What is Newtonian mechanics: Definition and 201 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. JD_PM

    Conservation of Energy and Angular Momentum in a Rotating Train-Disk System

    Homework Statement [/B] A train stands in the middle of a rotating disk with an initial angular velocity of $\omega_i$. The mass of the train is m and the moment of inertia of the train-disk is I. At one point the train departs on a straight track to a distance R from the disk's centre. (R...
  2. S

    What is the Velocity of a Rotating Weight?

    Homework Statement A weight is suspended from a spring 50 cm long and stretches it by 1 cm. Take the other end of the spring in your hand and rotate the weight in a horizontal plane so that the spring is stretched by 10 cm. What is the velocity of the weight? (The force with which the stretched...
  3. L

    Does Gravity Deflect Light according to Newtonian Mechanics?

    I have read in several popular physics texts that general relativity predicts that gravity deflects light, but that Newtonian mechanics, in contrast, predicts that the trajectory of light is not affected by gravity. However, I am very skeptical and confused about this result. We of course have...
  4. R

    Particle Newtonian Mechanics: Father Pulling 100 lb Sled

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  5. Navin

    Finding the Accelation Of A Body In Presence Of Frictions

    1. Homework Statement A 60 kg block is pushed horizontally with just enough force to start its motion Accross a floor and the same force acts on it afterwards.The coefficient of static and sliding frictions are 0.5 and 0.4 respectively. Find acceleration of the body. Options 6m/s^2 4.9m/s^2...
  6. navneet9431

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  7. A

    B What we mean in physics definition (quantity or property)?

    Many books sometimes for example define energy as quantity and sometimes as property. Also the definition of energy is the ability to do work or the meter of the ability to do work ? we define for example force as a quantity or as some quality and then we quantify this ?
  8. A

    B What the equal sign means in physics

    For example F=ma means that the definition of force is m*a or the quantity of left side equals to the quantity of right side or both ? or kinetic energy..we know K=1/2mu^2 but is this the definition of kinetic energy or just the formula to calculate it ?
  9. Abhishek11235

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  10. BookWei

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    I studied the vector analysis in Arfken and Weber's textbook : Mathematical Methods for Physicists 5th edition. In this book they give the definition of vectors in N dimensions as the following: The set of ##N## quantities ##V_{j}## is said to be the components of an N-dimensional vector ##V##...
  11. N

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  12. Fia Ismi Nur Alfiah

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  13. Eyris

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    The situation: The mass is pushed up an incline with an angle of 1 degree with an initial velocity of 1 m/s, and it comes back down to its original position. The questions to answer: What is the total distance the object travels on the frictionless inclined plane? How long will the object...
  14. J

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  15. V

    Classical mechanics: motion and acceleration

    Homework Statement Referring to the attached diagram, the object ABCD is kept in an isolated system where it is under no external influence of any kind. A· An instantaneous force F acts along the edge BC of the block ABCD, where M is its mass, with its center of mass located at O...
  16. R

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  17. R

    Newton's first law of motion and Inertial Systems

    I have just begun my journey in Classical Mechanics with the book "An Introduction to Mechanics" by Kleppner and Kolenkow. I find myself stuck at Newton's first law. The book presents Newton's first law as follows: "Newton's first law is an assertion that inertial frames exist." The book also...
  18. 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...
  19. SciencyBoi

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  20. Muthumanimaran

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  21. SciencyBoi

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    Homework Statement How do we determine a specific force mentioned in a question to be conservative or non-conservative? 2. Relevant data Conservative force is a force whose work done does not depend on the path that is taken while doing it. Examples include electrostatic force, gravitational...
  22. S

    Rotational Motion in Newtonian Mechanics

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  23. M

    Newtonian energy integral and suitable boundary conditions

    I have a (somewhat) strange energy equation which has the following form: KE = A + B W + C \exp(-D W), where A,B,D are known constant, C is an unknown constant to be determined and kinetic and potential energy are given by KE and W respectively with W\equiv W(r) i.e. is a function of...
  24. J

    I How to model Solar System formation accurately and realistically

    I've been working on a crude N-body simulator which allows N bodies of equal masses to interact gravitationally in 2 dimensions. My goal is to model the formation of Solar System. Each body is modeled as a circle with a radius as a function of its mass, in such a way that all bodies have the...
  25. zwierz

