What is Newton mechanics: Definition and 55 Discussions

In classical mechanics, Newton's laws of motion are three laws that describe the relationship between the motion of an object and the forces acting on it. The first law states that an object either remains at rest or continues to move at a constant velocity, unless it is acted upon by an external force. The second law states that the rate of change of momentum of an object is directly proportional to the force applied, or, for an object with constant mass, that the net force on an object is equal to the mass of that object multiplied by the acceleration. The third law states that when one object exerts a force on a second object, that second object exerts a force that is equal in magnitude and opposite in direction on the first object.
The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems, which laid the foundation for Newtonian mechanics.

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  1. TheGreatDeadOne

    Conservation of momentum (center of mass) in projectile launches

    I've already solved this problem using another resource (just get the coordinate of the range of the center of mass and from there, get it for the larger mass ##R_{2}=(3v_{0}^{2})/(4g))##: Range CM: $$R_{(CM)} = \frac{v_{0}^2 sin{2\theta}}{2g}=\frac{v_{0}^{2}}{2}$$ then: $$ R_{(CM)}=...
  2. cianfa72

    A Hamiltonian formulation of classical mechanics as symplectic manifold

    Hi, in the Hamiltonian formulation of classical mechanics, the phase space is a symplectic manifold. Namely there is a closed non-degenerate 2-form ##\omega## that assign a symplectic structure to the ##2m## even dimensional manifold (the phase space). As explained here Darboux's theorem since...
  3. cianfa72

    I Invariant definition of acceleration in Newtonian physics vs proper acceleration in GR

    Does it exist an invariant way to define acceleration in Newton physics like the proper acceleration in GR ? In Newton physics if an accelerometer attached to an object reads 0 it does not mean it is actually not accelerating (since gravity is a force). To define inertial motion the concept of...
  4. cianfa72

    I Newton Galilean spacetime as fiber bundle

    Hi, Penrose in his book "The Road to Reality" claims that Newton/Galilean spacetime has actually a structure of fiber bundle. The base is one-dimensional Euclidean space (time) and each fiber is a copy of ##\mathbb E^3##. The projection on the base space is the "universal time mapping" that...
  5. SacCno

    B Help Scaling Gravity Simulation

    I'm trying to make a 2D game on Unity similar to Universe Sandbox 2. I currently am working with a star and planet, both with roughly the masses of the sun and earth respectively for comparison and at a distance of 31,000,000km. My current model uses Newton's formula for gravitational force (F...
  6. Venturi365

    Relationship between horizontal force and friction in an exercise

    The thing with this exercise is that I don't think that the question makes sense at all (or, at least, is incomplete). First of all, we don't know if the mass moves with any of those tensions, therefore I cannot know which coefficient apply. Second of all, even if we suppose that the mass is...
  7. Venturi365

    Find the unkown tensions and masses in the situation below

    TL;DR Summary: I don't know if my procedure is correct in this excercise I've tried to solve this problem but I find my solution unintuitive and I think I might be wrong. First of all, applying Newton's Laws I calculated the value for ##T_1## like this: $$ \begin{align} \sum F_{x} &=0\\...
  8. cianfa72

    I About the use of nominal definitions in physics

    Hi, I was reading the interesting lecture of Feynman about Characteristics of Force -- https://www.feynmanlectures.caltech.edu/I_12.html He basically says that nominal definitions like mathematical definitions of "abstract" objects have actually no physical meaning. For instance take the...
  9. cianfa72

    I Spring balance analysis from a system point of view

    Hi, I was thinking about a simple scenario in the framework of Newton (classic) mechanics. Take a spring scale/balance fixed at one end (wall) with a body attached to the other end's hook. From an analysis point of view we can consider as "system" the spring scale + the wall + the body. Then...
  10. J

    I How do we calculate the energy we used to do something?

