Force
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Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:
- In the absence of force, a body either is at rest or moves in a straight line with constant speed.
- A body experiencing a force F experiences an acceleration a related to F by F = ma, where m is the mass of the body. Alternatively, force is proportional to the time derivative of momentum.
- Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction.
These laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687. Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
First law
There exists a set of inertial reference frames relative to which all particles with no net force acting on them will move without change in their velocity. This law is often simplified as "A body persists in a state of rest or of uniform motion unless acted upon by an external force." Newton's first law is often referred to as the law of inertia.
- An object that is not moving will not move until a force acts upon it.
- An object that is moving will not change its velocity until a net force acts upon it.
Newton placed the law of inertia first to establish frames of reference for which the other laws are applicable. To understand why the laws are restricted to inertial frames, consider a ball at rest inside an airplane on a runway. From the perspective of an observer within the airplane (that is, from the airplane's frame of reference) the ball will appear to move backward as the plane accelerates forward. This motion appears to contradict Newton's second law (F = ma), since, from the point of view of the passengers, there appears to be no force acting on the ball that would cause it to move. However, Newton's first law does not apply: the stationary ball does not remain stationary in the absence of external force. Thus the reference frame of the airplane is not inertial, and Newton's second law does not hold in the form F = ma.
Second law
Observed from an inertial reference frame, the net force on a particle is equal to the time rate of change of its linear momentum: F = d(mv)/dt. When mass is constant, this law is often stated as, "Force equals mass times acceleration (F = ma): the net force on an object is equal to the mass of the object multiplied by its acceleration."
Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:
LAW II: If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.
Third law
Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. The strong form of the law further postulates that these two forces act along the same line. This law is often simplified into the sentence, "To every action there is an equal and opposite reaction."
LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. — Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.
In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation: one can consider the laws to be a definition of these quantities.
Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law only holds when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second.[3] The explicit concept of an inertial frame of reference was not developed until long after Newton's death.
At speeds approaching the speed of light the effects of special relativity must be taken into account.
