We explain what Newton's Laws are, how they explain inertia, dynamics and the action-reaction principle.

## What are Newton's laws?

Newton's Laws or Newton's Laws of Motion ** are the three fundamental principles on which classical mechanics is based** one of the branches of physics. They were postulated by Sir Isaac Newton in his work *Philosohiae naturalis principia mathematica *(“Mathematical principles of natural philosophy”) of 1687.

This set of physical laws revolutionized humanity's basic concepts regarding the movement of bodies. Together with the contributions of Galileo Galilei, it constitutes the basis of the dynamics. When combined with Albert Einstein's Law of Universal Gravitation, it allows deducing and explaining Kepler's Laws of planetary motion.

However, Newton's Laws ** are valid only within inertial reference systems** that is, those that are not accelerated and in which only real forces intervene. Furthermore, these laws are valid for objects moving at a speed much slower than the speed of light (300,000 km/s).

Newton's Laws are based on the consideration of movement as the displacement of an object from one place to another, taking into account the place where it occurs, which can also move at a constant speed in relation to another place.

## Newton's first law or Law of inertia

Newton's first Law contradicts a principle formulated in ancient times by the Greek wise man Aristotle, for whom a body could only maintain its motion if a sustained force was applied to it. Newton establishes instead that:

** “Every body perseveres in its state of rest or uniform rectilinear motion unless it is forced to change its state by forces imposed on it.”**.

Therefore, an object that is moving or that is at rest cannot alter this state, unless some type of force is applied to it.

According to this principle, **Movement involves magnitudes that are vectors (endowed with direction and sense)**. It is possible to calculate the acceleration from the initial and final speed. Furthermore, he proposes that bodies in motion always tend to move in a straight and uniform path.

A perfect example of the law of inertia is a shot putter in the Olympics. The athlete gains momentum by moving in circles, rotating the weight tied with a rope around its own axis (circular movement), until he reaches the necessary acceleration to release it and see it fly in a straight line (uniform rectilinear movement).

This rectilinear movement continues until gravity curves its path. At the same time, the friction of the object with the air decreases its speed (negative acceleration) until it falls.

## Second law or fundamental law of dynamics

In this law Newton defines the concept of force (represented with *F*), stating that:

**“The change in a movement is directly proportional to the force impressed on it.” ** and it takes place according to the straight line along which that force is impressed.”

This means that the acceleration of a moving object always responds to the amount of force applied to it at a given moment, to modify its trajectory or speed.

From these considerations arises the **fundamental equation of dynamics** for objects of constant mass:

**Resulting force (F _{resulting}) = mass (m) x acceleration (a)**

A net force acts on a body of constant mass and gives it a given acceleration. In cases where the mass is not constant, the formula will focus rather on the momentum (p), according to the following formula:

Momentum (p) = mass (m) x velocity (v). Therefore: F_{net} = d (mv) / dt.

Thus force can be related to acceleration and mass, regardless of whether the latter is variable or not.

To exemplify this second law, the case of free fall is ideal: if we drop a tennis ball from a building, the acceleration it experiences will increase as time passes, since the force of gravity will be acting on it. Thus, its initial velocity will be zero, but a constant force will be applied to it in a straight line, downwards.

Continue in: Newton's Second Law

## Third law or Principle of action and reaction

According to Newton's third law,

**“Every action has an equal reaction but in the opposite direction.”**: which means that the mutual actions of two bodies are always equal and directed in opposite directions.”

In this way, whenever a force is exerted on an object, it exerts a similar force in the opposite direction and of equal intensity, so if two objects (1 and 2) interact, the force exerted by one on the other will be equal. in magnitude to that exerted by the other on the first, but of opposite sign.

That is: F_{1-2} =F_{2-1}. The first force will be known as “action” and the second force as “reaction”.

To demonstrate this third law, it is enough to observe what happens when two people of similar weight run in opposite directions and collide: both will receive the force of the other and will be thrown in the opposite direction. The same thing happens when a ball bounces off the wall and is thrown in the opposite direction, with a force similar to that projected when throwing it.

## Isaac Newton Biography

**Isaac Newton (1642-1727) was born in Lincolnshire, England** The son of Puritan peasants, his birth was traumatic and he came into the world so thin and weak that they assumed he would not live long.

However, he grew up to be an eccentric child, with early talents for mathematics and natural philosophy. **He entered the University of Cambridge at the age of eighteen** to continue his studies. It is said that he rarely entered the classroom, since his main interest was in the library and self-taught training.

This did not hinder his academic development. **He became an important physicist, theologian, philosopher and mathematician, recognized by the Royal Society**. He is credited with the invention of mathematical calculation, as well as various studies on optics and light.

Besides, **contributed enormously to the development of mathematics and physics**: He discovered the color spectrum of light, formulated a law of thermal conduction, another on the origin of stars, on the speed of sound in air and the mechanics of fluids, and a huge etcetera. **His great work was Philosophiae naturalis principia mathematica**.

Newton died in 1727, after having been a respected and honored scientist, who received a sir from Queen Anne of England. He suffered from renal colic and other kidney ailments that, after many hours of delirium, finally took him to the grave on March 31.

#### References

- “Newton's Laws” on Wikipedia.
- “Newton's Laws in 2 minutes” (video) in Quantum Fracture.
- “Newton's Laws” at the Scientific Computing Center of Andalusia.
- “Newton's Forces and Laws of Motion” on Khan Academy.
- “Newton's Laws of Motion” at NASA.
- “Newton's the Laws of Motion” at Stanford University.
- “Newton's Laws of Motion” in The Encyclopaedia Britannica.