Newton's laws of motion

Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:

The three laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687.[3] Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. In the time since Newton, the conceptual content of classical physics has been reformulated in alternative ways, involving different mathematical approaches that have yielded insights which were obscured in the original, Newtonian formulation. Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics).

Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each. For instance, the Earth and the Sun can both be approximated as pointlike when considering the orbit of the former around the latter, but the Earth is not pointlike when considering activities on its surface.[note 1]

The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates. The simplest case is one-dimensional, that is, when a body is constrained to move only along a straight line. Its position can then be given by a single number, indicating where it is relative to some chosen reference point. For example, a body might be free to slide along a track that runs left to right, and so its location can be specified by its distance from a convenient zero point, or origin, with negative numbers indicating positions to the left and positive numbers indicating positions to the right. If the body's location as a function of time is , then its average velocity over the time interval from to is[6]

Newton's laws of motion, combined with his law of gravity, allow the prediction of how planets, moons, and other objects orbit through the Solar System, and they are a vital part of planning space travel. During the 1968 Apollo 8 mission, astronaut Bill Anders took this photo, Earthrise; on their way back to Earth, Anders remarked, "I think Isaac Newton is doing most of the driving right now."[1]
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Artificial satellites move along curved orbits, rather than in straight lines, because of the Earth's gravity.
A free body diagram for a block on an inclined plane, illustrating the normal force perpendicular to the plane (N), the downward force of gravity (mg), and a force f along the direction of the plane that could be applied, for example, by a string.
Rockets work by producing a strong reaction force downwards using rocket engines. This pushes the rocket upwards, without regard to the ground or the atmosphere.
A bouncing ball photographed at 25 frames per second using a stroboscopic flash. In between bounces, the ball's height as a function of time is close to being a parabola, deviating from a parabolic arc because of air resistance, spin, and deformation into a non-spherical shape upon impact.
Two objects in uniform circular motion, orbiting around the barycenter (center of mass of both objects)
Simple harmonic motion
Rockets, like the Space Shuttle Atlantis, propel matter in one direction to push the craft in the other. This means that the mass being pushed, the rocket and its remaining onboard fuel supply, is constantly changing.
The total center of mass of the forks, cork, and toothpick is on top of the pen's tip
Animation of three points or bodies attracting to each other
Three double pendulums, initialized with almost exactly the same initial conditions, diverge over time.
Emmy Noether (1882–1935), who proved a celebrated theorem that relates symmetries and conservation laws, a key development in modern physics that is conveniently stated in the language of Lagrangian or Hamiltonian mechanics.
A simulation of a larger, but still microscopic, particle (in yellow) surrounded by a gas of smaller particles, illustrating Brownian motion.
The Lorentz force law in effect: electrons are bent into a circular trajectory by a magnetic field.
Page 157 from Mechanism of the Heavens (1831), Mary Somerville's expanded version of the first two volumes of Laplace's Traité de mécanique céleste.[110] Here, Somerville deduces the inverse-square law of gravity from Kepler's laws of planetary motion.