What is Classical mechanics: Definition and 1000 Discussions

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. rudransh verma

    When will the particles collide?

    I am stuck. Please ignore my handwriting. I am working on latex. All I am taking is x and y coordinates same of both particles. Yes they will meet at some time t.
  2. rudransh verma

    A particle motion problem in the x-y plane with constant acceleration

    I have attempted but I don’t get anywhere.
  3. rudransh verma

    What kind of motion is this? (bicycle velocity vectors)

    How the heck the bicycle reach from point A to point B with that velocity vector directions?
  4. rudransh verma

    Car traffic producing shock wave

    I don’t get where exactly the lengths start and end in figure.
  5. Einstenio

    I Classical Mechanics - Motion of a particle

    Show that a point with acceleration given by: a=c*((dr/dt)×r)/|r|3 where c is a constant, moves on the surface of a cone. This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that...
  6. rudransh verma

    B A Question about a Quote from the Feynman lectures

    “incidentally, to a good approximation we have another law, which says that the change in distance of a moving point is the velocity times the time interval, Deltas=vdeltat This statement is true only iF the Velocity is not changing during that time interval, and this condition is true only in...
  7. rudransh verma

    Classical What Are Some General Physics Books to Complement Resnick and Halliday?

    I am currently reading some introductory physics. I am following resnik and Halliday. Can anyone suggest me some good general books on physics which would go comfortably with my resnik book. I need to read some general material not something technical. If possible on classical mechanics and...
  8. rudransh verma

    Trip from San Antonio to Houston

    How do you approach the problem as if you have never done it before?
  9. rudransh verma

    A scooterist trying to overtake truck

    If 150s is the time in which overtaking has to occur then why are they using this eqn: xp=x0+xs.
  10. rudransh verma

    Comparing 1000m Race Velocities: Runner 1 vs Runner 2

    First I calculated the avg velocity with 1000m for both runners. It came 6.76m/s and 6.75m/s. It suggests that the velocities are same. This means yes that the L2 track is slightly longer than L1. Then why is it asking this question (…that runner 1 is faster)? Both are at equal speeds. I don’t...
  11. rudransh verma

    Pigeon Problem Solved: Calculating Car Velocities and Meeting Time

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  12. rudransh verma

    Intro Physics Exploring Potential Errors in Feynman Lectures on Physics: A Scientific Inquiry

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  13. K

    A When is Hamilton's principle valid?

    When is Hamilton's principle##\delta \int L d t=0## valid ? Is it only valid for monogenic and holonomic systems? What about monogenic and non holonomic systems? (I'm asking this because I got confused because I've found that Goldstein has got something wrong related to this in his 3rd edition)
  14. brochesspro

    What is the speed of the bicycle?

  15. K

    A Two equations of generalized forces

    Wikipedia article under generalized forces says Also we know that the generalized forces are defined as How can I derive the first equation from the second for a monogenic system ?
  16. R

    Calculate quality factor of a damped oscillation from a graph

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  17. K

    A Hamilton's principle and virtual work by constraint forces

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  18. K

    A Non holonomic constraints in classical mechanics textbook

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  19. T

    Exponential potential energy state diagram

    It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...
  20. K

    I Virtual displacement is not consistent with constraints

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  21. K

    I Independent coordinates are dependent

    (This is not about independence of ##q##, ##\dot q##) A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates. However the system will trace a path in the...
  22. T

    Circular motion of a mass on a string on an inclined plane

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  23. T

    Conserving Momentum in Emptying a Freight Car

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  24. Rikudo

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  25. raisins

    I Phase space integral in noninteracting dipole system

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  26. T

    Understanding Acceleration and Center of Mass in Shock Absorption

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  27. V

    Books that teach classical mechanics through a discourse method

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  28. T

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  29. T

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  30. p1ndol

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  31. p1ndol

    I Trouble understanding coordinates for the Lagrangian

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  32. p1ndol

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  33. Mr.Husky

    B How is the acceleration proportional to the removed force?

