Video Transcript
Where does the center of gravity of a uniform circular disk lie?
Let’s say that this here is our uniform circular disk. And as we’ve seen, we want to figure out where its center of gravity is located. Hearing this phrase “center of gravity” may remind us of a related expression “center of mass.” For a given object, this is where all of the mass of that object is effectively concentrated. It turns out that for any object in a uniform gravitational field, its center of gravity and its center of mass are at the same location.
If we assume then that our uniform circular disk exists in a uniform gravitational field, then by finding its center of mass, we’ve also found its center of gravity. As we mentioned, an object’s center of mass is where all of its mass is effectively concentrated. For our uniform circular disk, we can see that if we start at the center of this disk and move out in any direction, we encounter just as much of the disk and, therefore, just as much mass whichever way we go. We can describe this by saying that this disk is radially symmetric.
This tells us that if we were to pick one point on this disk where all of its mass is concentrated, that point would need to be at its very center. This, then, is where the disk’s center of mass lies and also where its center of gravity is located, at the center of the circle.
