After introducing the aforementioned idea to my introductory physics class this morning, I decided to film one of my favorite objects -- a baseball bat -- in flight. With the help of my experimentalist colleague, Will Roach, we made the video below (click on the image for a larger view).
I marked the location of my bat's center of mass and then tossed it across our campus lawn. The red circles and red line in the clip above show the path of the center of mass. What does that path look like? Check out the graph below, which shows the location of the vertical coordinate as a function of time (click on the image for a larger view).
The red circles are the data. The blue curve is a parabolic fit to the data. The constant vertical acceleration predicted by the fit is 9.838 m/s2 (pointing down), which is almost exactly the magnitude of the acceleration due to gravity of a point particle moving in a vacuum near Earth's surface. Given that air resistance on my bat was not a big player in my simple toss experiment, I think the above video illustrates rather well the fact that the bat's center of mass follows the path predicted by relatively simple introductory physics.
To understand the more complicated motion about the center of mass, one must study rotations, a topic coming soon to my introductory physics course.