9.1: Center of Gravity
The center of gravity is the point at which an object's weight appears to be concentrated and can be used to balance the object perfectly. This point is essential in mechanics as it provides information regarding a body's stability and moments of inertia. The center of gravity does not always have to fall within the shape or boundaries of the body; it may also lie outside the body in certain cases.
To determine its location, the principle of moments can be utilized by dividing the object into several infinitesimal elements, each with its own differential weight and centroid, the geometric center of a body. The sum of all the moment equations around a given axis should equal the moment of the resultant gravitational force around that same axis. For a three-dimensional object, the location of the center of gravity is provided by the following equation:
In engineering and physics, knowing the location of the center of gravity helps determine how loads affect the body. A load applied to one part of a structure may cause a shift in its center of gravity, leading to instability if not accounted for properly. For example, it is necessary to keep the center of gravity low for cars to reduce the risk of them tipping over when taking sharp turns. Likewise, for cranes, the center of gravity must be carefully managed to avoid the crane from tipping over when lifting heavy loads. Additionally, knowledge about the center of gravity can help determine moments of inertia for structures such as rotating bodies or beams that are subject to bending forces. The center of gravity also plays a role in sports and other activities, as athletes must maintain balance over their support base while performing different movements.
