The Laws of Motions
"Nature and Nature's laws lay hid in the night; God said, Let Newton be! And all was light." Alexander Pope
Sir Isaac Newton
Isaac Newton (1642-1727) is perhaps the most famous Lucasian Professor of Mathematics. He is probably best known to the average person because of the story of the falling apple and its relationship to the discovery of gravity. Newton discovered the force of gravity, and today the search is for its carrier: gravity waves.
Newton studied in Trinity at Cambridge in 1661. During a wonderful surge of scientific production Newton produced three great achievements in the short space of two years. The first great achievement was the invention of fluxions, which resulted in calculus. He used this knowledge to advance his other work. Newton's second great achievement was the discovery of the law of the composition of light, later used in the development of optics. His third great achievement, the discovery of the universal force of gravity, was the basis for the Principia , his ultimate achievement. A milestone event in Newton's life was the controversy with Leibniz, revolving around the question of who was to receive the credit for the invention of calculus.
Newton's monumental work Philosophiae Naturalis Principia Mathematica (1687) forever changed science, providing the basis for the modern understanding of the universe. The Principia is composed of three books. The first and second books present the laws and conditions of motions and forces. The third deduces the constitution of the universe from the principles offered in books one and two.
Newton served in governmental seats and was knighted in 1705 by Queen Anne.
The Apple Tree
When Newton was studying at the University of Cambridge, a plague epidemic struck the area and he was dismissed to live at his home for a short time. The weather had been very hot and Newton took the habit of sitting under his orchard on the cool evenings. The year was unusually hot and dry, and the apple trees had many dry apples, which occasionally fell. As Newton was sitting under a tree one night studying from a book, an apple fell on his head and as he lifted his head, he saw the moon facing him. Then, he asked himself-"Why did the apple not go upwards or sideways instead of downwards?
Although this famous story says this was the occasion Newton first thought of gravity, it is probably untrue. Newton did a great deal of astronomical work in 1664, and therefore it is very likely that he was aware that a force (gravity) existed.
General Information
When the forces on an object do not cancel each other, that is to say, are not of equal force, they will change the motion of the object. The object's speed, direction of motion, or both will change. The rules that explain the way forces function were first derived by Sir Isaac Newton. The greater the mass of an object, the greater the force needed to change its motion. This resistance to change in motion is inertia; you can think of it as laziness of an object. The speed of an object is usually measured in meters per second. Velocity is the speed of an object in a particular direction. Acceleration, which only occurs when a force is applied, is the rate of change in speed. It is measured in meters per second per second, or meters per second square. One particular force keeps the Moon in orbit around the Earth and the Earth in orbit around the Sun. This is the force of gravity or gravitation; its effects can be felt over great distances.
The Laws of Motion
In the first book of the Principia , Newton puts forth his three Laws of Motion.
First, "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it." Second,"The change of motion is proportional to the motive force impressed; and it is made in the direction of the right line in which that force is impressed." Third, "To every action there is always opposed an equal reaction: or the mutual action of two bodies on each other are always equal, and directed to contrary parts."
The third book contains his third great achievement, the discovery of the universal force of gravity. The great principle underlying the Principia is that of universal gravitation.
"That there is a power of gravity pertaining to all bodies, proportional to the several quantities of matter which they contain."
First Law
When no force acts on an object, it will remain in a state of rest or continue its uniform motion in a straight line.
Second Law
When a force acts on an object, the motion of the object will change. This change in motion is called acceleration and its equal to the size of the force divided by the mass of the object on which it acts.
When mass is in kilograms and acceleration is in meters/second/second, force is in newtons (N). One newton equals the force required to accelerate on kilogram of mass at one meter/second/second.
1 N = 1 kg × 1 m/sec/sec
Third Law
The third law of motion states that for every action, there is an equal and opposite reaction. In other words, every force (action) must have an equal force in the opposite direction (reaction). All forces come in pairs.