Final answer:
The center of mass in physics is the point that behaves as if all the mass of a system were concentrated there, and it's calculated using the position vectors and masses of the components of the system.
Step-by-step explanation:
The center of mass is a fundamental concept in physics that describes the average position of all the mass in a system. In AP Physics C and other physics courses, the center of mass is calculated by taking the weighted sum of the position vectors of the masses in the system and then dividing by the total mass.
This is exemplified in situations like finding the center of mass of a system of point particles, a uniform hoop, or even in celestial mechanics, where gravitational force acts along a line joining the centers of mass of two bodies, as per Newton's law of universal gravitation.
Specifically, in a system of three point masses located at the corners of a triangle, you would calculate the center of mass by creating position vectors for each mass, scaling these vectors by their respective masses, summing them, and then dividing by the total mass of the system.
This method ensures that the center of mass of an object behaves according to Newton's second law of motion, as if all the mass of the object were concentrated at that point. Similarly, when considering the motion of two particles of different masses released from the same height, the vertical position of their center of mass can be found using laws of motion, assuming no air resistance.