Center of Mass Physics Problems  Basic Introduction  Summary and Q&A
TL;DR
Understand how to calculate the position and center of mass for different masses using equations.
Questions & Answers
Q: How is the position of the center of mass determined when mass is distributed in different locations?
The position of the center of mass is determined by weighing the mass at each location and considering its distance from the origin. The more massive objects have a greater influence on the center of mass.
Q: What is the formula to calculate the position of the second mass for a specific center of mass location?
The formula is (mass2 * position2) = (center of mass * total mass)  (mass1 * position1). This allows us to find the placement of the second mass to achieve the desired center of mass location.
Q: How do we calculate the center of mass for a system with multiple masses?
For the xcoordinate, use the equation (m1 * x1 + m2 * x2 + m3 * x3 + m4 * x4) / (total mass). For the ycoordinate, use the equation (m1 * y1 + m2 * y2 + m3 * y3) / (total mass).
Q: Why is it important to calculate the center of mass?
Calculating the center of mass helps determine the balancing point of an object or system and is crucial in understanding stability, equilibrium, and rotational motion.
Summary & Key Takeaways

The center of mass is located closer to the more massive object.

To calculate the center of mass, use the equation: (mass1 * position1 + mass2 * position2) / (total mass).

To determine the position of the second mass for a specific center of mass location, use the equation: (mass2 * position2) = (center of mass * total mass)  (mass1 * position1).

To calculate the center of mass for a system with multiple masses, use the equations: (m1 * x1 + m2 * x2 + m3 * x3 + m4 * x4) / (total mass) for the xcoordinate, and (m1 * y1 + m2 * y2 + m3 * y3) / (total mass) for the ycoordinate.