# Newtons law of motion

Newtons law of motion are the physical laws that form the basis of classical mechanics . This law explains the relationship between the force acting on an object and the motion of that object produced by it. These have been expressed in many ways over the three centuries. Newtons three law of motion, traditionally, are summarized as follows:

• First Law : Every body remains in its state of rest or in a state of uniform motion in a straight line until an external force compels it to move. It is also called rule.
• Second Law : The rate of change of momentum of any body is proportional to the applied force and its direction is the same as that of the force.
{\displaystyle F\propto {\frac {mv-mu}{t}}}
{\displaystyle F\propto {\frac {m(vu)}{t}}}
{\displaystyle F\propto ma}
{\displaystyle F=ma}
{\displaystyle F}= ~force ~, ~Newton ~(N) ~or ~({\displaystyle kg.m/s^{2}}{\displaystyle kg.m/s^{2}},
{\displaystyle m}= mass ~({\displaystyle kg})
{\displaystyle a}= ~acceleration~ ({\displaystyle ms^{-2}})
• Third Law : For every action there is always an equal and opposite reaction.

Newton first compiled them in his treatise Philosophy Naturalis Principia Mathematica (1687).  Newton used them in many places in the explanation of problems related to the motion of physical objects. In the third part of his book, Newton showed that these three laws of motion and their law of universal gravitation together are able to explain Kepler’s law related to the motion of celestial bodies .

## Overview

Newtons law of motion is applied only to those objects which we can consider as a particle.  Meaning that when measuring the speed of those objects, their size is ignored. These rules are applied by considering the body of those objects as centered in one point. This is done when the distances are very large compared to the objects in the analysis. Therefore, considering the planets as a particle, their orbital speed can be measured.

In their original form, these laws of motion cannot be applied to rigid and deformable bodies. In 1750, Leonard Euler extended Newton’s laws of motion and created Euler’s laws of motion that could also be applied to rigid and deformable bodies. If an object is considered to be a combination of discrete particles, in which Newtons law of motion can be applied separately, then Euler’s law of motion can be derived from Newtons law of motion.

Newton’s laws of motion also apply in some reference systems , which are called inertial reference systems . Many authors believe that the first law defines the inertial reference system and the second law is valid only in those reference systems, for this reason the first law cannot be called a special form of the second law. But some consider the first law to be a consequence of the second.   A clear concept of instructional systems developed long after Newton’s death.

Newtonian mechanics has now been replaced by Einstein’s theory of special relativity, but it is still used for objects moving less than the speed of light.

## First rule

In Newton’s original words
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

“Every object remains in its stationary state or state of uniform velocity unless it is induced to change state by an external factor (force).”

In other words, an object that is at rest will remain at rest and an object that is in motion will remain in motion unless an external force is applied to it.

Newton’s first law defines inertia as a natural property of matter that opposes a change in motion. Therefore the first law is also called the law of inertia . This law indirectly defines the inertial reference system (directive system in which both the other laws are valid) and also the force. Due to this, this law was put first by Newton.

This rule does not apply in any arbitrary frame. This rule only applies in special types of frames, known as “inertial frames”. Therefore, the inertial frame is the frame in which Newton’s first law applies. Any frame moving with constant velocity with respect to an inertial frame is an inertial frame.

Simple validation of this law is difficult because most bodies feel the effects of friction and gravity .

In fact, Galileo described this observation before Newton . Newton expressed it in other words.

## Second rule

In Newton’s original words:
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

“The change in momentum of an object is directly proportional to the force exerted on that object and occurs in the same direction.”
The following points can be derived from Newton’s law:

{\displaystyle {\vec {F}}=\mathrm {d} {\vec {p}}/\mathrm {d} t},
Where~~{\displaystyle {\vec {F}}}~~Force,{\displaystyle {\vec {p}}}~~ momentum

and t are time . According to this equation, when there is no external force on a body, the momentum of the body remains constant.

When the mass of the body is constant , the equation can be written more simply as:

{\displaystyle {\vec {F}}=m{\vec {a}},}

Where m is the mass and a is acceleration . That is, the force exerted on a body is proportional to the acceleration of that object.

## Impulse

Impulse is related to the second law, lmpulse means change in momentum. In other words:

{\displaystyle \mathbf {I} =\Delta \mathbf {p} =m\Delta \mathbf {v} }

where I is the impulse. Impulse is very important in the analysis of collisions. Let the mass of a body be m. On applying a law force F on it for an interval of time t, the velocity changes to v. Then Newton-

F = ma = m.∆v/∆t

F∆t = m∆v. m∆v = p

F∆t = p

Therefore, the impulse given to a body is equal to the change of momentum produced in the body. Therefore, the unit of impulse is the same as that of momentum (Newton-second).

## Third rule

Third law means that corresponding to a force there is another force which is equal and opposite to it. Newton used this law to describe the law of conservation of momentum, but in reality conservation of momentum is a more fundamental principle. There are many examples in which momentum is conserved but the third law is not valid.

## Significance and extent of validity

Newton’s laws were verified by experiment and observation for more than 200 years, and they are excellent approximations on the scale and motion of everyday life. Newton’s laws of motion, along with his law of universal gravitation and the mathematical techniques of calculus, provide for the first time a unified quantitative explanation for a wide range of physical phenomena. For example, in the third volume of the Principia , Newton showed that his laws of motion, along with the law of universal gravitation, explain Kepler’s laws of planetary motion.

Newton’s laws apply to bodies that are idealized as a single point mass,  in the sense that the shape and size of the body are neglected to focus more readily on its motion. This can be done when the line of action of the resultant of all external forces acts through the center of mass of the body. In this way, a planet can also be idealized as a particle for the analysis of its orbital motion around a star.

In their basic form, Newton’s laws of motion are not sufficient to characterize the motion of rigid bodies and deformed bodies, in 1750 Leonhard Euler introduced a generalization of Newton’s laws of motion for rigid bodies, called Euler’s laws of motion, which were later applied to deformed bodies assumed to be continuums. If a body is represented as a combination of discrete particles, each governed by Newton’s laws of motion, then Euler’s laws can be derived from Newton’s laws. However, Euler’s laws can be taken as an axiom describing the laws of motion for extended bodies, independently of any particle structure. 

Newton’s laws are only with respect to a fixed set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; From this point of view, the second law is valid only if 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 regard the first law as a consequence of the second.   The explicit concept of an inertial reference frame was not developed until long after Newton’s death.

These three laws make for a good approximation to macroscopic objects in everyday situations. However, Newton’s laws (combined with universal gravitation and classical electrodynamics) are unsuitable for use in certain circumstances, particularly on very small scales, at very high speeds, or in very strong gravitational fields. Therefore, laws cannot be used to explain phenomena such as electrical conduction in semiconductors, optical properties of materials, errors in non-relativistically correct GPS systems and superconductivity. The explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory.

In special relativity, the second law basically holds as F  = D P / D T , where F and P are four vectors. Special relativity is reduced to Newtonian mechanics when the speed involved is much less than the speed of light.

Some also describe the fourth law which is considered but never stated by Newton, which states that forces add up like vectors, i.e. forces obey the principle of superposition.