Newton's laws of motion

Hecny Perez Candelario 

      Newton's laws of motion are three physical laws that form the basis for classical mechanics, directly relating the forces acting on a body to the motion of the body. They were first compiled by Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, . Newton used them to explain and investigate the motion of many physical objects and systems.

      Here is a brief introduction of the three laws of 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 its state of rest or of uniform motion unless acted upon by an external unbalanced force." Newton's first law is often referred to as the law of inertia. 

Second law

      Observed from an inertial reference frame, the net force on a particle of constant mass is proportional to the time rate of change of its linear momentum: F = d(mv)/dt. When the 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. 

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."

      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. 

 

 

The complete explanation of the three laws of motion:

Newton's first law: law of inertia

      Newton's first law is also called the law of inertia. In a simplified form, it states that if the vector sum of all forces (also known as the net force) acting on an object is zero, then the state of motion of the object does not change. In particular: Newton's first law: An object at rest remains at rest and an object in motion will remain in motion unless acted on by an unbalanced force.

•An object that is not moving will not move until a net force acts upon it. 

•An object that is moving will not change its velocity (accelerate) until a net force acts upon it.

      The first point needs no comment, but the second seems to violate everyday experience. A hockey puck sliding along a table doesn't move forever; rather, it slows and eventually comes to a stop. According to Newton's laws, though, the hockey puck does not stop of its own accord, but because of a force applied in the opposite direction to the direction of motion. That force is easily identified as a frictional force between the table and the puck. In the absence of such a force, as approximated by an air hockey table or ice rink, the puck's motion would not slow.

      There are no perfect demonstrations of the law, as friction usually causes a force to act on a moving body, and even in outer space gravitational forces act and cannot be shielded against, but the law serves to emphasize the elementary causes of changes in an object's state of motion.

      The above treatment of Newton's first law is an over-simplification, though. A more sophisticated approach to the law of inertia is given by:

      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.

      Newton placed the law of inertia first to establish frames of reference for which the other laws are applicable. Such frames are called inertial frames. 

Newton's second law

       The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. — 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. 

Using modern symbolic notation, Newton's second law can be written as a vector differential equation: 

 

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 the momentum of the object (which Newton himself called "quantity of motion"). Therefore, this equation expresses the physical relationship between force and momentum for systems of constant relativistic mass. The equation implies that, under zero net force, the momentum of a system is constant; however, any mass that enters or leaves the system will cause a change in system momentum that is not the result of an external force. This equation does not hold in such cases.

Newton's third law: law of reciprocal actions

       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 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).

      Newton used the third law to derive the law of conservation of momentum;[19] 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. 

      Bibliografy

      http://en.wikipedia.org/

      http://www.newton.ac.uk/newtlife.html

      http://en.wikipedia.org/wiki/Isaac_Newton