Center of mass

Back in the early twentieth century, athletes competing in the high jump used several different techniques to clear the bar.

Image from the film Olympia, which documents the 1936 Olympics in Berlin

All these techniques had a common feature: the bulk of the jumper's body was ABOVE the level of the bar. How else could one clear it?

But in the 1960s, an American jumper named Dick Fosbury introduced a new technique. As he approached the bar, he turned away from it and jumped so that he went over it backwards; in addition, and crucially, he arched his back sharply. By contorting his body in this manner, Fosbury was able to lower his center of mass compared to the other competitors.

Still image from "How One Man Changed the High Jump Forever" on the Olympic Channel; linked video from "An athlete uses physics to shatter world records"> by Asaf Bar-Yosef

That addition of physics into the sport allowed Fosbury to win the gold medal at the Olympics in 1968, and transformed the high jump forever.

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

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

For more information

The physics of high jumping