Up to now, every object we have dealt with we have treated as if it were a point particle that has no extent.  We have worked problems with cars, boxes, people, even planets, and in each case, we have used a point particle model for the object.  We have been able to do this because the size and shape of the objects haven’t mattered for the questions we have been asking.  However, clearly there are numerous physical problems were the shape of an object and how its mass is distributed does matter.  To consider these questions, we will need a new model that we can use that allows us to think about how the different parts of the object are moving.

To build up to our new model that we will use for extended objects, we will start by thinking about a system of point masses.  Instead of focusing on the motion of each individual mass, however, we need to come up with a way to combine the motions of the individual particles to talk about the motion of the system as a whole.  The best choice for the point to define our system and how it moves is the center of mass of the system.  Once we have located where the center of mass is, we can begin to describe the aggregate motion of the system by describing the motion of its center of mass.