In this section, we will learn how to calculate the center of mass of a thin plate.
Mass of the Region
Suppose we have a region , with density . Then we calculate the mass by the following:
Moments of the Region
Moments are used to measure the tendency of the region about the -axis, and -axis. There are two moments: & . They can be computed as follows:
Center of Mass
The center of mass is a point where if you put a pencil underneath the plate at that point, then the plate would balance without falling.
The x-coordinate of the point (denoted as ), and the y-coordinate of the point (denoted as ) is calculated as follows: