Translational and Static Equilibrium

When the forces acting on an object are balanced and the resultant force is 0 (∑F=0), the object is said to be in translational equilibrium. This means the object is either at rest or moving at a constant velocity. When both the resultant force and the resultant torque (∑τ=0) where clockwise torque = anticlockwise torque) are 0, then the object is said to be in static equilibrium.

Centre of Mass and Gravity

The centre of mass of an object is a position which represents the average mass of that object. There is as much mass above the centre of mass as there is below it. It is important to note that it is possible for the centre of mass can be outside the object. For example a donut; it’s centre of mass is in the middle where there is empty space.

The centre of gravity of an object is the same position as its centre of mass and it represents the position where the entire weight of the object is considered to act.

Stability

The height of the centre of mass of an object is important as it determines the stability of the object. An object, for simplicity let’s consider a box, will not tip over until the centre of mass point moves past the end of its base. As soon as the centre of mass point moves outside the base, it will tip over.

Hence having a lower centre of mass in comparison to a higher one would mean that the object would need to be rotated more for it to tip over and would make the object more stable. Compare the stability of the uniform boxes A and B below where box A has a higher centre of mass than box B. Common sense tells us that a small push would easily cause box A to tip over whilst it would require a larger push to tip over box B, concluding that box B is more stable. In terms of physics, box B would require to be tipped by a larger angle to move the line of the centre of mass outside the base compared to box A, and box B has a wider base than A, making it more stable.

The stability of a structure can be increased through a number of ways. These include; lowering the centre of mass which can be done by concentrating most of the mass as low as possible, increasing the width of the base, and increasing the angle between the centre of mass and the edge of the base.

Types of Equilibrium

There are 3 types of equilibrium; stable, unstable, neutral.

In a stable equilibrium, the object will return to its equilibrium position even when it experience a force, as long as the centre of mass line does not move outside the base

In an unstable equilibrium, the object will accelerate and not move to its equilibrium position. The height of its centre of mass will change permanently.

In a neutral equilibrium, the object will remain stationary no matter where it is placed.