    Usually, I like to take a physical approach to phenomena that occur in everyday life. But I feel difficult to solve problems because I don't have higher education My question stems from this question (What's the difference between running up a hill and running up an inclined treadmill?), which...
  11. T

    System of two pulleys and three masses

    I used m1=m2=15,0kg System: FBD: Note: I believe I have solved a) correctly and am more confused about b). a) I started with drawing the FBD. Knowing that the net sum has to be zero for the system to be at rest I used the left mass to find the tension on the rope: S1 = G1 = 15kg*9,81m/s2 =...
  12. sachin

    Choosing what consists of a "system" in Newton's laws of motion

    The question is solved in a single step by taking the blocks as a system and using conservation of linear momentum in the horizontal direction as there is no net force acting in the horizontal direction. Conserving the momentum we get, m x v + M x 0 = (m+M)v', so,,v' = mv/(m +M).where v' is the...
  13. M

    B Conservation of Momentum for system of particles

    We know that if we take two particles and assume no external force is applied then by Newtons third law total momentum gets conserved after collision. If we take three particles and there is collision between them and no external force then the momentum is again conserved for each pair like in...
  14. L

    I Proving Galilean Transformation for Inertial Frames

    I know we can prove that a Galilean transformation sends one inertial frame to another inertial frame, by proving ##\frac{d^2 f(\vec{r})}{d(f(t))^2} = \frac{d^2 \vec{r}}{dt^2}##, but can we prove the reverse? Can we prove that if the acceleration seen in two frames are the same, then the...
  15. cianfa72

    I Principle of relativity for proper accelerating frame of reference

    Hi, I've a doubt about the application of the principle of relativity as follows. Assume as principle of relativity the following statement: It is impossible by any experiment performed inside a "closed" laboratory to say whether we are moving at constant velocity or staying at rest. Consider...
  16. MaratZakirov

    Rail Car with a Sail in the Wind

    I solve the following problem, there is a particle of mass ## m_p ## and velocity ## \vec{v}_p ## which collide with sail installed on rail car with mass ## m_c ## resting in the frame of reference associated with it before the collision. The cart is fixed on straight rails for which the vector...
  17. Nexus99

    Understanding Work Calculation in an Engine: External vs. Internal Forces

    I'm really struggling with this problem. I can't understand which are the forces that i need to calculate work. Probabily when the sand falls the force of which i need to calculate work is weight force, but which is the force that carries the sand at the top of the roller?
  18. Hajarmq

    I Total energy of an isolated system

    If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system? I think I have a small misunderstanding of the...
  19. Hajarmq

    I Conservative force pairs

    Let F_ki be the force applied by a point mass i on a point mass k. This force depends on the variables x_k and x_i which are the position vectors of respectively k and i (to simplify let´'s consider this in 1 dimension). Suppose this force is conservative. Then, according to my course and...
  20. archaic

    Acceleration after applying a force

    Hello, 1) Suppose I throw a ball with a force ##F=ma##, the instant it leaves my hand, does it have the same acceleration ##a## added to it accelerations due to "ambient" forces (air resistance, gravity..)? 2) If I am right about 1), doesn't my hand already carry the acceleration/deceleration...
  21. M

    Can 3 forces of 9N, 4N, and 6N be in equilibrium?

    Homework Statement A mass of 3kg is acted upon by three forces of 4.0 N, 6.0N, and 9.0N and is in equilibrium. The 9N force is suddenly removed. Determine the acceleration of the mass. Homework Equations F=ma. The Attempt at a Solution My main problem with this question is that I cannot think...
  22. BookWei

    Velocity is a vector in Newtonian mechanics

    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##...
  23. G

    Pure rolling of sphere having non uniform mass density ?

    in case of rolling without slipping of a solid sphere having uniform mass density the condition is Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...
  24. Amitayas Banerjee

    Kinetic energy as seen from a different frame

    Homework Statement A mass m is initially at rest. A constant force $F$ (directed to the right) acts on it over a distance d. The increase in kinetic energy is therefore $Fd$. Consider the situation from the point of view of someone moving to the left at speed $V$ . Show explicitly that this...
  25. H

    Find the forces on a table that is lifted in a tilted position

    Homework Statement Homework EquationsThe Attempt at a Solution what's the Fa and Fb? my logic is Fa = Wa - N = mg - ##\frac{N}{\cos \theta}## so is Fb... so the ratio is 1. But I know it's wrong. What will make the difference between Fa and Fb? can anyone give a clue please?
  26. S

    Height of edge of billiard table

    Homework Statement Consider a billiard table with balls of radius r. How high should be the edge of the table to not allow undesirable pressures (and thus slips of the ball)? I.e. if there was no gravity, the billiard ball would still bounce off parallelly to the table plane. However I do not...
  27. SciencyBoi

    Three Pulley - two masses system.

