The center of mass of a system is the location where the average mass of a system can be assumed to exist. If two equally massive children sit at opposite ends of a seesaw, their average mass will be located at the midpoint between them. When dealing with other systems of masses, determining the center of mass location may not be as straightforward. Let’s first consider a circumstance where three charged particles of equal mass sit a the corners of an imaginary equilateral triangle:
Each side of the triangle has a midpoint center of mass associated with the charges they separate:
Notice how each charge is opposite to a center of mass location. If a ray is used to connect each of the three charge/center-of-mass pairs, the center of mass of the system can be determined:
The center of mass of the system is located at the region where the three rays overlap. Furthermore, the center of mass’ position below the uppermost charge and along the vertical ray can be shown to be two-thirds of the ray’s total distance. This information is extremely useful when determining the magnitude of force experienced by a positive test charge placed at the system’s center of mass.
RENAISSANCE PHYSICS 