The Moment of Inertia Tensor — Lesson 4

The video starts with the study of the rate of change of linear and angular momentum for rigid bodies. The rigid body rotates and translates from one position to another in space. The rigid motion is expressed in terms of the motion of the center of mass and rotation about the center of mass. In this way, any motion can be described. Similarly, the expression for velocity is written in terms of the velocity of the center of mass and the velocity about the center of mass.

We discover that linear momentum is a product of mass times the velocity of the center of mass. The rate of change of the linear momentum is the total force acting on the body. Its effect on the body can be defined by replacing the body with the center of mass. Similarly, the rate of change of angular momentum is studied and the moment of inertia tensor about the center of mass is defined. The Euler tensor is also defined.