energy storage elements
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Rotating Rigid Bodies, Moments of Inertia, Parallel Axis and Perpendicular Axis Theorem. The moment of inertia for a rigid body around an axis of rotation is introduced, and related to its rotational kinetic energy. Flywheels can be used to store energy. Planets and stars have spin rotational kinetic energy, and the Crab Nebula pulsar is presented as a spectacular example.
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The lecture begins with a review of the loop-the-loop problem. Professor Shankar then reviews basic terminology in relation to work, kinetic energy and potential energy. He then goes on to define the Work-Energy Theorem. Finally, the Law of Conservation of Energy is discussed and demonstrated with specific examples.
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In this lecture, bound and unbound orbits are discussed. Professor Lewin begins with a description of escape velocity, or the minimum speed required to escape the gravitational pull. Various sources of energy, energy storage, energy conversion, and the world's energy consumption are discussed. Power, or the rate at which a force does work on an object, is central to the conversation. Professor Lewin concludes with a few words on global ...more
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Professor Kleiner discusses domestic architecture at Pompeii from its beginnings in the fourth and third centuries B.C. to the eruption of Vesuvius in A.D. 79. She describes the plan of the ideal domus italica and features two residences that conform to that layout. She then presents the so-called Hellenized domus that incorporates elements of Greek domestic architecture, especially the peristyle court with columns. The primary example is ...more
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In this lecture, Professor Lewin displays how the conservation of mechanical energy can be used to derive the equation of motion for simple harmonic oscillators (SHO). In doing so he covers gravitational potential energy, equilibrium points where the net force is zero, parabolic potential energy, and circular potential energy.
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Kepler's Laws, Elliptical Orbits, Change of Orbits, and the famous passing of a Ham Sandwich by astronauts in orbit. Kepler's three Laws summarize the motion of the planets in our solar system. Following Newton's law of universal gravitation, the conservation of angular momentum and mechanical energy allow us to calculate the semimajor axis of the elliptical orbits, the orbital period and other orbital parameters. All we have to know is on...more
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Professor Kleiner discusses the development of Third Style Roman wall painting in late first century B.C. villas belonging to the imperial family and other elite patrons. Third Style painting, as Professor Kleiner demonstrates, is characterized by departure from the perspectival vistas and panoramas of the Second Style toward an attenuation of architectural elements and a respect for the inherent flatness of the wall. The Third Style remai...more
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The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers). Likewise energy and momentum are unified into the energy-momentum four-vector.
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Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a p...more
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Writing a Recursive Power Set Function in Scheme, Using a Lambda Mapping Function that Cons-Es the Car to Every Element in the Power-Set of the Cdr to Make the Recursive Step in the Power-Set Function, Using a Let Binding to Cause Power-Set to Only Make One Recursive Call Rather than Two, Structure of a Let Binding, How Expressions Within a Let Binding Cannot Depend On Each Other Unless the Let* Keyword Is Used, How a Let Binding Is Compil...more
