Lesson 1: Introduction to The Mechanical Universe
Provocative questions begin the quest of The Mechanical Universe. This introductory preview enters an Aristotelian world in conflict, introduces the revolutionary ideas and heroes from Copernicus through Newton, and, like a space shuttle from past to present, links the physics of the heavens to the physics of the Earth.
Lesson 2: The Law of Falling Bodies
With the conventional wisdom of the Aristotelian world view, almost everyone could see that heavy bodies fell faster than lighter ones. Then along came Galileo. His genius deduced that the distance a body has fallen at any instant is proportional to the square of the time spent falling. From that, speed and acceleration follow with the help of a mathematical tool called a derivative.
Lesson 3: Derivatives
The function of mathematics in physical science. From a theoretical concept to a practical tool, the derivative helps to determine the instantaneous speed and acceleration of a falling body. Differentiation is developed further to calculate how any quantity changes in relation to another. The power rule, the product rule, the chain rule -- with a few simple rules, differentiating any function becomes a simple mechanical task.
Lesson 4: Inertia
The rise of Galileo and his fall from grace. Copernicus conjectured that the Earth spins on its axis and orbits around the sun. Considering its implications, a rather dangerous assumption that prompted rather risky questions: Why do objects fall to Earth rather than hurtle off into space? And in this heretical scheme of things in which the Earth wasn't at the center, where was God? Risking more than his favored status in Rome, Galileo helped to answer such questions with the law of inertia.
Lesson 5: Vectors
Physics must explain not only why and how much, but also where and which way. Physicists and mathematicians invented a way of describing quantities that have direction as well as magnitude. Laws that deal with such phenomena as distance and speed are universal. And vectors, which describe quantities such as displacement and velocity, universally express the law of physics in a way that is the same for all coordinate systems.
Lesson 6: Newton's Laws
For all the phenomena of The Mechanical Universe, Isaac Newton laid down the laws. A refinement on Galileo's law of inertia, Newton's first law states that every body remains at rest or continues in uniform motion unless an unbalanced force acts on it. His second law, the most profound statement in classical mechanics, relates the causes to the changes of motion in every object in the cosmos. Newton's third law explains the phenomenon of interactions: for every action, there's an equal and opposite reaction.
Lesson 7: Integration
Newton and Leibniz sprint for the calculus. Winning the longest race in scientific history -- more than 2000 years, from the Golden Age of Greece to the end of the seventeenth century in Europe -- Newton and Leibniz arrived at the conclusion that differentiation and integration are inverse processes. Their exciting intellectual discovery, dramatically rerun to reflect the times, ended in an extremely controversial dead heat.
Lesson 8: The Apple and the Moon
The first authentic steps toward outer space. Seeking an explanation for Kepler's laws, Newton discovered that gravity described the force between any two particles in the universe. From an English orchard to Cape Canaveral and beyond, Newton's universal law of gravity reveals why an apple but not the moon falls to the Earth.
Lesson 9: Moving in Circles
The original Platonic ideal, with derivatives of vector functions. According to Plato, stars are heavenly beings that orbit the Earth with uniform perfection -- uniform speed and perfect circles. Even in this imperfect world, uniform circular motion make perfect mathematical sense.
Lesson 10: The Fundamental Forces
All physical phenomena of nature are explained by four forces. Two nuclear forces -- strong and weak -- dwell within the atomic nucleus. The fundamental force of gravity granges across the universe at large. So does electricity, the fourth fundamental force, which binds the atoms of all matter.
Lesson 11: Gravity, Electricity, Magnetism
Forces at play in the Physics Theater. The gravitational force between two masses, the electric force between two charges, and the magnetic force between two magnetic poles -- all these forces take essentially the same mathematical form. Newton's script suggested connections between electricity and magnetism. Acting on scientific hunches, Maxwell saw the matter in an entirely new light.
Lesson 12: The Millikan Experiment
How does science progress? Through painstaking trial and error, illustrated with a dramatic re-creation of Robert Millikan's classic oil-drop experiment. Understanding the electric force on a charged droplet and viscosity, the measured the charge of a single electron.