A Brief History of the Development of Forces and Motion

Before one can attempt to understand mechanics, one needs to have a fundamental idea of gravity. The first theories of gravity began to surface in the Ancient Greek times. Plato’s theory of gravity, which was later expanded on by Aristotle¹, stemmed from his model that the universe can be deconstructed into four elements: earth, water, air and fire, and that all objects were composed of these elements.

The gravitational theory was that the elements within objects tended towards their ‘natural place’²: the earth element would gravitate towards earth, water towards water, air towards the sky, and fire towards the sun—and so a flame rises upwards but dirt falls downwards. He also stated that the speed at which objects fall is relative to the proportions of the elements within them³, such that a rock will fall faster than a leaf because rocks have more ‘earth’ in them.

Aristotle called this ‘natural motion’: it required no interference in order to occur because of the elements’ intrinsic attraction to their ‘natural place.’ The (one) other type of motion, he stated, was ‘violent motion’⁴, which did require interference in order to occur—that is, forces: pushing and pulling. This model stated that in order to keep moving, an object must be in contact with a continuous force. It also stated that any object on earth without power acting on it should consequently come to rest⁵.

There were some apparent holes in this theory, specifically in such concepts as projectiles. Why do arrows continue to travel through the air even after the force is removed? Aristotle managed to offer an explanation for this: as the arrow travels through air, it leaves behind it a vacuum⁶; the surrounding air rushes into this vacuum and this action creates a motive force⁴ which propels the arrow forwards.

John Philoponus, another Greek thinker, from c. 6th century, generally accepted Aristotle’s theory but was dissatisfied with his explanation of projectiles. He posited an early model for the transfer of power from one body to another. In the bow-and-arrow case, the bow would provide an amount of power, a force, to the arrow. This force would eventually cease and the arrow would come down (towards its ‘natural place’)⁷. This eliminated Aristotle’s requirement of constant contact in order to maintain motion, and so enabled the possibility of motion through a vacuum, or ‘void’, as it came to be called⁸.

This idea was adopted and developed by Islamic scientists around the 11th/12th Centuries. They called this power ‘mail’ (an Arabic word). Ibn Sina, for instance, stated that in the absence of any external resistance, the ‘mail’ would remain acting on an object indefinitely, such that it would continue in its path of motion indefinitely, which, again, implied a sort of hypothetical ‘void’⁴.

Another Arabic thinker, Ibn Bajjah (also known as Avempace), contradicted a different Aristotelian principle. Aristotle had stated that violent force on an object is inversely proportional to the density of the medium through which it is travelling⁶. Avempace found that despite the fact that all the planets travel through the same medium, the ‘heavens’, they travel at different speeds, i.e. experience different violent motion⁴. He therefore invalidated Aristotle’s theory that the speed of the object is related to the density of the external medium.

These ideas culminated in a theory which would come to be known as ‘impetus’, a term coined by French philosopher Jean Buridan. After circulating throughout the Islamic world, these ideas eventually came back to the West, where they were adopted by Buridan. He integrated them into his version of a final theory, the theory of impetus, stating that motion is maintained so long as the power provided by the ‘mover’ (e.g. bow) is greater than the resistance on the ‘moved’ (e.g. arrow)⁹.

The main difference between Buridan’s theory and the earlier ones was that Buridan believed in a gradual diminishment of the impetus by external resistive forces, as opposed to the spontaneous cessation previously postulated by the likes of Philoponus and Ibn Sina¹⁰.

More problems with Aristotle’s theory started appearing during the 1500s, wherein people began to suspect air resistance and weight might affect an object’s motion⁵.

Controversy arose with the publication of Copernicus’ heliocentric model of the universe¹¹ because it explicitly contradicted Aristotle’s theory which had been based on a geocentric model¹. Aristotle's theory stated that the earth was stationary, resting in its ‘natural place’, whereas Copernicus stated that the earth was orbiting the sun¹². If Copernicus were correct, Aristotle’s entire theory would be invalidated. He proposed other contradictions to Aristotle’s theories, but lacked evidence to adequately support these contradictions. This, alongside the seemingly blasphemous nature of the theory, meant Copernicus’ view wasn’t widely accepted¹³.

Galileo was able to provide some of the explanations Copernicus’ theory lacked. He investigated the motion of falling objects. Galileo is famously alleged to have dropped two balls of equal size but of different mass from the Leaning Tower of Pisa expecting them to accelerate at different rates, only to find that they accelerated at basically the same rate. As charming as it is, this story is widely regarded as nothing more than that—a story: based on extensive documentation, it is evident that he actually arrived at the conclusion of uniform acceleration by investigating the motion of balls rolling down inclined planes.

He rolled different-sized balls down a slope and recorded the distance travelled by each one in a given time period. He observed that the acceleration down the slope was the same regardless of the size of the ball, and thus arrived at the conclusion of uniform acceleration regardless of weight⁸.

He also performed several experiments rolling balls down one inclined plane and up another (i.e. in a V shape). He found that if you roll a ball down a smooth plane from a specific height, it reaches approximately the same height on the upward plane. Rolling the balls down planes with a coarser surface resulted in a lesser height being reached, in a longer amount of time (he used water clocks to measure time¹⁴.)

He also found that if the upward slope is shallower than the downward slope, the ball rolls a greater distance in order to reach the same height; if the upward slope isn't inclined at all but flat, rather, the ball will continue rolling along the slope forever. Of course, this is assuming zero friction. The ball will always seek the same height but will never quite reach it due to the presence of friction, he stated¹⁵.

These findings provided the initial foundations for the principle of inertia. Galileo eventually came out with: ‘A body moving on a level surface will continue in the same direction at constant speed unless disturbed¹⁶.’ This is markedly similar to Newton’s famous First Law of Motion. Descartes, too, presented a similar sentiment in his first Law of Nature, stating ‘The first thing, insofar as in it lies, always perseveres in the same state, and when once moved, always continues to move.’¹⁷

Newton clearly studied the publications of Galileo and Descartes and ended up with his own principle of inertia. Based on Galileo’s ideas, Newton made the key observations that to change direction or speed (including zero speed) of an object, a force must be applied, and if no force is applied, then the object will continue at the same speed and direction¹⁸. He made the distinction that the cessation of motion is not due to a lack of force, but rather to a presence of a different force. This is the basis of Newton’s first law of motion: ‘Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.¹⁹’

Newton’s second law of motion states, ‘The acceleration produced by a particular force acting on a body is directly proportional to the magnitude of the force and inversely proportional to the mass of the body¹⁹’ It is often just stated in the form of the mathematical formula F = ma. In developing this formula, Newton also discovered differentiation, since it actually came from F = m(dv/dt), where dv/dt is (change in velocity divided by change in time) the derivative of a (acceleration)²⁰.

Newton’s third law of motion states, ‘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.¹⁹’ Interestingly enough, the aforementioned Avempace came to this conclusion, that every action has a reaction, almost half a century before—although he didn’t quite deduce that these reactions are equal and opposite²¹.

Newton published these three laws in his book Philosophiæ Naturalis Principia Mathematica, alongside his theory of gravity. Newton made the critical link between objects (such as an apple) falling to the ground on earth, and planetary motion. He said all bits of matter experience an attraction to all other bits of matter of strength proportional to their mass and inversely proportional to the distance between them¹³. He was able to form a mathematical equation to represent (and calculate) this force of attraction, and he used this newly-discovered equation (F= GMm/r²) to prove Kepler’s laws²².

Newton’s laws are still studied today. Some of Galileo’s concepts are still in use too, such as his ideas about pendulums¹³. However, nowadays most major advancements come from the study of quantum mechanics²³.