9.1:
Center of Gravity
The center of gravity is the point where the object’s entire weight appears to be concentrated. A forklift crane with load is perfectly balanced, when its center of gravity lies inside the stability triangle.
To locate the center of gravity of any object, apply the principle of moments.
Divide the object into n number of thin slices of a weight of dW each, with each dot representing the center of gravity.
The sum of the moments of the gravitational forces, dW, acting on all the slices about the y-axis equals the moment of the resultant gravitational force, W, about the same axis. This gives the position of the center of gravity in the x-direction.
If the slices are made thinner and thinner such that the number of slices tends to infinity, the summation becomes an integration.
Similarly, the y-coordinate of the center of gravity can be determined.
This method can be generalized to three-dimensional objects.
The center of gravity of any object can lie on the object or outside the object.
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.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Section 9.1, Pp. 465-466.