21 October 2013

The Point of Center of Mass

There is a reason so many complicated problems may be analyzed with relatively simple introductory physics.  We in physics sometimes refer to the "spherical cow approximation" when simplifying complicated problems.  The main principle behind the simplification is that an object's center of mass moves under the influence of the net external force acting on the object.  So if we are not interested in all the goofy motion about the center of mass, we need only focus on the translational motion of the center of mass.  The cow is thus approximated by a point particle.

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.

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