Video Transcript
Fill in the blank: The center of mass of a uniform rod 𝐴𝐵 with length six centimeters is at what from 𝐴.
To answer this question, let’s begin by recalling what it means to model the center of mass of an object. In a uniform gravity field, the center of mass or center of gravity is a unique point at which the object’s weight force acts. It allows us to assume that the object’s mass is concentrated at the center of mass as if it were a particle. And if we support a rigid body at its center of mass, then it will be perfectly balanced at this single point.
So, what does this mean for modeling the center of mass of a uniform rod? Well, in a rigid body with constant density, the center of mass is located at the geometric center of the body. And by its very definition, a rod is a rigid body. Since it’s uniform, we know it has constant density. So, we can say that the center of mass of a uniform rod must be at its midpoint.
So, for a uniform rod 𝐴𝐵, we can model the downwards force of its weight as acting at a point exactly halfway between 𝐴 and 𝐵. Now, of course, we’re actually told that 𝐴𝐵 has a length of six centimeters. And so, the center of mass will be located at a distance half of this from either point 𝐴 or 𝐵. That’s six divided by two, which is, of course, three centimeters.
And so, this allows us to fill in the blank. The center of mass of uniform rod 𝐴𝐵 with length six centimeters is at three centimeters from 𝐴.
