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. mattlfang

    A bullet collides perfectly elastically with one end of a rod

    A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...
  2. P

    B Confused about force body diagram for 2 body collision

    I'm trying to understand Newton's third law in the context of collisions. Assume that one body has mass M kg and is traveling in the positive x direction with acceleration A m/s^2. Assume that the second body has mass m kg and is traveling in the negative x direction with acceleration a m/s^2...
  3. rudransh verma

    B How do mechanical (weighing) scales work?

    I want to understand how the weight machines work that we use in homes and shops. I have been working on force and motion chapter and I was curious how this weight machine actually push up and how it applies force to the feet of the person being weighed? What reading is this that we see in...
  4. 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...
  5. 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...
  6. rudransh verma

    What are the forces at play in an elevator cab?

    I mentioned answers above in the question.
  7. rudransh verma

    B A question from Resnik about g-force

    Suppose there is one force gravitational force ##\vec{f_g}##. We can relate this downward force and downward acceleration with Newton sec law. This law can be written as ##F_{net,y}=ma_y## which becomes $$-F_g=m(-g)$$ or $$F_g=mg$$ $$\vec{F_g}=-F_g \hat j=-mg \hat j=m\vec g$$. Is it right...
  8. rudransh verma

    Confusion with force components

    x component of ##F_3## ##F_{3x}= m a_x- F_{1x}-F_{2x}## = ##ma\cos 50-F_1\cos(-150)-F_2\cos90## y component of ##F_3## ##F_{3y}= m a_y-F_{1y}-F_{2y}## =##ma\sin50-F_1\sin(-150)-F_2\sin90## And so on… My question how we can represent it in diagram ##F_1\sin(-150)##. I suppose...
  9. 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...
  10. rudransh verma

    Understanding the Use of the Long Jump Formula R=9.21m and Its Derivation

    $$R=9.21 m$$ $$Difference = 9.21-8.95$$ $$D=0.26m$$ My question is when do we use the formula for R given above. Because we could have calculated the Rmax by ##R=(v0\cos(\theta))t## and then subtracted R from it to get the answer. Why the x and y component in the derivation of this (R)formula...
  11. rudransh verma

    A stone projectile hitting the target

    $$(y-y0)=ut-1/2gt^2$$ $$y= -1/2gt^2$$ $$t^2=-1/98$$ If I get t I will be able to solve for x=ut
  12. 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.
  13. rudransh verma

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

    I have attempted but I don’t get anywhere.
  14. 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?
  15. rudransh verma

    Car traffic producing shock wave

    I don’t get where exactly the lengths start and end in figure.
  16. 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...
  17. 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...
  18. 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...
  19. rudransh verma

    Trip from San Antonio to Houston

    How do you approach the problem as if you have never done it before?
  20. 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.
  21. 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...
  22. rudransh verma

    Pigeon Problem Solved: Calculating Car Velocities and Meeting Time

    The solution was done adding the two velocities of the car while finding the total time it took for the two cars to meet. I don’t really get the solution.
  23. rudransh verma

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

    I was reading Motion chapter 8 in Vol 1 and I came across a line in speed topic which seemed confusing. So I checked with others and we concluded that its a mistake. Are there printing mistakes in this book? I will be surprised. Its pearson.
  24. 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)
  25. brochesspro

    What is the speed of the bicycle?

  26. 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 ?
  27. R

    Calculate quality factor of a damped oscillation from a graph

    I'm trying to find the quality factor of a damped system. I know 3 points from the graph, ##(t,x): (\frac{\pi}{120},0.5), (\frac{\pi}{80},0), (\frac{\pi}{16},0)## From this I found that ##T = \frac{\pi}{20}## ##\omega_d = \frac{2\pi}{T} = 40 rad## Then, from the solution ##x(t) = A_0...
  28. K

    A Hamilton's principle and virtual work by constraint forces

    Found a question on another website, I have the exact same question. Please help me Goldstein says : I do not understand how (2.34) shows that the virtual work done by forces of constraint is zero. How does the fact that "the same Hamilton's principle holds for both holonomic and...
  29. K

    A Non holonomic constraints in classical mechanics textbook

    I want to learn about the non holonomic case in lagrangian and Hamiltonian mechanics. I've seen that many people say that Goldstein 3rd ed is wrong there. Where should I go to learn it. My mathematics level is at the level Goldstein uses. Please help
  30. 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...
  31. K

