14. N

    Classical Mechanics: Retarding force on a satellite

    Homework Statement A spherical satellite of radius r is moving with velocity v through a uniform tenuous atmosphere of density ρ. Find the retarding force on the satellite if each particle which strikes it (a) adheres to the surface and (b) bounces off it elastically. I know the answer should...
  15. V

    I Why exactly does the ocean bulge on both sides of the Earth?

    Here's what my prof says: "Define F_{mean} to be the mean force, F_close to be the force on the side of the Earth closer to the moon, and F_far to be the force on the side of the Earth furthest away from the moon. On the closer side the net force is F_close - F_mean > 0 On the further side the...
  16. patrickmoloney

    Rotational Motion (Neutron Star)

    Homework Statement I'm doing a question from a past paper, preparing for an upcoming exam. There is no solutions so I was wondering if my answer is correct for all parts. Take a star to be a uniform sphere with mass M_{i}=3.0 \times 10^{30} Kg and radius R_{i} = 7.0 \times 10^{8}m that...
  17. AntonPannekoek

    Find angle for the ring to be in equilibrium

    Homework Statement Find the angle Theta so that the system is in equilibrium Mass of each block: 2 Kg Mass of ring: 4π Kg Homework Equations Static equilibrium: Rotational equilibrium The Attempt at a Solution Static equilibrium: 2g + 2g + 4πg = Normal N = 4g + 4πg Taking...
  18. L = K - U

    Infinite Atwood Machine (Morin Problem 3.3)

    I could've peeked at the solution manual and end with it at that. However, I'm trying to change this nasty habit and solve this problem myself. I might be too ambitious. Here goes. Homework Statement Consider the infinite Atwood's machine shown. A string passes over each pulley, with one end...
  19. P

    Solving Part c of Repulsive Force Homework Problem

    Homework Statement (2) Suppose a particle of mass m is subjected to a repulsive force F = +kx. (a) What is the general solution for the motion of the system? (b) If the particle begins with a position x(0) = x0 and with velocity v(0) = v0 at t = 0 what are the values of the constants appearing...
  20. Hercuflea

    Sailboat Speed Question: Can a Motor Increase Speed Beyond 10 Knots with Sails?

    This is not a homework question, I'm just curious. Suppose you had a sailboat sailing on calm water. Let's say the sailboat is capable of sailing at 10 knots under the current wind conditions using only its sails. Now say the sailboat had a small propeller motor that was capable of propelling...
  21. A

    Finding the force of constraint--compound pendulum on spring

    Homework Statement From Fetter and Walecka 5.1:[/B] Consider the compound pendulum in FIg 28.1 (mass M, moments of inertia Iij relative to the center of mass, which is a distance L from the point of support Q) but with Q attached to the bottom of a vertical spring (force constant k) and...
  22. B

    Height of the rise of the object attached to the spring ?

    Homework Statement Question :- A block of mass ##5 kg## is attached to a spring. The spring is stretched by ##10 cm## under the load of the block. A impulse is provided to the block such that it moves up with a velocity of ##2 m/s##. Find the height it will rise. Homework Equations ##F_s =...
  23. S

    Calculate the Orbital Radius of a Planet

    Homework Statement Planet X of mass mx = 2.1 × 1024 kg orbits S in uniform circular motion at a distance rx and with a period Px = 2.1 years (=66225600 s). The mass of the star S is MS = 2 × 1031 kg and its radius is RS = 3.2 × 108m. Homework Equations T=2pi * sqrt(r3/(GM) The Attempt at a...
  24. B

    Pulley system on rough surface.

    Homework Statement [/B] Question :- Find the acceleration of block of mass ##M##. The coefficient of friction between blocks is ##\mu_1## and between block and ground is ##\mu_2##. free body diagram at the end. Variables :- ##f_1## - friction between blocks. ##f_2## - friction between block...
  25. Arij

    How Does Frequency Depend on Gravity in Classical Mechanics?

    Homework Statement how from this question using Energy principles I can find how frequency depends on g? Homework EquationsThe Attempt at a Solution I know that frequency is sqrt(k/m) this is a formula you use in introductory physics. but I am lost on how to do it from energy route or...
  26. B

    Maximum uniform speed on a arc of a circular path ?

    Question :- A car has to move on a path, that is a arc of a circle of radius (##R##). The length of the path is (##L##). Suppose it starts on the highest point of the path, find the highest uniform speed for which, it does not lose contact with the path on any point ? My attempt :- I made a...
  27. dexterdev

    A Can a molecular dynamics simulation enter a limit cycle?

    In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because you have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields. In principle this system can...
  28. P

    I Numerical Calculus of Variations

    I attempt to solve the brachistochrone problem numerically. I am using a direct method which considers the curve ##y(x)## as a Lagrange polynomial evaluated at fixed nodes ##x_i##, and the time functional as a multivariate function of the ##y_i##. The classical statement of the problem requires...
  29. 1

    Center of mass of a sphere with cavity removed

    Homework Statement A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of...
  30. 1

    How do I find the equation of motion for this object?

