14.0 EQUILIBRIUM AND CENTRE OF GRAVITY

Why does a bus not topple over when it goes around a corner? Why does a vase with a heavy base stay upright, while a tall, thin one falls over easily? The answers lie in the concepts of centre of gravity and equilibrium. This chapter explores how the distribution of weight affects stability and the conditions for an object to be balanced.

14.1 CENTRE OF GRAVITY (CoG)

The centre of gravity of an object is the point through which the entire weight of the object appears to act. It is the average location of the weight of the object. For symmetrical objects with uniform density, the centre of gravity is at the geometric centre.

14.1.1 Locating the Centre of Gravity

For regular shapes:

• For a uniform rod, the CoG is at its midpoint.
• For a rectangular or square lamina, the CoG is at the intersection of its diagonals.
• For a circular lamina, the CoG is at its centre.
• For a triangular lamina, the CoG is at the centroid (intersection of medians).

For irregular shapes (lamina): We use the plumb line method.

1. Make three small holes near the edge of the irregular lamina (not in a straight line).
2. Suspend the lamina from the first hole, with a plumb line (a string with a weight) hanging from the same point. Mark the position of the plumb line on the lamina.
3. Re