Suspension Principle: When an object is freely suspended from a pivot, it will naturally settle in a position where its centre of gravity is directly below the pivot point. This occurs because the weight force acting through the CoG creates no turning moment only when the line of action passes through the pivot.
The Plumb Line Technique: To find the CoG of an irregular lamina, the object is hung from a hole near its edge along with a plumb line (a weighted string). A line is drawn on the object following the vertical path of the string, indicating that the CoG must lie somewhere along that line.
Intersection of Lines: By repeating this process from at least two other suspension points, the resulting lines will intersect at a single point. This intersection is the precisely located centre of gravity for the irregular shape.
Verification: A third suspension point is often used to ensure accuracy; if all three lines intersect at the same coordinate, the result is verified.
Dynamic Shifting: The centre of gravity is not necessarily a fixed physical location within the material; it is a point relative to the object's current shape. For example, when a person bends forward, their centre of gravity shifts to a new position to account for the redistribution of their body mass.
External CoG: In certain geometries, the centre of gravity can actually lie in empty space outside the physical matter of the object. Common examples include a hollow ring, a horseshoe, or a boomerang, where the point of average weight distribution is in the air.
Stability Principle: An object remains stable as long as the vertical line drawn from its centre of gravity falls within its base of support. If the CoG shifts outside this base due to tilting, the weight force will create a turning moment that causes the object to topple.
| Feature | Symmetrical Object | Irregular Object |
|---|---|---|
| Location Discovery | Geometry/Calculation | Experimental (Suspension) |
| Symmetry Dependency | High | Low/None |
| Typical Examples | Spheres, Cubes, Planks | Tools, Scraps, Human Body |
Vector Placement: When drawing force diagrams, examiners look for the weight vector () starting exactly at the centre of gravity. Placing it at the bottom or the top of an object is a common mistake that loses marks.
Verification Steps: In suspension method descriptions, always mention using at least two points (preferably three) and describe the intersection as the final Mentioning the plumb line is essential for full credit.
Reasonableness Check: Always ask if the located CoG makes sense visually. If an object is much heavier on the left side, the CoG must be positioned to the left of the geometric center.
Unit Awareness: Remember that the position of the CoG is a coordinate or point, not a value with units like Newtons, though the force acting through it is measured in Newtons.