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  34. T

    Tension in rope wrapped around a rod

  35. warhammer

    Work & Energy (Question on Classical Mechanics/Slope based Problems)

    I used the Change in Kinetic Energy and equated that with the Work Done. The "Work Done" part comprises of two different functions- one is work done by Gravitational Force while the other is the work done by frictional force (or the brakes). /Delta KE (magnitude wise)= 0.5*1350* (20^2)=270,000...
  36. Istiak

    How to find the constant in this indefinite integration?

    $$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$ That's what I did. But, book says $$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$ Seems like, $$x_0 + \dfrac{a_0}{2}t^2$$ is constant. How to find constant is equal to what?
  37. Istiak

    Calculating Velocity when Stuntman Jumps from 1.25m Height

    > >A stuntman jumped from $1.25 \ \text{m}$ height and, landed at distance $10 \ \text{m}$. Find velocity when he jumped. (Take $\text{g}=10 \ ms^{-2}$) I had solved it following way. $$h=\frac{1}{2}gt^2$$ $$=>1.25=5\cdot t^2$$ $$=>t=\frac{1}{2}$$ And, $$s=vt$$ $$v=\frac{s}{t}$$ $$=\frac{10 \...
  38. Istiak

    Why used $\cos\theta$ for $\text{y}$ axis or, gravitational force?

    >![figure 3.2](https://physics.codidact.com/uploads/B5XdWq6GbB4vwyADQdALaCrC)![figure 3.1](https://physics.codidact.com/uploads/pkmWFgoesvQaiAfv5yKj6ynB)<br/> >Mass M1 is held on a plane with inclination angle θ, and mass M2 hangs over the side. The two masses are connected by a massless string...
  39. Istiak

    How much of the wooden timber was submerged in water?

    >Mass of a timber is $20 \ g$. And, density of that timber is $0.27 \ g/cc$. That timber was bind to a metallic materials and, it was released to $0.970 \ g/cc$ water. How much the wood was submerged in water? I was trying to solve the problem following way. $$F=Ah\rho g$$ $$=V\rho g$$ $$=V \...
  40. Rikudo

    I Total angular momentum of a translating and rotating pancake

    I have read Classical Mechanics book by David Morin, and there are some parts that I do not understand from its derivation. Note : ## V## and ##v## is respectively the velocity of CM and a particle of the body relative to the fixed origin , while ##v'## is velocity of the particle relative to...
  41. Rubberduck2005

    Tricky conceptual Projectile motion question

    So far all I have determined is the equations of motion for the two and that is as follows. It is trivial that y(t)=v1sin(Q)t -gt^2/2 and that x(t)=v2cos(Q)t. Now the angle that is anticlockwise from the negative horizontal of the robber is 90 - Q using basic trigonometry, using this we can...
  42. rudransh verma

    I Verse from "A Brief History of Time"

    1.One can now see why all bodies fall at same rate: A body of twice the weight will have twice the force of gravity pulling it down, but it will also have twice the mass. According to Newton’s second law these two effects will exactly cancel each other, so the acceleration will be same in all...
  43. L

    I Help with Goldstein Classical Mechanics Exercise 1.7

    I'm trying to solve the Goldstein classical mechanics exercises 1.7. The problem is to prove: $$\frac{\partial \dot T}{\partial \dot q} - 2\frac{\partial T}{\partial q} = Q$$ Below is my progress, and I got stuck at one of the step. Now since we have langrange equation: $$\frac{d}{dt}...
  44. A

    I Time derivative of the angular momentum as a cross product

    I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...
  45. E

    What is the tension of the rope?

    I have attached two different attempts to solve this problem. They both look correct to me but they give two different answers! Which one is correct, which one is wrong and why?
  46. sophiatev

    Symmetries in Lagrangian Mechanics

    In Classical Mechanics by Kibble and Berkshire, in chapter 12.4 which focuses on symmetries and conservation laws (starting on page 291 here), the authors introduce the concept of a generator function G, where the transformation generated by G is given by (equation 12.29 on page 292 in the text)...
  47. Feroyn

    Building a motorcycle, need classical mechanics help

    Hi! I am an engineering graduate that took my bachelor's degree in Mechanical Engineering much too long ago, but I have forgotten a lot of the classical mechanics/mechanics of materials theory that I had learned many years ago. I am building a motorcycle right now, and I want to calculate the...
  48. PiEpsilon

    Analyzing an Angular Impulse Problem

    What we know: The ball is dropped at the tip A with some speed ##v_0## and rebounds with speed ##v##. This collision produces an angular impulse, changing the angular momentum of the bar with the flywheels. Solution inspired by an answer provided by @TSny in the similar question. Angular...
  49. warhammer

    Question on Moment of Inertia Tensor of a Rotating Rigid Body

    Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...
  50. D

    Finding the period of an orbit ##r=a(1+\cos\theta)##

    I've already found the potential and force that produce the given orbit. my results were: ##V=-\frac{al^2}{mr^3}## ##\vec{F}=-\frac{-3al^2}{mr^4}\hat{r}## Now, I've been trying to find the period using the equation ##t=\sqrt{\frac{m}{2}}\int_{r_0}^{r}\frac{dr'}{\sqrt{E-V_{eff}}}## Using...
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