The center of mass is an important feature of single objects, and perhaps even more important for collections of objects.

- Exactly where does gravity pull an object? At its center of mass
- If I need to compute the gravitational force between two objects,
what is the
**R**I should use in the formula? The distance between the centers of mass. - If we want to design a plane so that the engine will push the plane forward, without any rotation, where should be put the engine? Behind the center of mass.
- If if a system consists of several pieces
which break up or come together under mutual
forces only,
then the center of mass of the system
will continue to move with a constant velocity;
that can be useful when dealing with
objects which fly through the air while exploding

Image courtesy of Gizmodo

Now, when an object is a compact sphere, the center of mass is easy to find: it's just the geometric center of the body. But what happens if we need to find the center of mass of a system consisting of several objects?

What about

" ... in projectile motion, the x-velocity remains constant while the y-velocity changes linearly with time. The trajectory of an object thus traces a parabolic curve ...."

don't seem to work if you pick any arbitrary part of an extended body. For example, if I toss a baseball bat up into the air, a movie might show this:

Speaking of real movies, look at this real motion of a sort of dumbbell-shaped object:

But how can we find the center of mass of an extended object?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.