    Homework Statement The given system is released from rest. Assuming no friction, mass-less pulleys and ideal strings; calculate the accelerations of the pulleys. Homework Equations Constraint equations. F=ma The Attempt at a Solution Taking the above assumptions; And applying constraints...
  28. Lafith

    Where is the force coming from to compress the spring

    Homework Statement Given a plank is moved with uniform velocity v. To which a mass is connected by a spring of force constant k. What is work done by the external agent on the maximum compression of the spring Homework Equations Work done by spring=0.5*k*x2 Work-energy theorem: total work...
  29. E

    I Why can I assume the force to be constant in this interval?

    If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I assumed the spring force, which is a function of its elongation x (F =...
  30. E

    The total tension acting on a rotating rod

    Homework Statement Find the total tension acting on a rod rotating about its end with an angular velocity of w as a function of its length x(length) Homework Equations F = ma[/B] The Attempt at a Solution Let the function be T(x) where x is the length of the rod. Considering an interval...
  31. M

    Change in gravitational potential below the surface of the Earth

    Homework Statement Hi, Infinitely far away from a mass-->gravitational potential is zero. As get closer-->becomes negative. At surface-->it is the smallest value of r, i.e. the radius of the mass, hence the most negative value for gravitational potential. But as you go below surface of Earth...
  32. Al_Pa_Cone

    Mechanical Principles -- Assignment question

    Can anyone help me? I have a question with 3 part answers on my Mechanical Principles assignment. I believe I have answered question part 'a' and 'b' but I have been stuck on question part 'c' for days! So the question is: Q5. The simply supported beam shown in FIG 4 is 5meters long with a...
  33. 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...
  34. StarWarsNerd

    B Calculating Linear and Angular Quantities from Applied Force

    In the image above, a centroid with radius 1 is depicted. F1 is pointing directly at point A (which is the center of the circle), and F2 is pointing directly at point B. The radius for finding the torque would be the perpendicular between the center of the object and the force vector, so r1...
  35. 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...
  36. 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...
  37. 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...
  38. donaldparida

    B Force required to move an object upwards

    Standing within a field, should the force required to move an object in the opposite direction of the field without acceleration be equal to the force exerted by the field on it or a little more than that?
  39. S

    Velocity of Bead Relative to Wedge on a Smooth Hemispherical Surface

    Homework Statement A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge. Homework Equations $$MV=m(v\cos(\theta)-V)$$ and...
  40. ThinkerCorny

    Understanding gravitational potential due to spherical shell

    I know that gravitational potential due to uniform sherical shell at a point outside the shell is equivalent to the potential due to particle of same mass situated at the centre and got proof here http://m.sparknotes.com/physics/gravitation/potential/section3.rhtml. But I was looking for more...
  41. U

    Tension on a string attached to two objects

    Homework Statement A person would like to pull a car out of a ditch. This person ties one end of a chain to the car's bumper and wraps the other end around a tree so that the chain is taut. The person then pulls on the chain perpendicular to its length. If the distance between the car and tree...
  42. E

    How do I use a free body diagram in this case?

    In the above cases I want to find the acceleration a for m1. I can do it by considering m1 and m2 to be a system, which would give me a = F/(m1+m2). How can I use a free-body diagram instead to calculate the acceleration? Using a free-body diagram, m2 only affects the vertical motion by exerting...
  43. F

    Acceleration due to fictitious force independent of mass?

    I have been asked by someone if it is true that in general, for a constantly accelerating reference frame, i.e. a non-inertial reference frame, the acceleration of a particle (as observed in this frame) due to the corresponding fictitious force is independent of its mass. My response was yes...
  44. J

    Two blocks collide with spring in-between.

    Homework Statement Block 1 (mass 2 kg) is moving rightward at 10 m/s and block 2 (mass 5kg kg) is moving rightward at 3 m/s. The surface is frictionless, and a spring with spring constant of 1120 N/m is fixed on the left side on block 2. When the blocks collide, the compression of the spring is...
  45. faiziqb12

    An atomic explanation of Newton's Third Law of Motion

    let's look at force at the atomic level to understand the Newtons third law of motion. I'll use Helium atoms as an example. Now imagine we start with one atom HE2 stationary, and throw another atom HE1 at it.It is the velocity of HE1 that affects the motion of HE2 , because the system of these...
  46. V

    Non-Zero Potential Energy in SHM: Is Spring Stretched in Mean Position?

    in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched. eg mass attached to a vertical spring.