    Homework Statement Find the equation of motion of the object by setting the derivative of the total energy equal to zero. Homework Equations r(theta)=(Rcos(theta), Rsin(theta), q*theta) v(theta)=dr/dt=(-Rsin(theta)dtheta/dt, Rcos(theta)dtheta/dt, q*dtheta/dt) derivative of Total Energy =...
  31. J

    Lagrangian of a double pendulum system (with a spring)

    Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...
  32. R

    Find x(t) with Kx Force and Mass m | KxForce

    Homework Statement A particle of mass m is subject to force F(x)=kx with K>0. The initial starting position is x0 and the initial speed is zero. Find x(t). Homework Equations F(x)=kx F=ma The Attempt at a Solution Honestly, I am totally lost on this. I've written acceleration as v(dv/dx)...
  33. Faisal Moshiur

    Classical Mechanics Book Recommendation

    How can I start Classical Mechanics, I mean by the help of which book...
  34. weezy

    Proof of independence of position and velocity

    A particle's position is given by $$r_i=r_i(q_1,q_2,...,q_n,t)$$ So velocity: $$v_i=\frac{dr_i}{dt} = \sum_k \frac{\partial r_i}{\partial q_k}\dot q_k + \frac{\partial r_i}{\partial t} $$ In my book it's given $$\frac{\partial v_i}{\partial \dot q_k} = \frac{\partial r_i}{\partial q_k}$$...
  35. A

    Calculus of Variations: Functional is product of 2 integrals

    Homework Statement Minimize the functional: ∫01 dx y'2⋅ ∫01 dx(y(x)+1) with y(0)=0, y(1)=aHomework Equations (1) δI=∫ dx [∂f/∂y δy +∂f/∂y' δy'] (2) δy'=d/dx(δy) (3) ∫ dx ∂f/∂y' δy' = δy ∂f/∂y' |01 - ∫ dx d/dx(∂f/∂y') δy where the first term goes to zero since there is no variation at the...
  36. D

    Particle motion when wrapped around drum; elastic string

    Homework Statement A uniform cylindrical drum of mass M and radius a is free to rotate about its axis, which i is horizontal. An elastic cable of negligible mass and length l is wrapped around the drum and carries on its free end a mass m. The cable has elastic potential energy \tfrac12...
  37. Cocoleia

    Time for a block to come to a stop on a horizontal surface

    Homework Statement I have a block of mass m on a horizontal surface, which is covered in oil. The tell me the viscous resistance force is a function of the velocity, F(v)=-cv1/2, where I am assuming c is a constant of some kind. I need to find the time that it will take for the block to stop...
  38. weezy

    Verifying the Correctness of My Proof

    1. I have to show: 2. Given: 3. My attempt : I just want to verify if what I've done is correct or not. Thanks!
  39. S

    Rocket Launch: Achieving Escape Velocity w/ Fuel-Mass Ratio of 300

    Homework Statement Rockets are propelled by the momentum of the exhaust gases expelled from the tail. Since these gases arise from the reaction of the fuels carried in the rocket, the mass of the rocket is not constant, but decreases as the fuel is expended. Show that for a Rocket starting...
  40. INAM KHAN

    I Classical Mechanics v Quantum Mechanics

    I was thinking that what is solid reason behind the failure of Classical Mechanics in Black body radiation? Why classical mechanics not explain the curve at lower or higher range of frequncies.
  41. Cocoleia

    Block attached to a cord on an inclined plane

    Homework Statement I have a block of mass M attached to a cord of mass m on an inclined plane of angle θ . A force F is pulling the cord & block up the plane. I have to find the force exerted on the block by the cord. The surface is frictionless Homework Equations F = ma The Attempt at a...
  42. Cocoleia

    Block projected up inlcline with initial speed

    Homework Statement I have a block on an inclined plane (the angle is 40). The block is projected with an initial speed of 2m/s and μ=0.05. I need to find the time it takes the block to go up the inclined plane and return to the point it started out. Homework EquationsThe Attempt at a Solution...
  43. Gopal Mailpalli

    Classical Good book for Lagrangian and Hamiltonian Mechanics

    This book should introduce me to Lagrangian and Hamiltonian Mechanics and slowly teach me how to do problems. I know about Goldstein's Classical Mechanics, but don't know how do I approach the book.
  44. certainice

    Energy principle example problem in classical mechanics book

    Homework Statement A man of mass 100 kg can pull on a rope with a maximum force equal to two fifths of his own weight. [Take g = 10 ms^2] In a competition, he must pull a block of mass 1600 kg across a smooth horizontal floor, the block being initially at rest. He is able to apply his maximum...
  45. P

    How Do Polar Coordinates Explain a Bead's Velocity on a Rotating Wheel?

    Note: All bold and underlined variables in this post are base vectors I was reading the book 'Introduction To Mechanics' by Kleppner and Kolenkow and came across an example I don't quite understand. The example is this: a bead is moving along the spoke of a wheel at constant speed u m/s. The...
  46. F

    Hamiltonian as the generator of time translations

    In literature I have read it is said that the Hamiltonian ##H## is the generator of time translations. Why is this the case? Where does this statement derive from? Does it follow from the observation that, for a given function ##F(q,p)##, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial...
  47. VitorPAguiar

    What are the aspects that can help a car to flip in a turn?

    I am not sure if this is the right place to ask it, but this is a question that I thought today, and it gave me some curiosity to understand. Imagine that a car will curve, we can say the turn is a bit tight , what are the factors that can help it to flip? I was wondering about some aspects...
  48. steele1

    Prove area of triangle is given by cross products of the vertex vectors....

    Homework Statement The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|. Homework EquationsThe Attempt at a Solution I know that the magnitude of the cross product of any two vectors...
  49. L

    Oscillations: mass in the center of an octahedron -- eigenvalues?

    You have an infinitesimally small mass in the center of octahedron. Mass is connected with 6 different springs (k_1, k_2, ... k_6) to corners of octahedron. Equilibrium position is in the center, you don't take into account gravity, only springs. Find normal modes and frequencies. Relevant...
  50. S

    A Planar orbit of planets around sun

    Imagine thee planets interacting through gravity, mathematically how should they come and rotate in a same plane, like planets and sun?
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