Certainly we would not be able to ignore the role played by each part of the body if we were to analyze the dynamics of an extended object. However, there is one point, associated with the geometric mean center of the mass distribution of an extended system, known as the center of mass, always behaves like a point particle as if all the external forces, and the mass of the entire system, are on that point. In this view, all the

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To simplify our discussion, we will first consider the case of a particle on a circular path or orbit. Later we will remove the constraint of the circular orbit. 4.2 Uniform circular motion

When we watch a child riding a horse on a merry-go-round such as the ones shown in Fig. 4.5, we know that the motion of the child is circular, meaning that the distance between the child and the fixed center of the carousel never changes. if the motion is stable, not at the beginning or the end of the ride, it is also nearly uniform, referring to the speed of the child not changing.

But we know for sure that the velocity of the child, at least its direction, is constantly changing, because every moment we look at the situation, the child is moving in a different direction. This is sketched in Fig. 4.6(a). Can we figure out how the velocity changes, provided that the speed is constant, that is, v1 = v2 = v and the distance between the child and the carousel center remains constant, too?

First we can qualitatively see from point 1 to point 2 that the change of the velocity is pointing at the center of the circle. The velocities involved are sketched in Fig. 4.6(b). The amount of change is the magnitude