The Mechanical Universe Season 1, Episode 7: Integration

1

Introduction

This preview introduces revolutionary ideas and heroes from Copernicus to Newton, and links the physics of the heavens and the earth.

2

The Law of Falling Bodies

Galileo's imaginative experiments proved that all bodies fall with the same constant acceleration.

3

Derivatives

The function of mathematics in physical science and the derivative as a practical tool.

4

Inertia

Galileo risks his favored status to answer the questions of the universe with his law of inertia.

5

Vectors

Physics must explain not only why and how much, but also where and which way.

6

Newton's Laws

Newton lays down the laws of force, mass, and acceleration.

7

Integration

Newton and Leibniz arrive at the conclusion that differentiation and integration are inverse processes.

8

The Apple and the Moon

The first real steps toward space travel are made as Newton discovers that gravity describes the force between any two particles in the universe.

9

Moving in Circles

A look at the Platonic theory of uniform circular motion.

10

Fundamental Forces

All physical phenomena of nature are explained by four forces: two nuclear forces, gravity, and electricity.

11

Gravity, Electricity, Magnetism

Shedding light on the mathematical form of the gravitational, electric, and magnetic forces.

12

The Millikan Experiment

A dramatic recreation of Millikan's classic oil-drop experiment to determine the charge of a single electron.

13

Conservation of Energy

According to one of the major laws of physics, energy is neither created nor destroyed.

14

Potential Energy

Potential energy provides a powerful model for understanding why the world has worked the same way since the beginning of time.

15

Conservation of Momentum

What keeps the universe ticking away until the end of time?

16

Harmonic Motion

The music and mathematics of periodic motion.

17

Resonance

Why a swaying bridge collapses with a high wind, and why a wine glass shatters with a higher octave.

18

Waves

With an analysis of simple harmonic motion and a stroke of genius, Newton extended mechanics to the propagation of sound.

19

Angular Momentum

An old momentum with a new twist.

20

Torques and Gyroscopes

From spinning tops to the precession of the equinoxes.

21

Kepler's Three Laws

The discovery of elliptical orbits helps describe the motion of heavenly bodies with unprecedented accuracy.

22

The Kepler Problem

The deduction of Kepler's laws from Newton's universal law of gravitation is one of the crowning achievements of Western thought.

23

Energy and Eccentricity

The precise orbit of a heavenly body — a planet, asteroid, or comet — is fixed by the laws of conservation of energy and angular momentum.

24

Navigating in Space

Voyages to other planets use the same laws that guide planets around the solar system.

25

Kepler to Einstein

From Kepler's laws and the theory of tides, to Einstein's general theory of relativity, into black holes, and beyond.

26

Harmony of the Spheres

A last lingering look back at mechanics to see new connections between old discoveries.

27

Beyond the Mechanical Universe

The world of electricity and magnetism, and 20th-century discoveries of relativity and quantum mechanics.

28

Static Electricity

Eighteenth-century electricians knew how to spark the interest of an audience with the principles of static electricity.

29

The Electric Field

Faraday's vision of lines of constant force in space laid the foundation for the modern force field theory.

30

Potential and Capacitance

Franklin proposes a successful theory of the Leyden jar and invents the parallel plate capacitor.

31

Voltage, Energy, and Force

When is electricity dangerous or benign, spectacular or useful?

32

The Electric Battery

Volta invents the electric battery using the internal properties of different metals.

33

Electric Circuits

The work of Wheatstone, Ohm, and Kirchhoff leads to the design and analysis of how current flows.

34

Magnetism

Gilbert discovered that the earth behaves like a giant magnet. Modern scientists have learned even more.

35

The Magnetic Field

The law of Biot and Sarvart, the force between electric currents, and Ampère's law.

36

Vector Fields and Hydrodynamics

Force fields have definite properties of their own suitable for scientific study.

37

Electromagnetic Induction

The discovery of electromagnetic induction in 1831 creates an important technological breakthrough in the generation of electric power.

38

Alternating Current

Electromagnetic induction makes it easy to generate alternating current while transformers make it practical to distribute it over long distances.

39

Maxwell's Equations

Maxwell discovers that displacement current produces electromagnetic waves or light.

40

Optics

Many properties of light are properties of waves, including reflection, refraction, and diffraction.

41

The Michelson-Morley Experiment

In 1887, an exquisitely designed measurement of the earth's motion through the ether results in the most brilliant failure in scientific history.

42

The Lorentz Transformation

If the speed of light is to be the same for all observers, then the length of a meter stick, or the rate of a ticking clock, depends on who measures it.

43

Velocity and Time

Einstein is motivated to perfect the central ideas of physics, resulting in a new understanding of the meaning of space and time.

44

Mass, Momentum, Energy

The new meaning of space and time make it necessary to formulate a new mechanics.

45

Temperature and Gas Laws

Hot discoveries about the behavior of gases make the connection between temperature and heat.

46

Engine of Nature

The Carnot engine, part one, beginning with simple steam engines.

47

Entropy

The Carnot engine, part two, with profound implications for the behavior of matter and the flow of time through the universe.

48

Low Temperatures

With the quest for low temperatures came the discovery that all elements can exist in each of the basic states of matter.

49

The Atom

A history of the atom, from the ancient Greeks to the early 20th century, and a new challenge for the world of physics.

50

Particles and Waves

Evidence that light can sometimes act like a particle leads to quantum mechanics, the new physics.

51

From Atoms to Quarks

Electron waves attracted to the nucleus of an atom help account for the periodic table of the elements and ultimately lead to the search for quarks.

52

The Quantum Mechanical Universe

A last look at where we've been and a peek into the future.