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.
This lecture offers detailed analysis of the Lorentz transformations which relate the coordinates of an event in two frames in relative motion. It is shown how length, time and simultaneity are relative.
This is the first of a series of lectures on relativity. The lecture begins with a historical overview and goes into problems that aim to describe a single event as seen by two independent observers. Maxwell’s theory, as well as the Galilean and Lorentz transformations are also discussed.
Midterm Exam covers the first half of the course.
This lecture is a continuation of an analogue to Newton’s law: τ= lα. While previous problems examined situations in which τ is not zero, this time the focus is on extreme cases in which there is no torque at all. If there is no torque, α is zero and the angular velocity is constant. The lecture starts with a simple example of a seesaw and moves on to discuss a collection of objects that are somehow subject to a variety of forces but remain in static equilibrium.
Part II of Rotations. The lecture begins with an explanation of the Parallel Axis Theorem and how it is applied in problems concerning rotation of rigid bodies. The moment of inertia of a disk is discussed as a demonstration of the theorem. Angular momentum and angular velocity are examined in a variety of problems.
Part I of Rotations. The lecture begins with examining rotation of rigid bodies in two dimensions. The concepts of “rotation” and “translation” are explained. The use of radians is introduced. Angular velocity, angular momentum, angular acceleration, torque and inertia are also discussed. Finally, the Parallel Axis Theorem is expounded.
The dynamics of a many-body system is examined. Through a variety of examples, the professor demonstrates how to locate the center of mass and how to evaluate it for a number of objects. Finally, the Law of Conservation of Momentum is introduced and discussed. The lecture ends with problems of collision in one dimension focusing on the totally elastic and totally inelastic cases.
The focus of the lecture is problems of gravitational interaction. The three laws of Kepler are stated and explained. Planetary motion is discussed in general, and how this motion applies to the planets moving around the Sun in particular.
The discussion on the Law of Conservation of Energy continues but is applied in higher dimensions. The notion of a function with two variables is reviewed. Conservative forces are explained and students are taught how to recognize and manufacture them.
