Video Transcript
Where does the center of gravity of
a fine rod, 𝐴𝐵, of uniform density lie?
Let’s begin by reminding ourselves
what we mean when we talk about the center of gravity of an object. The center of gravity, sometimes
called center of mass, is the unique point from which the object’s weight force
acts.
In particular, we’re interested in
this rod 𝐴𝐵, which has uniform density. And the fact that the rod is
uniform gives us information about the point at which the center of gravity
acts. Specifically, let’s call the weight
force of the rod 𝐴𝐵 𝑤. This is located at the geometric
center of the body. Of course, since a uniform rod is a
linear object with constant linear density, its center of mass is exactly at its
midpoint.
And so we can say the center of
gravity or the center of mass of 𝐴𝐵 lies at the midpoint of 𝐴𝐵.
