Center of Mass - of a single point We will use the center...

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Center of Mass Up to this point in our study of classical mechanics, we have studied primarily the motion of a single particle or body. To further our comprehension of mechanics we must begin to examine the interactions of many particles at once. To begin this study, we define and examine a new concept, the center of mass, which will allow us to make mechanical calculations for a system of particles. The Center of Mass of Two Particles We start by defining and explaining the concept of the center of mass for the simplest possible system of particles, one containing only two particles. From our work in this section we will generalize for systems containing many particles. Before quantifying our idea of a center of mass, we must explain it conceptually. The concept of the center of mass allows us to describe the movement of a system of particles by the movement
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Unformatted text preview: of a single point. We will use the center of mass to calculate the kinematics and dynamics of the system as a whole, regardless of the motion of the individual particles. Center of Mass for Two Particles in One Dimension If a particle with mass m 1 has a position of x 1 and a particle with mass m 2 has a position of x 2 , then the position of the center of mass of the two particles is given by: x cm = Thus the position of the center of mass is a point in space that is not necessarily part of either particle. This phenomenon makes intuitive sense: connect the two objects with a light but rigid pole. If you hold the pole at the position of the center of mass of the objects, they will balance. That balancing point will often not exist within either object....
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