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    http://www.pitt.edu/~jdnorton/Goodies/Dome/ I think that most wonderful point in this story is that the person who writes such texts is Distinguished Professor of University of Pittsburgh. Nevertheless I believe that the question he stated up can confuse an undergraduate student and thus...
  26. S

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    Homework Statement The space shuttle is in a 300 km-high circular orbit. It needs to reach a 520 km - high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.5 E4 kg. Mass of the Earth = 5.98 E24 kg. Radius of Earth = 6.37 E6 m. How much energy is required...
  27. E

    I Rigorous Explanation of dW in Problem 121

    In the solution of this problem(121), dW = (kmgcosΦ + mgsinΦ) ds, where ds is the differential element along the curve. Now they have done kmg dscosΦ + mg ds(sinΦ) = kmgdx +mgdy. Makes sense intuitively, but I want to know how this is rigorous. What I'm thinking is, the curve is broken into N...
  28. Khunpol Jermsiri

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  29. Ayenyen

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  30. J

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    Homework Statement A rocket with initial mass of m0. The engine that can burn gas at a rate defined by m(t)=m0-αt, and expel gas at speed (relative to the rocket) of u(t)=u0-βt. Here, m0, α, u0, and β are all constants. Assume the lift-off from ground is immediate a) The rocket speed v(t)=...
  31. G

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  32. D

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    Homework Statement A cylindrical vessel of height ##H## and radius ##R## contains liquid of density ##\rho##. Determine the circumferential tension at a height ##h##; also determine its maximum and minimum values. This is the scan of the original question(solved), I couldn't understand what...
  33. D

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    Homework Statement A chain of length ##l\lt \dfrac{\pi r }{2}## is placed on a smooth hemispherical surface of radius R with one of its ends fixed at the top of the hemisphere. What will be the tangential acceleration of the chain when it starts sliding down. Homework EquationsThe Attempt at a...
  34. L

    Problem Newtonian mechanics French

    A prisoner in jail decides to escape by sliding to freedom down a rope provided by an accomplice. He attaches the top end of the rope to a hook outside his window; the bottom end of the rope hangs clear of the ground. The rope has a mass of 10 kg, and the prisoner has a mass of 70 kg. The...
  35. Daquicker

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  36. G

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    Homework Statement I need to find the period of small vertical oscillations about equilibrium position of a string whose motion can be described by the following equation: d2x/dt2 = (-g/h)*x Answer: 2π√(h/g) Homework Equations I know that the time period is given by the formula T = 2πω where...
  37. D

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    Homework Statement It is a Matching Type Problem(a single entry in a column can be matched with more than one in the other column):- A block is projected with an initial velocity ##v_{\text{Block}}## on a long conveyor belt moving with velocity ##v_{\text{Belt}}##(at that instant) having...
  38. 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 =...
  39. B

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    Homework Statement Question :- Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible. Homework Equations $$V(r) = {-G Mm \over r}$$ The Attempt at a Solution...
  40. 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...
  41. 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 =...
  42. brotherbobby

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    The following problem is from Sears and Zemansky's textbook. A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.500 kg clings to one end of the stick, and a mouse with mass 0.200 kg clings to the other end. The...
  43. D

    Understanding Forces in a Whirling Tube Filled with Liquid

    Homework Statement A tube of length '##L##' is filled completely with an incompressible liquid of mass '##M##' and closed at both of the ends. The tube is then rotated in a horizontal plane about one of it's ends with a uniform angular velocity '##\omega##'. Then which of the following...
  44. D

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    Homework Statement A particle of mass ##m## rotates about ##Z-##axis in a circle of radius ##a## with a uniform angular speed ##\omega##. It is viewed from a frame rotating about the ##Z-##axis with a uniform angular speed ##\omega_0##. Find the centrifugal force on the particle. Homework...
  45. D

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  46. D

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    Homework Statement Find the maximum compression in the spring, if the lower block is shifted to rightwards with acceleration of '##a##'. All the surfaces are smooth. Homework Equations $$\vec{F}=m\vec{a}$$ $$\vec{F}_{sp}=k\vec{x}$$ The Attempt at a Solution FBD of the upper block: From...
  47. A

    B General Relativity and Newtonian Mechanics

    Hello, I wanted to know how Einstein's General Relativity and its equations simplify to Newton's Universal Law. Einstein's equation is obviously a much more generalized version of Newton's law and gives much more accurate predictions that Newton's laws even if we don't think of Newton's gravity...
  48. D

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  49. D

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  50. D

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