Center of mass, its connection to momentum

We've been looking at collisions -- situations in which one object separates into several pieces, and situations in which several objects smash together. It certainly looks like momentum is a good tool to use when dealing with collisions.

There's another tool which can also help you to solve problems involving collisions: the center of mass of a system. What's the center of mass, and why should we care? Well, for one thing, it can explain why, ever since Dick Fosbury in 1968, high jumpers bend their bodies backward, instead of using the traditional styles. (Want to know more about the physics of high jumping?)

First, we'll define just what the center of mass is, and do a few simple calculations.

Computing the center of mass for a set of discrete objects

Next, let's see how this concept is related to the that concept of momentum, and why it might be useful in some types of collision.

Joe Cool and his skateboard

Okay, so now you know how to compute the center of mass for a set of discrete objects. But in real life, many objects are not compact little point masses -- they are big, extended conglomerations of mass, sometimes with bits sticking out here and there. How can we compute the center of mass for these more realistic objects?

Computing center of mass for extended objects