NEWTON’S LAW

1. NEWTON’S LAW Muhammad arif 8-@ 12

2. NEWTON’S LAW OF MOTION Newton's laws of motion are three physical lawsthat form the basis for classical mechanics. They are: 1. In the absence of net external force, a body either is at rest or moves in a straight line with constant velocity. 2. Force is proportional to mass times acceleration (when proper units are chosen, F = ma). Alternatively, force is proportional to the time rate of change of momentum. 3. 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 size and opposite in direction.

3. These laws describe the relationship between the forces acting on a body to the motion of the body. They were first compiled by Sir Isaac Newton in his work PhilosophiæNaturalis Principia Mathematica, first published on July 5, 1687.[1] Newton used them to explain and investigate the motion of many physical objects and systems.[2] 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. Contents [hide] [hide] 1 The three laws 1.1 Newton's first law 1.1.1 History of the first law 1.2 Newton's second law 1.2.1 Impulse 1.2.2 Variable-mass systems 1.3 Newton's third law: law of reciprocal actions 2 Importance and range of validity 3 Relationship to the conservation laws 4 See also 5 Notes

4. Third Laws 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." 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. Notice that the second law only holds when the observation is made from an inertial reference frame, and since an inertial reference frame is defined by the first law, asking a proof of the first law from the second law is a logical fallacy. At speeds approaching the speed of light the effects of special relativity must be taken into account.

5. Newton’s First Law Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.[3] Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is, the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is constant. Consequently: 1.An object that is not moving will not move until a net force acts upon it. 2.An object that is moving will not change its velocity until a net force acts upon it. The first point needs no comment, but the second seems to violate everyday experience. For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop. According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion. This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and the puck were traveling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed. Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law holds true.

6. The first point needs no comment, but the second seems to violate everyday experience. For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop. According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion. This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and the puck were traveling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed. Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law holds true. There is a class of frames of reference (called inertial frames) relative to which the motion of a particle not subject to forces is a straight line.

7. 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.

8. where F is the force vector, m is the mass of the body, v is the velocity vector and t is time. The product of the mass and velocity is momentump (which Newton himself called "quantity of motion"). Therefore, this equation expresses the physical relationship between force and momentum. Consistent with the law of inertia, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude (see time derivative). The equation implies that, under zero net force, the momentum of a body is constant. This formulation of the second law is only valid for constant-mass systems,[8][9][10] since any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems. Because the mass m is constant, it can be moved outside the differential operator: Then, by substituting the definition of acceleration, this differential equation can be rewritten in the form: F=ma.

9. Newton’s Second Law Newton's Latin wording for the second law is: Lex II: Mutationemmotusproportionalemesse vi motriciimpressae, et fierisecundumlineamrectam qua visillaimprimitur. This was translated quite closely in Motte's 1729 translation as: LAW II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. According to modern ideas of how Newton was using his terminology,this is understood, in modern terms, as an equivalent of: The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading: 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. Using modern symbolic notation,Newton's second law can be written as a vectordifferential equation:

10. Newton’s Third Law Lex III: Actionicontrariamsemper et æqualemessereactionem: sivecorporumduorumactiones in se mutuosemperesseæquales et in partescontrariasdirigi.For a force there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions. Newton's third law. The skaters' forces on each other are equal in magnitude, but act in opposite directions. A more directtranslation is: 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.

11. In the above, as usual, motion is Newton's name for momentum, hence his careful distinction between motion and velocity. The Third Law means that all forces are interactions, and thus that there is no such thing as a unidirectional force. If body A exerts a force on body B, simultaneously, body B exerts a force of the same magnitude body A, both forces acting along the same line. As shown in the diagram opposite, the skaters' forces on each other are equal in magnitude, but act in opposite directions. Although the forces are equal, the accelerations are not: the less massive skater will have a greater acceleration due to Newton's second law. It is important to note that the action and reaction act on different objects and do not cancel each other out. The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road).

12. Newton used the third law to derive the law of conservation of momentum; however from a deeper perspective, conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean invariance), and holds in cases where Newton's third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics.