The discussion of four-vector in relativity continues but this time the focus is on the energy-momentum of a particle. The invariance of the energy-momentum four-vector is due to the fact that rest mass of a particle is invariant under coordinate transformations.
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.
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.
Reading assignment:
Wolfson and Pasachoff, Physics with Modern Physics, chapters 13-14.
Lecture 10 - Rotations, Part II: Parallel Axis Theorem
Overview:
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.
Reading assignment:
Wolfson and Pasachoff, Physics with Modern Physics, chapter 10.