Lesson 13: Conservation of Energy
The myth of the energy crisis. According to one of the major laws of physics, energy is neither created nor destroyed.
Lesson 14: Potential Energy
The nature of stability. Potential energy provides a clue, and a powerful model, for understanding why the world has worked the same way since the beginning of time.
Lesson 15: Conservation of Momentum
If The Mechanical Universe is a perpetual clock, what keeps it ticking away till the end of time? Taking a cue from Descartes, momentum -- the product of mass and velocity -- is always conserved. Newton's laws embody the concept of conservation and momentum. This law provides a powerful principle for analyzing collisions, even at the local pool hall.
Lesson 16: Harmonic Motion
The music and mathematics of nature. The restoring force and inertia of any stable mechanical system cause objects to execute simple harmonic motion, a phenomenon that repeats itself in perfect time.
Lesson 17: Resonance
The music and mathematics of nature, Part II. As Galileo noted, the swings of a pendulum increasingly grow with repeated, timed applications of a small force. When the frequency of an applied force matches the natural frequency of a system, large-amplitude oscillations result in the phenomenon of resonance. Resonance explains why a swaying bridge collapsed in a mild wind, and how a wineglass can be shattered by a human voice.
Lesson 18: Waves
The medium disturbances of nature. With an analysis of simple harmonic motion and a stroke of genius, Newton extended mechanics to the propagation of sound.
Lesson 19: Angular Momentum
An old momentum with a new twist. Kepler's second law of planetary motion, which is rooted here in a much deeper principle, imagined a line from the sun to a planet that sweeps out equal areas in equal times. Angular momentum is a twist on momentum -- the cross product of the radius vector and momentum. A force with twist is torque. When no torque acts on a system, the angular momentum of the system is conserved.
Lesson 20: Torques and Gyroscopes
Why a spinning top doesn't topple. When a torque acts on a spinning object, the angular momentum changes, but the object only precesses. The object may be a child's toy, or a part of a navigation system, or Earth itself.
Lesson 21: Kepler's Three Laws
The wandering mathematician. Kepler's three laws described the motion of heavenly bodies with unprecedented accuracy. However, the planets still moved in paths traced by the ancient Greek mathematicians -- the conic section called an ellipse.
Lesson 22: The Kepler Problem
The combination of Newton's law of gravity and F = ma. The task of deducing all three of Kepler's laws from Newton's universal law of gravitation is known as the Kepler problem. Its solution is one of the crowning achievements of Western thought.
Lesson 23: Energy and Eccentricity
The precise orbit of any heavenly body -- a planet, asteroid, or comet -- is fixed by the laws of conservation of energy and angular momentum. The eccentricity, which determines the shape of an orbit, is intimately linked to the energy and angular momentum of the heavenly body.
Lesson 24: Navigating in Space
Getting from here to there. Voyages to other planets require enormous expenditures of energy. However, the amount of energy expended can be minimized by using the same principles that guide planets around the solar system.
Lesson 25: From Kepler to Einstein
The orbiting planets, the ebbing and flowing of tides, the falling body as it accelerates -- these phenomena are consequences of the law of gravity. Why that's so leads to Einstein's general theory of relativity, and into the black hole, but not back out again.
Lesson 26: Harmony of the Spheres
The music of the spheres.