Final answer:
To find the centroid of a system, establish a coordinate system, calculate momenta using mass and position, sum the vectors, and divide by the total mass. This process identifies the center of mass, which may not correspond to a point with actual mass.
Step-by-step explanation:
To find the centroid of a system by solving systems of equations, a well-defined coordinate system must be established. First, consider the position vectors for each object in the system. In the case of the Earth and another body, you would define the origin of the coordinate system as Earth's center. With this reference point, the sum of the individual momenta in both x and y directions is calculated. These vectors are then scaled by the mass of the corresponding body and added together. The resulting vector is divided by the total mass to locate the center of mass. This point might not have any actual mass associated with it as in the example of a salt crystal's center of mass. Remember to include the mass of the object at the origin in your calculations for the accurate location of the centroid. When working with an object like a car, one can define the coordinate system with the pivot at the center of mass for simplifying the equilibrium conditions equations.