    I Virtual displacement is not consistent with constraints

    Goldstein 3rd ed says "First consider holonomic constraints. When we derive Lagrange's equation from either Hamilton's or D'Alembert's principle, the holonomic constraint appear in the last step when the variations in the ##q_i## were considered independent of each other. However, the virtual...
  32. 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...
  33. T

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

    (I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing) I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...
  34. T

    Conserving Momentum in Emptying a Freight Car

    $$\overrightarrow{p_i}=\overrightarrow{0},~\overrightarrow{p_f}=m_c\overrightarrow{v_f}$$ $$\overrightarrow{p_f}-\overrightarrow{p_i}=\int\limits_{t_i}^{t_f}\overrightarrow{F}dt$$ $$t_i=0,~t_f=\frac{m_s}{b}$$ $$m_c\overrightarrow{v_f}=\overrightarrow{F}\frac{m_s}{b}\Rightarrow...
  35. Rikudo

    Why is the tension in a falling chain not equal to ρgy?

    Firstly, There is something I want to clarify. When the system starts moving, parts of the chain that still lies on the table, which have mass ## \frac {(L- y_0)M} {L}##, will be pulled by the force that the hanging chain's weight exert,right? If yes, then : As far as I know, the formula ##F=...
  36. raisins

    I Phase space integral in noninteracting dipole system

    Hi all, Consider a system of ##N## noninteracting, identical electric point dipoles (dipole moment ##\vec{\mu}##) subjected to an external field ##\vec{E}=E\hat{z}##. The Lagrangian for this system is...
  37. T

    Understanding Acceleration and Center of Mass in Shock Absorption

    I don't attempt solving a problem until I fully understand it, conceptually. After the hit (when maximum velocity is reached) the person starts losing momentum, having a constant upwards acceleration. The forces acting on the person are gravity and the normal to the ground. $$N - mg = ma$$...
  38. V

    Books that teach classical mechanics through a discourse method

    Books that teaches classical mechanics through a discourse method ie asking interesting questions and answering them maybe a similar one to Understanding Basic Chemistry Through Problem Solving: The Learner's Approach Book by Jeanne Tan and Kim Seng Chan. Not exactly asking numerical questions...
  39. T

    Stopping a Bullet: Calculate umin and xf

    (a) ##u_{min}=\big(1+\frac{m_2}{m_1}\big)\sqrt{2\mu_k g d}## (b) ##x_f=\sqrt{\frac{2h}{g}\Big(\big(\frac{m_1}{m_1+m_2}u\big)^2-2\mu_k g d\Big)}## Can someone check please?
  40. T

    Two Pulleys, Two Strings and Two Blocks

    Someone pls solve this. I've done it but I'm not sure if it's correct. Thanks!
  41. p1ndol

    I Trouble simplifying the Lagrangian

    Hello, I have posted a similar thread on this question before, but I'd like to get some help to simplify the answers I've got so far in order to match the solutions provided. If anyone could help me, I would really appreciate it. Since (c) is quite similar to (b), I'll leave here what I've done...
  42. p1ndol

    I Trouble understanding coordinates for the Lagrangian

    Hello, I'm having some trouble understanding this solution provided in Landau's book on mechanics. I'd like to understand how they arrived at the infinitesimal displacement for the particles m1. I appreciate any kind of help regarding this problem, thank you!
  43. p1ndol

    I Understanding the Coordinates in the Lagrangian for a Pendulum

    So I've been studying classical mechanics and have come across a small doubt with the solution provided to the problem in question from Landau's book. My question is: why are the coordinates for the particle given as they are in the solution? I imagine it has something to do with the harmonic...
  44. Mr.Husky

    B How is the acceleration proportional to the removed force?

    Image above is the question. Below image depicts solution. if F1 is removed then the acceleration of that mass must be sum of accelerations of remaining forces. Right?? But answer says that acceleration of that mass is equal to acceleration of F1. I don't understand it. Can someone explain it??
  45. T

    Tension in rope wrapped around a rod

  46. 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...
  47. 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?
  48. 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 \...
  49. 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...
  50. 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 \...
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