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Sunday, January 18, 2015

Center of mass of systems: Position and Velocity

The center of mass is a really useful concept. It can be used to reduce a large object, say a planet or star, to a single point that has the entire mass of the object at that location. This is the key concept for calculating the gravitational force between the objects, for example.

But this is also a useful concept for system of objects or particles. We can define the center of mass for a system with a weighted average of
           x_cm = [sum of (individual mass)(individual x-coordinate)] / (total mass of system)

We have used this to find the center of mass of a binary system, which is then the center of each object's orbit. But for even more numerous particles, the center of mass of a system describes the motion of the entire system, even if all the particles are flying around seemingly at random. This video presents two simple 1-D collision problems to show how the momentum of the center of mass of a system is conserved, and moves at a constant velocity (assuming no external forces acting on the system that would cause the center of mass to accelerate).

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