Center of Mass

Center of Mass, that point at which the entire mass of an object may be considered to be located for purposes of understanding the object's motion. The center of mass of a uniform sphere is the point at the center of the sphere; the center of mass of a uniform rod with a circular cross-section is the point at the center of the cross-sectional slice of the rod that is located at the middle of the rod lengthwise. In some irregularly shaped objects, the center of mass may lie outside the object.

When trying to understand and calculate the motion of an object, focusing attention on the center of mass often simplifies the problem. For example, a rod thrown into the air moves in a complicated manner; the rod moves through the air, and at the same time it tends to rotate. If the motion of a point at the tip of the rod were tracked, the path that point would follow would be very complicated. But if the motion of the rod's center of mass were tracked, the point would follow a parabolic path that can easily be described mathematically. Additionally, the complicated rotation of the rod can be described as simple rotational motion about the center of mass. The center of mass can also be useful when examining the motions of complicated systems that are composed of many objects or particles, such as the motion of the planets around the sun.