Laws Of Motion

Newton's laws of motion are three physical laws which directly relate the forces acting on a body to the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiae Naturalis Principia Mathematica, first published on July 5, 1687. These laws form the basis for classical mechanics. Newton, himself, 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 from which an observer will observe that all particles with no net force acting on them will move without change in their velocity. This law is often simplified as "A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." Newton's first law is often known as the law of inertia.
Second law
Observed from an inertial reference frame, the net force on a particle is proportional to the time rate of change of its linear momentum: F = d(mv)/dt. Momentum mv is the product of mass and velocity. Force and momentum are vector quantities and the resultant force is found from all the forces present by vector addition. This law is often stated as, "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 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.