The center of gravity (CG) is the point in a body or system of bodies at which the entire weight of the body or system may be considered to act.
Position of centre of gravity: Objects or systems with a lower centre of gravity tend to be more stable. For example, a low-slung car has a lower center of gravity compared to a high-standing SUV. The lower CG contributes to better stability during turns and manoeuvres.
Base of support: The wider the base of support, the more stable the object. The base of support is the area beneath the object that prevents it from tipping over. For example, a wide-based chair is more stable than a narrow-legged stool.
When the centre of gravity is low or when the base of support is wide (in the direction of a pushing force), it will take a larger angle of tilt in order for the object to topple. As observed in the applet below, if the object is tilted about the pivot at the edge of its base, it will take a larger angle of tilt for the line of action of the weight to go beyond the pivot and exert a moment that topples the object. For a larger range of the angle of tilt, the object returns to its original position when the force is removed.
Stable Equilibrium refers to a state in which a system, once displaced from its original position, tends to return to that position. It is characterized by a restoring torque that acts to bring the system back to its equilibrium state. In the context of a ball placed in a bowl, if the ball is disturbed slightly from the bottom, it will roll back to the lowest point, indicating a stable equilibrium. Systems in stable equilibrium are often associated with energy minima (e.g. lowest gravitational potential energy), where any deviation results in a force opposing the deviation, restoring the system to its original configuration.
Neutral Equilibrium occurs when a system, after being displaced, remains in its new position without experiencing any net force or torque to return it to its original state. In this state, potential energy is unchanged regardless of the system's position. An example is a ball on a flat surface. If disturbed slightly, the centre of gravity will stay at the same height.
Unstable Equilibrium is characterized by a situation where a small displacement from the equilibrium position leads to a net force or torque that magnifies the displacement, causing the system to move further away from its original state. In the case of a ball balanced precariously at the peak of a hill, a slight disturbance will cause it to roll away, gaining momentum as it descends. Systems in unstable equilibrium are associated with energy maxima, where any deviation leads to a force or torque that amplifies the deviation, driving the system away from its equilibrium.