12.3:
Center of Gravity
Center of gravity of a body is an imaginary point at which the body's gravitational force effectively acts.
It helps to predict a moving object's behavior under gravity and design static structures such as buildings and bridges.
To understand it better, consider balancing a basketball on a forefinger. The basketball placed on the forefinger experiences a gravitational force at the center of gravity in the downward direction.
If the center of gravity of the basketball lies on the axis that passes through the finger, the gravitational force is countered by the normal force balancing the basketball on the finger.
If the basketball slightly moves from the equilibrium position, the center of gravity of the basketball shifts outside the axis line of the finger. As a result, the torque due to its weight acts at this point, and the basketball topples.
12.3:
Center of Gravity
The center of gravity (COG) of an object is the point where the object's total weight is considered to be concentrated. Knowing the location of the center of gravity is useful when predicting the behavior of a moving object or designing static structures. In a uniform gravitational field, the center of gravity is similar to the center of mass (COM); yet, these two points can be positioned differently. For example, the Moon's center of mass lies very close to its geometric center, but its center of gravity is shifted slightly towards the Earth due to the Earth's stronger gravitational force.
In an equilibrium situation, one of the forces acting on any body is its weight. In free-body diagrams, the weight vector is attached to the center of gravity of the body. The center of gravity for symmetrical objects is the same as the object's geometric center. However, the center of gravity for an asymmetrical object is located at some distance away from the object's geometric center. In the case of irregularly shaped objects, the center of gravity can lie outside the object or at a point external to the physical material. In practical situations, however, even objects as large as buildings or cruise ships are located in a uniform gravitational field on the Earth’s surface, where the acceleration due to gravity has a constant magnitude. In these situations, the center of gravity is identical to the center of mass.
This text is adapted from Openstax, University Physics Volume 1, Section 12.1: Conditions for Static Equilibrium.