Lecture #2 Notes: Mechanics, Matter and Motion

A bit of history and some numbers too!

Pre-Socratics – gave birth to science since they looked for logical answers to the natural world without turning to myth and gods.

Thales of Miletus – Suggested that water is the essential substance of the Universe. Predicted a solar eclipse in 585 BC. He probably used Babylonian tables. He was the Einstein of his day.

Anaximander of Miletus (610-545 B.C.)– Defined the primary ingredient of the cosmos as apieron, or “the indefinite” primordial chaos of our beginnings.

Pythagoras of Samos (530 B.C.)– Numbers were the underlying foundation of reality.

Parmenides of Elea (480 B.C.) – All being is eternal and that change is impossible. (the phenomena of movement and change are simply appearances of a static, eternal reality. Essentially argued that there was no void.

Empedocles of Acragas (440 B.C.) – Universe stems from four root elements: fire, air, water, and earth. Aristotle considered him the father of rhetoric. He leaped into a Volcano! In 2006 a huge underwater volcano off the coast of Sicily was named after him.

Aristarchus of Samos (Greek Copernicus) (250 B.C.)– Originated the heliocentric hypothesis (according to Archimedes) He had both identified the central fire with the Sun, as well as putting other planets in correct order from the Sun. His astronomical ideas were rejected in favor of the geocentric theories of Aristotle and Ptolemy until they were successfully revived and extensively developed by Copernicus nearly 2000 years later.

Archimedes of Syracuse (287-121 B. C.)– In the ranks of Isaac Newton and Einstein regarding mathematics. Invented many machines before his time along with the lever. Killed by a Roman Soldier during the Second Punic War. A theoretical mathematician. We used his mathematical theory to create 2-D maps from spheres.

==============================================

Romans (200 BC to 400AD) Roman Numerals would dominate Europe for over 2,000years!

Not one roman mathematician is celebrated today. Lack of curiosity for big numbers.

Mnemonic helps to recall the order of Roman numerals from big to small.

My Dear Cat Loves Xtra Vitamins Intensely

Egyptian astronomer Ptolemy (165AD) Almagest – Geocentric model. It would survive for 14 centuries.

Why?

Augustine of Hippo (400AD) would say it best.

“It is enough for Christians to believe that the only cause of all created things is the goodness of the Creator.”

===============================================

India – 450 AD – Zero my hero makes an appearance. Muslim Scholars – created algebra, quadratic equations, and trigonometry. These numbers use the base 10.

Leonardo of Pisa (1200) – Italian Mathematician called Fibonacci took the base 10 numerals to Europe. It too 500 years for Roman and Arabic numerals to battle it out for dominance.

Copernicus (1540) was the first to suggest an Infinite Universe and it would take 70 years before Kepler (1620) would determine that the real orbit of the planets were elliptical and not circular.

Galileo (1632) Rejected Kepler’s model of ellipses but came up with the Law of Inertia:

Objects not acted on by a force travel in straight lines at constant speeds. Or if they are at rest they stay at rest. His theory of all objects falling at the same rate despite whether they were heavy or light could not be tested during his time because there was no way to create a vacuum to test the matter. See the Apollo 15 Experiment done in Galileo’s honor.

Gottfried Leibniz (1700) created the binary system. “On the Art of Combination” Wanted a universal language using symbols. He came across a copy of the “I Ching” which discussed the Universe as a progression of contradictory dualities with a series of yes/no possibilities.

1. Only numbers we needed were 0 and 1
2. created a stepped wheel calculator, but never built his binary machine
3. Binary is also the smallest numbering system available
4. Based in all computers.

The number 15 (1111)

128	64	32	16	8	4	2	1
				1	1	1	1

The number 40 would read (101000)

128	64	32	16	8	4	2	1
		1	0	1	0	0	0

The number 200 would read (11001000)

128	64	32	16	8	4	2	1
1	1	0	0	1	0	0	0

Dealing with Mass and Motion

What is mass? The amount of matter in an object.

What is matter? The “stuff” of which physical objects are composed (however, go to Wikipedia and look up this definition.) Technically, this has not been defined in physics.

Elemental Particle Physicists are still arguing.

What is weight? The force upon an object due to gravity.

Inertia is the property of an object to remain at constant velocity unless acted upon by an outside force.

What is speed? The distance a moving object has traveled over a period of time.

1. Instantaneous speed
2. Average speed

Average speed = total distance covered/ time interval

If we drive 80km in an hour, we say our average speed was 80km/hr. If we travel 320km in 4 hours we say 320km/4h = 80 km/h.

What is Velocity? It is speed and the direction of motion. Velocity brings in the vector quantity.

Acceleration: change of velocity / time interval (Think Galileo and his inclined planes.)

How far does something travel in free fall? d= ½ gt²

Distance is equal to one half times the acceleration of free fall times the time of the fall squared.

Newton’s Laws of Motion

First Law: (Law of Inertia): An object 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.

Second Law: The force acting on an object is equal to the product of the object’s mass and acceleration. (F=ma)

Third Law: For every action there is an equal and opposite reaction. Check out the desk toy, Newton’s Cradle, sometime as a reference.

The Law of Universal Gravitation: The gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. (F=Gm₁m₂/r²).

Newton’s laws of motion he used them to derive Kepler’s laws of planetary motion and in one fell swoop demonstrated that planets obey the same laws as everything else! Thus Newton created the branch of Physics known as Mechanics – the science that seeks to understand the behavior of objects as they interact among each other by forces.

Newton’s laws cannot be proven, they can only be postulated and then tested experimentally.

Newton’s first and third laws may be considered hypotheses open to test whereas the second law is really a definition.